case study questions for class 11 maths chapter 3

CBSE Case Study Questions for Class 11 Maths Sets Free PDF

Mere Bacchon, you must practice the CBSE Case Study Questions Class 11 Maths Sets in order to fully complete your preparation . They are very very important from exam point of view. These tricky Case Study Based Questions can act as a villain in your heroic exams!

I have made sure the questions (along with the solutions) prepare you fully for the upcoming exams. To download the latest CBSE Case Study Questions , just click ‘ Download PDF ’.

CBSE Case Study Questions for Class 11 Maths Sets PDF

Checkout our case study questions for other chapters.

• Chapter 2 Relations and Functions Case Study Questions
• Chapter 3 Trigonometric Functions Case Study Questions
• Chapter 4 Principle of Mathematical Induction Case Study Questions
• Chapter 5 Complex Numbers and Quadratic Equations Case Study Questions

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First, learn to sit for at least 2 hours at a stretch

Solve every question of NCERT by hand, without looking at the solution.

Solve NCERT Exemplar (if available)

Sit through chapter wise FULLY INVIGILATED TESTS

Practice MCQ Questions (Very Important)

Practice Assertion Reason & Case Study Based Questions

Sit through FULLY INVIGILATED TESTS involving MCQs. Assertion reason & Case Study Based Questions

After Completing everything mentioned above, Sit for atleast 6 full syllabus TESTS.

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CBSE Class 11 Maths – Chapter 3 Trigonometric Functions- Study Materials

NCERT Solutions Class 11 All Subjects Sample Papers Past Years Papers

Sets : Notes and Study Materials -pdf

• Concepts of  Trigonometric Functions
• Trigonometric Functions Master File
• Trigonometric Functions Revision Notes
• R D Sharma Solution of Trigonometric Functions
• NCERT Solution  Trigonometric Functions
• NCERT  Exemplar Solution Trigonometric Functions
• Trigonometric Functions : Solved Example 1

CBSE Class 11 Maths Notes Chapter 3 Trigonometric Functions

Angle Angle is a measure of rotation of a given ray about its initial point. The original ray is called the initial side and the final position of ray after rotation is called terminal side of the angle. The point of rotation is called vertex. If the direction of rotation is anti-clockwise, the angle is said to be positive and if the direction of rotation is clockwise, then the angle is negative.

Measuring Angles There are two systems of measuring angles Sexagesimal system (degree measure): If a rotation from the initial side to terminal side is  ( 1 360 ) t h  of a revolution, the angle is said to have a measure of one degree, written as 1°. One sixtieth of a degree is called a minute, written as 1′ and one-sixtieth of a minute is called a second, written as 1″ Thus, 1° = 60′ and 1′ = 60″

Circular system (radian measure):  A radian is an angle subtended at the centre of a circle by an arc, whose length is equal to the radius of the circle. We denote 1 radian by 1°.

Relation Between Radian and Degree We know that a complete circle subtends at its centre an angle whose measure is 2π radians as well as 360°. 2π radian = 360°. Hence, π radian = 180° or 1 radian = 57° 16′ 21″ (approx) 1 degree = 0.01746 radian

Six Fundamental Trigonometric Identities

• sinx =  1 c o s e c x
• cos x =  1 s e c x
• tan x =  1 c o t x
• sin 2  x + cos 2  x = 1
• 1 + tan 2 x = sec 2  x
• 1 + cot 2  x = cosec 2  x

Trigonometric Functions – Class 11 Maths Notes

Trigonometric ratios are defined for acute angles as the ratio of the sides of a right angled triangle. The extension of trigonometric ratios to any angle in terms of radian measure (real number) are called trigonometric function. The signs of trigonometric function in different quadrants have been given in following table.

Domain and Range of Trigonometric Functions

Sine, Cosine, and Tangent of Some Angles Less Than 90°

Allied or Related Angles The angles  n π 2 ± θ  are called allied or related angle and θ ± n × (2π) are called coterminal angles. For general reduction, we have following rules, the value of trigonometric function for ( n π 2 ± θ ) is numerically equal to

• the value of the same function, if n is an even integer with the algebraic sign of the function as per the quadrant in which angle lies.
• the corresponding co-function of θ, if n is an odd integer with the algebraic sign of the function for the quadrant in which it lies, here sine and cosine, tan and cot, sec and cosec are cofunctions of each other.

Functions of Negative Angles

For any acute angle of θ. We have,

• sin(-θ) = – sinθ
• cos (-θ) = cosθ
• tan (-θ) = – tanθ
• cot (-θ) = – cotθ
• sec (-θ) = secθ
• cosec (-θ) = – cosecθ

Some Formulae Regarding Compound Angles

An angle made up of the sum or difference of two or more angles is called compound angles. The basic results in direction are called trigonometric identities as given below: (i) sin (x + y) = sin x cos y + cos x sin y (ii) sin (x – y) = sin x cos y – cos x sin y (iii) cos (x + y) = cos x cos y – sin x sin y (iv) cos (x – y) = cos x cos y + sin x sin y

(ix) sin(x + y) sin (x – y) = sin 2  x – sin 2  y = cos 2  y – cos 2  x (x) cos (x + y) cos (x – y) = cos 2  x – sin 2  y = cos 2  y – sin 2  x

Transformation Formulae

• 2 sin x cos y = sin (x + y) + sin (x – y)
• 2 cos x sin y = sin (x + y) – sin (x – y)
• 2 cos x cos y = cos (x + y) + cos (x – y)
• 2 sin x sin y = cos (x – y) – cos (x + y)
• sin x + sin y = 2 sin( x + y 2 ) cos( x − y 2 )
• sin x – sin y = 2 cos( x + y 2 ) sin( x − y 2 )
• cos x + cos y = 2 cos( x + y 2 ) cos( x − y 2 )
• cos x – cos y = -2 sin( x + y 2 ) sin( x − y 2 )

Trigonometric Ratios of Multiple Angles

Product of Trigonometric Ratios

• sin x sin (60° – x) sin (60° + x) =  1 4  sin 3x
• cos x cos (60° – x) cos (60° + x) =  1 4  cos 3x
• tan x tan (60° – x) tan (60° + x) = tan 3x
• cos 36° cos 72° =  1 4
• cos x . cos 2x . cos 2 2 x . cos 2 3 x … cos 2 n-1  =  s i n 2 n x 2 n s i n x

Sum of Trigonometric Ratio, if Angles are in A.P.

Trigonometric Equations Equation which involves trigonometric functions of unknown angles is known as the trigonometric equation.

Solution of a Trigonometric Equation A solution of a trigonometric equation is the value of the unknown angle that satisfies the equation. A trigonometric equation may have an infinite number of solutions.

Principal Solution The solutions of a trigonometric equation for which 0 ≤ x ≤ 2π are called principal solutions.

General Solutions A solution of a trigonometric equation, involving ‘n’ which gives all solution of a trigonometric equation is called the general solutions.

General Solutions of Trigonometric Equation

• sin x = 0 ⇔ x = nπ, n ∈ Z
• cos x = 0 ⇔ x = (2n + 1)  π 2  , n ∈ Z
• tan x = 0 ⇔ x = nπ, n ∈ Z
• sin x = sin y ⇔ x = nπ + (-1) n  y, n ∈ Z
• cos x = cos y ⇔ x = 2nπ ± y, n ∈ Z
• tan x = tan y ⇔ x = nπ ± y, n ∈ Z
• sin 2  x = sin 2  y ⇔ x = nπ ± y, n ∈ Z
• cos 2  x = cos 2  y ⇔ x = nπ ± y, n ∈ Z
• tan 2  x = tan 2  y ⇔ x = nπ ± y, n ∈ Z

Basic Rules of Triangle

In a triangle ABC, the angles are denoted by capital letters A, B and C and the lengths of sides of opposite to these angles are denoted by small letters a, b and c, respectively. Sine Rule s i n A a = s i n B b = s i n C c

Cosine Rule a 2  = b 2  + c 2  – 2bc cos A b 2  = c 2  + a 2  – 2ac cos B c 2  = a 2  + b 2  – 2ab cos C

Projection Rule a = b cos C + c cos B b = c cos A + a cos C c = a cos B + b cos A

Trigonometric Functions Class 11 MCQs Questions with Answers

Question 1. The value of cos² x + cos² y – 2cos x × cos y × cos (x + y) is (a) sin (x + y) (b) sin² (x + y) (c) sin³ (x + y) (d) sin 4 (x + y)

Answer: (b) sin² (x + y) Hint: cos² x + cos² y – 2cos x × cos y × cos(x + y) {since cos(x + y) = cos x × cos y – sin x × sin y } = cos² x + cos² y – 2cos x × cos y × (cos x × cos y – sin x × sin y) = cos² x + cos² y – 2cos² x × cos² y + 2cos x × cos y × sin x × sin y = cos² x + cos² y – cos² x × cos² y – cos² x × cos² y + 2cos x × cos y × sin x × sin y = (cos² x – cos² x × cos² y) + (cos² y – cos² x × cos² y) + 2cos x × cos y × sin x × sin y = cos² x(1- cos² y) + cos² y(1 – cos² x) + 2cos x × cos y × sin x × sin y = sin² y × cos² x + sin² x × cos² y + 2cos x × cos y × sin x × sin y (since sin² x + cos² x = 1 ) = sin² x × cos² y + sin² y × cos² x + 2cos x × cos y × sin x × sin y = (sin x × cos y)² + (sin y × cos x)² + 2cos x × cos y × sin x × sin y = (sin x × cos y + sin y × cos x)² = {sin (x + y)}² = sin² (x + y)

Question 2. If a×cos x + b × cos x = c, then the value of (a × sin x – b²cos x)² is (a) a² + b² + c² (b) a² – b² – c² (c) a² – b² + c² (d) a² + b² – c²

Answer: (d) a² + b² – c² Hint: We have (a×cos x + b × sin x)² + (a × sin x – b × cos x)² = a² + b² ⇒ c² + (a × sin x – b × cos x)² = a² + b² ⇒ (a × sin x – b × cos x)² = a² + b² – c²

Question 3. If cos a + 2cos b + cos c = 2 then a, b, c are in (a) 2b = a + c (b) b² = a × c (c) a = b = c (d) None of these

Answer: (a) 2b = a + c Hint: Given, cos A + 2 cos B + cos C = 2 ⇒ cos A + cos C = 2(1 – cos B) ⇒ 2 cos((A + C)/2) × cos((A-C)/2 = 4 sin²(B/2) ⇒ 2 sin(B/2)cos((A-C)/2) = 4sin² (B/2) ⇒ cos((A-C)/2) = 2sin (B/2) ⇒ cos((A-C)/2) = 2cos((A+C)/2) ⇒ cos((A-C)/2) – cos((A+C)/2) = cos((A+C)/2) ⇒ 2sin(A/2)sin(C/2) = sin(B/2) ⇒ 2{√(s-b)(s-c)√bc} × {√(s-a)(s-b)√ab} = √(s-a)(s-c)√ac ⇒ 2(s – b) = b ⇒ a + b + c – 2b = b ⇒ a + c – b = b ⇒ a + c = 2b

Question 4. The value of cos 5π is (a) 0 (b) 1 (c) -1 (d) None of these

Answer: (c) -1 Hint: Given, cos 5π = cos (π + 4π) = cos π = -1

Question 5. In a triangle ABC, cosec A (sin B cos C + cos B sin C) equals (a) none of these (b) c/a (c) 1 (d) a/c

Answer: (c) 1 Hint: Given cosec A (sin B cos C + cos B sin C) = cosec A × sin(B+C) = cosec A × sin(180 – A) = cosec A × sin A = cosec A × 1/cosec A = 1

Question 6. If the angles of a triangle be in the ratio 1 : 4 : 5, then the ratio of the greatest side to the smallest side is (a) 4 : (√5 – 1) (b) 5 : 4 (c) (√5 – 1) : 4 (d) none of these

Answer: (a) 4 : (√5 – 1) Hint: Given, the angles of a triangle be in the ratio 1 : 4 : 5 ⇒ x + 4x + 5x = 180 ⇒ 10x = 180 ⇒ x = 180/10 ⇒ x = 18 So, the angle are: 18, 72, 90 Since a : b : c = sin A : sin B : sin C ⇒ a : b : c = sin 18 : sin 72 : sin 90 ⇒ a : b : c = (√5 – 1)/4 : {√(10 + 2√5)}/4 : 1 ⇒ a : b : c = (√5 – 1) : {√(10 + 2√5)} : 4 Now, c /a = 4/(√5 – 1) ⇒ c : a = 4 : (√5 – 1)

Question 7. The value of cos 180° is (a) 0 (b) 1 (c) -1 (d) infinite

Answer: (c) -1 Hint: 180 is a standard degree generally we all know their values but if we want to go theoretically then cos(90 + x) = – sin(x) So, cos 180 = cos(90 + 90) = -sin 90 = -1 {sin 90 = 1} So, cos 180 = -1

Question 8. The perimeter of a triangle ABC is 6 times the arithmetic mean of the sines of its angles. If the side b is 2, then the angle B is (a) 30° (b) 90° (c) 60° (d) 120°

Answer: (b) 90° Hint: Let the lengths of the sides if ∆ABC be a, b and c Perimeter of the triangle = 2s = a + b + c = 6(sinA + sinB + sinC)/3 ⇒ (sinA + sinB + sinC) = ( a + b + c)/2 ⇒ (sinA + sinB + sinC)/( a + b + c) = 1/2 From sin formula,Using sinA/a = sinB/b = sinC/c = (sinA + sinB + sinC)/(a + b + c) = 1/2 Now, sinB/b = 1/2 Given b = 2 So, sinB/2 = 1/2 ⇒ sinB = 1 ⇒ B = π/2

Question 9: If 3 × tan(x – 15) = tan(x + 15), then the value of x is (a) 30 (b) 45 (c) 60 (d) 90

Answer: (b) 45 Hint: Given, 3×tan(x – 15) = tan(x + 15) ⇒ tan(x + 15)/tan(x – 15) = 3/1 ⇒ {tan(x + 15) + tan(x – 15)}/{tan(x + 15) – tan(x – 15)} = (3 + 1)/(3 – 1) ⇒ {tan(x + 15) + tan(x – 15)}/{tan(x + 15) – tan(x – 15)} = 4/2 ⇒ {tan(x + 15) + tan(x – 15)}/{tan(x + 15) – tan(x – 15)} = 2 ⇒ sin(x + 15 + x – 15)/sin(x + 15 – x + 15) = 2 ⇒ sin 2x/sin 30 = 2 ⇒ sin 2x/(1/2) = 2 ⇒ 2 × sin 2x = 2 ⇒ sin 2x = 1 ⇒ sin 2x = sin 90 ⇒ 2x = 90 ⇒ x = 45

Question 10. If the sides of a triangle are 13, 7, 8 the greatest angle of the triangle is (a) π/3 (b) π/2 (c) 2π/3 (d) 3π/2

Answer: (c) 2π/3 Hint: Given, the sides of a triangle are 13, 7, 8 Since greatest side has greatest angle, Now Cos A = (b² + c² – a²)/2bc ⇒ Cos A = (7² + 8² – 13²)/(2×7×8) ⇒ Cos A = (49 + 64 – 169)/(2×7×8) ⇒ Cos A = (113 – 169)/(2×7×8) ⇒ Cos A = -56/(2×56) ⇒ Cos A = -1/2 ⇒ Cos A = Cos 2π/3 ⇒ A = 2π/3 So, the greatest angle is = 2π/3

Question 11. The value of tan 20 × tan 40 × tan 80 is (a) tan 30 (b) tan 60 (c) 2 tan 30 (d) 2 tan 60

Answer: (b) tan 60 Hint: Given, tan 20 × tan 40 × tan 80 = tan 40 × tan 80 × tan 20 = [{sin 40 × sin 80}/{cos 40 × cos 80}] × (sin 20/cos 20) = [{2 * sin 40 × sin 80}/{2 × cos 40 × cos 80}] × (sin 20/cos 20) = [{cos 40 – cos 120}/{cos 120 + cos 40}] × (sin 20/cos 20) = [{cos 40 – cos (90 + 30)}/{cos (90 + 30) + cos 40}] × (sin 20/cos 20) = [{cos 40 + sin30}/{-sin30 + cos 40}] × (sin 20/cos 20) = [{(2 × cos 40 + 1)/2}/{(-1 + cos 40)/2}] × (sin 20/cos 20) = [{2 × cos 40 + 1}/{-1 + cos 40}] × (sin 20/cos 20) = [{2 × cos 40 × sin 20 + sin 20}/{-cos 20 + cos 40 × cos 20}] = (sin 60 – sin 20 + sin 20)/(-cos 20 + cos 60 + cos 20) = sin 60/cos 60 = tan 60 So, tan 20 × tan 40 × tan 80 = tan 60

Question 12. If the angles of a triangle be in the ratio 1 : 4 : 5, then the ratio of the greatest side to the smallest side is (a) 4 : (√5 – 1) (b) 5 : 4 (c) (√5 – 1) : 4 (d) none of these

Question 13. The general solution of √3 cos x – sin x = 1 is (a) x = n × π + (-1)n × (π/6) (b) x = π/3 – n × π + (-1)n × (π/6) (c) x = π/3 + n × π + (-1)n × (π/6) (d) x = π/3 – n × π + (π/6)

Answer: (c) x = π/3 + n × π + (-1)n × (π/6) Hint: √3 cos x-sin x=1 ⇒ (√3/2)cos x – (1/2)sin x = 1/2 ⇒ sin 60 × cos x – cos 60 × sin x = 1/2 ⇒ sin (x – 60) = 1/2 ⇒ sin (x – π/3) = sin 30 ⇒ sin (x – π/3) = sinπ/6 ⇒ x – π/3 = n × π + (-1)n × (π/6) {where n ∈ Z} ⇒ x = π/3 + n × π + (-1)n × (π/6)

Question 14. If tan² θ = 1 – e², then the value of sec θ + tan³ θ × cosec θ is (a) 2 – e² (b) (2 – e²) 1/2 (c) (2 – e²)² (d) (2 – e²) 3/2

Question 15. The value of cos 20 + 2sin² 55 – √2 sin65 is (a) 0 (b) 1 (c) -1 (d) None of these

Answer: (b) 1 Hint: Given, cos 20 + 2sin² 55 – √2 sin65 = cos 20 + 1 – cos 110 – √2 sin65 {since cos 2x = 1 – 2sin² x} = 1 + cos 20 – cos 110 – √2 sin65 = 1 – 2 × sin {(20 + 110)/2 × sin{(20 – 110)/2} – √2 sin65 {Apply cos C – cos D formula} = 1 – 2 × sin 65 × sin (-45) – √2 sin65 = 1 + 2 × sin 65 × sin 45 – √2 sin65 = 1 + (2 × sin 65)/√2 – √2 sin65 = 1 + √2 ( sin 65 – √2 sin 65 = 1 So, cos 20 + 2sin² 55 – √2 sin65 = 1

Question 16. If the radius of the circumcircle of an isosceles triangle PQR is equal to PQ ( = PR), then the angle P is (a) 2π/3 (b) π/3 (c) π/2 (d) π/6

Answer: (a) 2π/3 Hint: Let S be the center of the circumcircle of triangle PQR. So, SP = SQ = SR = PQ = PR, where SP, SQ & SR are radii. Thus SPQ & SPR are equilateral triangles. ⇒ ∠QSP = 60°; Similarly ∠RQP = 60° ⇒ Angle at the center QSP = 120° So, SRPQ is a rhombus, since all the four sides are equal. Hence, its opposite angles are equal; so ∠P = ∠QSP = 120°

Question 17. If cos a + 2cos b + cos c = 2 then a, b, c are in (a) 2b = a + c (b) b² = a × c (c) a = b = c (d) None of these

Answer: (a) 2b = a + c Hint: Given, cos A + 2 cos B + cos C = 2 ⇒ cos A + cos C = 2(1 – cos B) ⇒ 2 cos((A + C)/2) × cos((A-C)/2 = 4 sin² (B/2) ⇒ 2 sin(B/2)cos((A-C)/2) = 4sin² (B/2) ⇒ cos((A-C)/2) = 2sin (B/2) ⇒ cos((A-C)/2) = 2cos((A+C)/2) ⇒ cos((A-C)/2) – cos((A+C)/2) = cos((A+C)/2) ⇒ 2sin(A/2)sin(C/2) = sin(B/2) ⇒ 2{√(s-b)(s-c)√bc} × {√(s-a)(s-b)√ab} = √(s-a)(s-c)√ac ⇒ 2(s – b) = b ⇒ a + b + c – 2b = b ⇒ a + c – b = b ⇒ a + c = 2b

Question 18. The value of 4 × sin x × sin(x + π/3) × sin(x + 2π/3) is (a) sin x (b) sin 2x (c) sin 3x (d) sin 4x

Answer: (c) sin 3x Hint: Given, 4 × sin x × sin(x + π/3) × sin(x + 2π/3) = 4 × sin x × {sin x × cos π/3 + cos x × sin π/3} × {sin x × cos 2π/3 + cos x × sin 2π/3} = 4 × sin x × {(sin x)/2 + (√3 × cos x)/2} × {-(sin x)/2 + (√3 × cos x)/2} = 4 × sin x × {-(sin 2x)/4 + (3 × cos 2x)/4} = sin x × {-sin 2x + 3 × cos 2x} = sin x × {-sin 2x + 3 × (1 – sin 2x)} = sin x × {-sin 2x + 3 – 3 × sin 2x} = sin x × {3 – 4 × sin 2x} = 3 × sin x – 4 sin 3x = sin 3x So, 4 × sin x × sin(x + π/3) × sin(x + 2π/3) = sin 3x

Question 19. If tan A – tan B = x and cot B – cot A = y, then the value of cot (A – B) is (a) x + y (b) 1/x + y (c) x + 1/y (d) 1/x + 1/y

Answer: (d) 1/x + 1/y Hint: Given, tan A – tan B = x ……………. 1 and cot B – cot A = y ……………. 2 From equation, 1/cot A – 1/cot B = x ⇒ (cot B – cot A)/(cot A × cot B) = x ⇒ y/(cot A × cot B) = x {from equation 2} ⇒ y = x × (cot A × cot B) ⇒ cot A × cot B = y/x Now, cot (A – B) = (cot A × cot B + 1)/(cot B – cot A) ⇒ cot (A – B) = (y/x + 1)/y ⇒ cot (A – B) = (y/x) × (1/y) + 1/y ⇒ cot (A – B) = 1/x + 1/y

Question 20. The value of (sin 7x + sin 5x) /(cos 7x + cos 5x) + (sin 9x + sin 3x) / (cos 9x + cos 3x) is (a) tan 6x (b) 2 tan 6x (c) 3 tan 6x (d) 4 tan 6x

Answer: (b) 2 tan 6x Hint: Given, (sin 7x + sin 5x) /(cos 7x + cos 5x) + (sin 9x + sin 3x) / (cos 9x + cos 3x) ⇒ [{2 × sin(7x+5x)/2 × cos(7x-5x)/2}/{2 × cos(7x+5x)/2 × cos(7x-5x)/2}] + [{2 × sin(9x+3x)/2 × cos(9x-3x)/2}/{2 × cos(9x+3x)/2 × cos(9x-3x)/2}] ⇒ [{2 × sin 6x × cosx}/{2 × cos 6x × cosx}] + [{2 × sin 6x × cosx}/{2 × cos 6x × cosx}] ⇒ (sin 6x/cos 6x) + (sin 6x/cos 6x) ⇒ tan 6x + tan 6x ⇒ 2 tan 6x

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Chapter 3 Class 11 Trigonometric Functions

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NCERT Solutions of Chapter 3 Class 11 Trigonometry is available free at teachoo. You can check the detailed explanation of all questions of exercises, examples and miscellaneous by clicking on the Exercise link below.

We had learned Basics of Trigonometry in Class 10. In this chapter, we will learn

• What is a positive or a negative angle
• Measuring angles in Degree , Minutes and Seconds
• Radian measure of an angle
• Converting Degree to Radians , and vice-versa
• Sign of sin, cos, tan in all 4 quadrants
• Finding values of trigonometric functions when one value is given (Example: Finding value of sin, cot, cosec, tan, sec, when cos x = -3/5 is given)
• Finding Value of trigonometric functions, given angle
• Solving questions by formula like  (x + y) formula, 2x 3x formula, Cos x + cos y formula , 2 sin x sin y formula 
• Finding principal and general solutions of a trigonometric equation
• Sin and Cosine Formula with supplementary Questions

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CBSE Class 11 Term-1 Maths 2021-22: Topic-Wise MCQs, Case-Based & Assertion/Reason

CBSE Class 11 Term-1 Maths 2021-22: Topic-Wise MCQs, Case-Based & Assertion/Reason

In this Post I Have Provided Mathematics  Class 11 Chapter-Wise MCQs, Case-Based Question And Assertion/Reason For Term-1 Session 2021-22 With Solutions. CBSE has Recently Included These Types Of MCQs  And Assertion/Reason For Term-1 Exam 2020.   Every Student Knows these types of Questions Are Very Important For Their Term-1 Examination.

Any student who want to download these MCQs, then they have to click on given respective download links and it will be automatically download in your Google Drive.

CBSE Class 11th  Physics  Term-1 2021-22: Topic-Wise MCQs, Case-Based & Assertion/Reason

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Given Below Are The Class 11 Mathematics Chapter Name with Respective Download Links Containing Study Material:

CBSE Sample Papers For Class 11 Mathematics

CBSE sample paper for class  11th Maths  is an important tools to analyse itself. Before going to final examinations every student try to solve different types of sample question paper. It will enhance your knowledge and also provide to increase mental ability. Sample question paper are the best resources for the student to prepare for their Board examinations.

These sample question papers are very helpful to the student to get an entire experience before attempting the Board examinations papers. If students solve different types of sample question papers then they get the good confidence about the appropriate answer and they make good score in their Board examinations.

As every student know CBSE always change their exam pattern and also the model paper for their Board examinations that is why it is very important to all the student to understand the Model paper pattern before going to the final examinations.

In this articles I have provided different types of question papers on the basis of CBSE latest exam pattern which will definitely help to the student for the good preparation for their examinations.

In every year before the Board examination, CBSE provide model test paper to the student, on the basis of these model test papers I have prepared sample question papers for class  11th Maths  which will help to the student to understand the concept of model test paper and also it will help to the student for good preparation for their board examination.

CBSE Sample Paper:

Maths And Physics With Pandey Sir  is a website which provide free study material and notes to every students who are preparing for their Board examinations. By going in Level Section you can select CBSE sample papers. In this section, I have provided CBSE sample paper for class 9th to 12th.

Also if you are preparing for any competitive exams, they can find out study material and important notes in Level Section. In this website I have also provided most important MCQs questions, Assertion/Reason based questions and case study based questions for Board examinations or any other competitive examinations.

Benefits Of Solving CBSE Sample Papers for Examination:

Time Management:-

With the help of CBSE sample question papers you can make a proper strategy for their examinations also by practicing sample question papers you can manage your time during the Board examinations.

Examination Strategy:-

After practicing different types of sample question papers you can understand on which section you have spend more time and which section is easy and which section is hard. In this way you can make a proper examination strategy.

Self Evaluation:-

Self evaluation is very important to every student because with the help of self evaluation, student can understand their weak and strong point, which is very important for any Board examinations. After practicing more and more simple paper you can evaluate himself.

To Identify Silly Mistakes:-

As every student know there are many questions in their question paper which are very easy  but student make mistakes in this types of question. By solving different types of sample question papers you can reduce their silly mistakes.

Advantages Of CBSE Sample Question Papers:

* To get a good exam ideas about your examination paper patterns

* Student can easily access to the question papers

* It is very helpful to know about the mark distribution system.

* Helpful in self evaluation

* To know about the pattern of CBSE

* Help to adjust a proper time management

* Available in PDF format

* Chapter wise CBSE sample papers

* CBSE sample papers for class 10

* CBSE sample paper class 12

* CBSE sample paper 2021-22 class 12 Solutions

* CBSE sample paper class 11

* CBSE Sample paper class 9

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Download Case Study Questions for Class 11 Maths

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[PDF] Download Case Study Questions for Class 11 Maths

Here we are providing case study questions for Class 11 Maths. In this article, we are sharing links for Class 11 Maths All Chapters. All case study questions of Class 11 Maths are solved so that students can check their solutions after attempting questions.

Click on the chapter to view.

Class 11 Maths Chapters

Chapter 1 Sets Chapter 2 Relations and Functions Chapter 3 Trigonometric Functions Chapter 4 Principle of Mathematical Induction Chapter 5 Complex Numbers and Quadratic Equations Chapter 6 Linear Inequalities Chapter 7 Permutation and Combinations Chapter 8 Binomial Theorem Chapter 9 Sequences and Series Chapter 10 Straight Lines Chapter 11 Conic Sections Chapter 12 Introduction to Three-Dimensional Geometry Chapter 13 Limits and Derivatives Chapter 14 Mathematical Reasoning Chapter 15 Statistics Chapter 16 Probability

What is meant by Case Study Question?

In the context of CBSE (Central Board of Secondary Education), a case study question is a type of question that requires students to analyze a given scenario or situation and apply their knowledge and skills to solve a problem or answer a question related to the case study.

Case study questions typically involve a real-world situation that requires students to identify the problem or issue, analyze the relevant information, and apply their understanding of the relevant concepts to propose a solution or answer a question. These questions may involve multiple steps and require students to think critically, apply their problem-solving skills, and communicate their reasoning effectively.

Importance of Solving Case Study Questions for Class 11 Maths

Case study questions are an important aspect of mathematics education at the Class 11 level. These questions require students to apply their knowledge and skills to real-world scenarios, helping them develop critical thinking, problem-solving, and analytical skills. Here are some reasons why case study questions are important in Class 11 maths education:

• Real-world application: Case study questions allow students to see how the concepts they are learning in mathematics can be applied in real-life situations. This helps students understand the relevance and importance of mathematics in their daily lives.
• Higher-order thinking: Case study questions require students to think critically, analyze data, and make connections between different concepts. This helps develop higher-order thinking skills, which are essential for success in both academics and real-life situations.
• Collaborative learning: Case study questions often require students to work in groups, which promotes collaborative learning and helps students develop communication and teamwork skills.
• Problem-solving skills: Case study questions require students to apply their knowledge and skills to solve complex problems. This helps develop problem-solving skills, which are essential in many careers and in everyday life.
• Exam preparation: Case study questions are included in exams and tests, so practicing them can help students prepare for these assessments.

Overall, case study questions are an important component of Class 11 mathematics education, as they help students develop critical thinking, problem-solving, and analytical skills, which are essential for success in both academics and real-life situations.

Feature of Case Study Questions on This Website

Here are some features of a Class 11 Maths Case Study Questions Booklet:

Many Case Study Questions: This website contains many case study questions, each with a unique scenario and problem statement.

Different types of problems: The booklet includes different types of problems, such as optimization problems, application problems, and interpretation problems, to test students’ understanding of various mathematical concepts and their ability to apply them to real-world situations.

Multiple-choice questions: Questions contains multiple-choice questions to assess students’ knowledge, understanding, and critical thinking skills.

Focus on problem-solving skills: The questions are designed to test students’ problem-solving skills, requiring them to identify the problem, select appropriate mathematical tools, and analyze and interpret the results.

Emphasis on practical applications: The case studies in the booklet focus on practical applications of mathematical concepts, allowing students to develop an understanding of how mathematics is used in real-life situations.

Comprehensive answer key: The booklet includes a comprehensive answer key that provides detailed explanations and step-by-step solutions for all the questions, helping students to understand the concepts and methods used to solve each problem.

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NCERT Solutions for Class 11 Maths Chapter 3 Free PDF Download

Ncert solutions for class 11 maths chapter 3 – trigonometric functions.

NCERT Solutions for Class 11 Maths Chapter 3 help you to solve the unsolved problems of the NCERT maths book prescribed by the CBSE. It breaks down into detailed steps and explains the answer, which helps you to understand the pattern of questioning. NCERT Solutions also contain questions, answers, images, explanations of questions given in the books.

NCERT Solutions for Class 11 Maths Chapter 3 are formed by our team of highly experienced and qualified faculties. Our NCERT Solutions will give you a complete grasp over the subject and shall help you in scoring higher marks. However, in case of doubts, we have a team of teachers who are ready to solve your doubts any time and are just a click away.

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Download NCERT Solutions for Class 11 Maths.

Download NCERT Solutions for Class 11 here.

Download NCERT Solutions for all subjects here.

CBSE Class 11 Maths Chapter 3 Trigonometric Functions NCERT Solutions

In NCERT Solutions for Class 11 Maths Chapter 3, you will learn about trigonometric functions and their representations, empty set, finite and infinite trigonometric functions, equal trigonometric functions. Sub trigonometric functions, union, and the intersection of trigonometric functions, the difference of trigonometric functions, the complement of a set, properties of complement trigonometric functions.

Sub topics covered under NCERT Solutions for Class 11 Maths Chapter 3

3.1 – Introduction

3.2 – Angles

3.2.1- Degree measure

3.2.2 – Radian measure

3.2.3 – Relation between radian and real numbers

3.2.4 – Relation between degree and radian

3.3 – Trigonometric Functions

3.3.1- Sign of trigonometric functions

3.3.2 – Domain and range of trigonometric functions

3.4 – Trigonometric Functions of Sum and Difference of Two Angles

3.5 – Trigonometric Equations

NCERT Solutions for Class 11 Maths Chapter 3

In NCERT Solutions for Class 11 Maths Chapter 3 you will learn about radian measure – conversion, arc length,  finding the value of trigonometric functions, given other functions, finding the value of trigonometric functions, given angle, (x + y) formula, finding principal solutions, general solutions, sine, and cosine formula. Let us now discuss the subtopics included in Chapter 3.

3.1 – Introduction

In this, you will study about trigonometric function.

3.2 – Angles

In this, you will study the angles formed.

In this, you will study the measure of the degree of angle.

In this, you will study the measure of the degree of angle by radian.

In this, you will study the relation between radian and real number.

In this, you will study the relationship between degree and radian

In this, you will study about trigonometric functions such as sin, cos, tan, cosec, sec, cot, the relation between them.

In this, you will study the sign of trigonometric functions in all four quadrants i.e. in the first quadrant all functions are positive, in II quadrant only sin and cosec are positive, in III quadrant only tan and cot are positive, in IV quadrant only cos and sec are positive.

In this, you will study about domain and range of trigonometric functions i.e. tan x increases from 0 to infinity, sin increases from 0 to 1 and increases from –1 to 0, cos increases from –1 to 0 increases from 0 to 1.

In this, you will derive expressions for trigonometric functions of the sum and difference of two numbers (angles) and related expressions, trigonometric identities.

In this, you will study about trigonometric equations are equations involving trigonometric functions of a variable, principal solution of a trigonometric equation is a solution for which 0≤x<2π, the expression involving integer ‘n’ that gives all solutions of a trigonometric equation is called the general solution.

You can download NCERT Solutions for Class 11 Maths Chapter 3 PDF by clicking on the button below.

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NCERT Solutions for Class 11

• NCERT Solutions for Class 11 Chemistry Chapter 7 Free PDF Download
• NCERT Solutions for Class 11 Physics Chapter 6
• NCERT Solutions for Class 11 Biology Chapter 6 Free PDF Download
• NCERT Solutions for Class 11 Biology Chapter 2 Free PDF Download
• NCERT Solutions for Class 11 Biology Chapter 18 Free PDF Download
• NCERT Solutions for Class 11 Biology Chapter 10 Free PDF Download
• NCERT Solutions for Class 11 Biology Chapter 22 Free PDF Download
• NCERT Solutions for Class 11 Biology Chapter 16 Free PDF Download
• NCERT Solutions for Class 11 Biology Chapter 20 Free PDF Download
• NCERT Solutions for Class 11 Biology Chapter 19 Free PDF Download

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• Applied Maths
• Class 11 Applied Mathematics...

Class 11 Applied Mathematics Case Study Questions

Table of Contents

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Finding good quality Class 11 Applied Mathematics case study questions can be quite challenging. This is because case study questions can be quite marked gaining, and hence a complete understanding of such Class 11 Applied Mathematics case study question is much needed. myCBSEguide is the only app where you’ll find ample Class 11 Applied Mathematics case study questions.

Trust us, if you’re serious about doing well in your CBSE exams, myCBSEguide is the app you need to have on your phone!

Applied Mathematics: Foundations for Class 11 students

Mathematics is already divided into two levels by CBSE: Basic (easy) and Standard (challenging, though not as difficult as Class 10). After Class 10, “Basic” is for students who do not wish to continue studying mathematics, and “Standard” is for those who want to continue

Now, the idea struck that people who don’t want to continue with math or aren’t permitted to do so with Mathematics (code 041), which covers Trigonometry, Vectors, 3D, etc., should still be given the opportunity to comprehend the practical necessity for it, therefore CBSE developed Applied Mathematics (code 241). Any skill topic has a certain job role as its focus. However, the elective course Applied Mathematics focuses on the field of Mathematics with a particular focus on its applications.

Much-needed Applied Mathematics Subject

Students who attend secondary school are better equipped to choose their career opportunities when they graduate. A crucial subject that aids students in selecting their career paths in mathematics. In higher education, mathematics is frequently employed as a supplementary topic in the fields of economics, commerce, social sciences, and many others. According to observations, students who want to study Commerce or Social Science in college may not be able to use the senior secondary mathematics curriculum designed for science topics. With this in mind, the mathematics curriculum for senior secondary classes is expanded to include an additional elective subject with the goal of giving pupils useful math training outside of the physical sciences.

Relevance of Class 11 Applied Mathematics Case Study Questions

• To understand the importance of data in modern society, case studies based on data from the fields of business, economics, psychology, education, biology, and census data will be used.
• Class 11 Applied Mathematics Case Study Questions also strengthen logical thinking abilities such as developing and verifying mathematical arguments, framing instances, and identifying counter examples.
• It motivates Class 11 Applied Mathematics students to do mathematical research and to forge linkages between mathematical concepts and other academic fields.
• Class 11 Applied Mathematics students will gain a solid grasp of descriptive and inferential statistics through the Class 11 Applied Mathematics case study questions, which they may then use to describe, evaluate, and draw conclusions from a given set of data.

Illustrations of Class 11 applied mathematics case study questions

The use of mathematical techniques to solve issues in the actual world is known as applied mathematics. A student’s capacity to apply mathematical ideas to situations that occur in the real world is evaluated using Class 11 applied mathematics case study questions

Below are some illustrations of applied mathematics case study problems for class 11

Class 11 applied mathematics case study question 1

Read the Case study given below and attempt any 4 subparts: A farmer, Ramgarh,  took a bank loan from SBI for repairing his house. But he could not pay the amount on time. This resulted in the accumulation of interest and the amount to pay reached Rs.1,00,000. After a few months, the farmer opened a shop that resulted in enough income and the income increased on a regular basis. So he decided to pay the bank loan in a different manner. The farmer visited the bank. He made an agreement with the bank that he will start paying the amount of Rs.1,00,000 without interest from Jan 2020. In January he will pay Rs.5000 and will increase the payment by Rs. 100 in each month, as shown in the figure.

Answer Key:

Class 11 applied mathematics case study question 2

Read the Case study given below and attempt any 4 sub parts: In a colony, as shown in the following picture, an electric pole has been installed. The pole has been tied by strong wire PQ to support this pole, some electricians were working on the staircase PS.

In the left and right side of the pole, two street lights are fixed at a height of 3m and 4m respectively. These lights are given supply by wires PM and PN. The height OP=5 m and O is the origin. Now answer the following questions:

• x + 15y = -75
• x – 15y + 75 = 0
• x + 5y = 50
• x – 5y = 20
• (b) x – 15y + 75 = 0

Class 11 applied mathematics case study question 3

• (b) 900 ways
• (c) 648 ways
• (d) 100 ways
• (a) 252 ways

Class 11 applied mathematics case study question 4

Read the Case study given below and attempt any 4 sub parts: villages of Shanu and Arun’s are 50km apart and are situated on Delhi Agra highway as shown in the following picture. Another highway YY’ crosses Agra Delhi highway at O(0,0). A small local road PQ crosses both the highways at pints A and B such that OA=10 km and OB =12 km. Also, the villages of Barun and Jeetu are on the smaller high way YY’. Barun’s village B is 12km from O and that of Jeetu is 15 km from O.

Now answer the following questions:

• 5x + 6y = 60
• 6x + 5y = 60
• (a) (10, 0)
• (b) 6x + 5y = 60
• (b) 60/√ 61 km
• (d) 2√61 km

Class 11 applied mathematics case study questions presented here are based on real-life applications of ideas learned in Class 11. These questions will assist students to understand how case study questions will be asked in papers. The questions are intended to assess the student’s comprehension of the principles as well as their ability to apply them to realistic conditions.

What students will study in Class 11 Applied Mathematics?

Students in Class 11 Applied Mathematics will study a number of topics. Topics in Class 11 Applied Mathematics are significant for students who want to career in mathematics or a related discipline. Students will build critical problem-solving abilities in their future studies and professions by studying Class 11 Applied mathematics themes.

CBSE Class 11 Applied Mathematics (Code No. 241)

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Syllabus for the Session 2023-24

CBSE Syllabus

Case Study Questions

Case Study on Sets      CS-2   CS-3   CS-4   CS-5

Case Study on Relations & Functions   CS-2   CS-3

Case Study on Trigonometric Functions

Case Study on Complex Numbers

Case Study on Linear Inequalities

Case Study on Permutations and Combinations

Case Study on Sequences & Series

Case Study on Straight Lines

Case Study on Conic Sections

Case Study on Statistics

Case Study on Probability

Pdf of  Case Studies

MCQs for Practice

Chapter 1 - Sets     

Chapter 2 - Relations & Functions

Chapter 3 - Trigonometric Functions

Chapter 4 - Complex Numbers & Quadratic Equations

Chapter 5 - Linear Inequalities

Chapter 6 - Permutations & Combinations

Chapter 7 - Binomial Theorem

Chapter 8 - Sequences & Series

Chapter 9 - Straight Line

Chapter 1 0 - Conic Sections

Chapter 1 1 - Introduction to Three-dimensional Geometry

Chapter 12 - Limits & D erivatives

Chapter 13 - Statistics

Chapter 14 - Probability

Answers of MCQs

Assertion & Reasoning Questions

Relations & Functions

Trigonometric Functions

Complex Numbers

Linear Inequalities

Permutations & Combinations

Binomial Theorem

Sequences & Series

Straight Lines

Conic Sections

Introduction to Three-Dimensional Geometry

Limits & derivatives

Probability

Topic Wise Assignments of Previous Year Questions

Relations and Functions

Straight Line

Limits & Derivatives

Question Papers - DoE, Delhi

Session 2015-2016

            SA2(QP)         SA2(MS)         COMP(QP)         COMP(MS)

Session 201 6 -20 17

            SA1(QP)      SA2(QP)         SA2(MS)         COMP(QP)        COMP(MS)

Session 201 7 -201 8

            SA2(QP)          SA2(MS)         COMP(QP)         COMP(MS)

Session 201 8 -201 9

            SA2(QP)          SA2(MS)         COMP(QP)         COMP(MS)

Session 201 9 -20 20

            SA2(QP)          SA2(MS)        

Session 2020-21

    Video Explanation:  Part A     Part B Section III     Part B Section IV   Part B Section V

Session 2021-22

Question Paper 

Video Explanation:  Section A     Section B     Section C

Session 2022-23

  Sample Question Paper for Mid-Term Exam

Video Explanation: Section A     Section B    Section C     Section D     Section E

Mid-Term Exam:  Question Paper

Video Explanation: Section A     Section B     Section C     Section D    Section E

Practice Paper for Final Exam

Video Explanation: Section A     Section B     Section C     Section D     Section E

Final Exam:  Question Paper     Marking Scheme

Video Explanation: Section A     Section B     Section C     Section D     Section E

Support Material Issued by DoE, Delhi

Session 202 3 -24

 Mid-Term Exam:  Question Paper

Video Explanation:   Section A    Section B     Section C     Section D     Section E

Practice Paper 1 for Final Exam: Question Paper

Practice Paper 2 for Final Exam: Question Paper

Short Capsules (Notes to Revise Concepts)

Chapter 1 - Sets

Chapter 4 - Mathematical Induction

Chapter 5 - Complex Numbers & Quadratic Equations

Chapter 6 - Linear Inequalities

Chapter 7 - Permutations & Combinations

Chapter 8 - Binomial Theorem

Chapter 9 - Sequences & Series

Chapter 10 - Straight Line

Chapter 11 - Conic Sections

Chapter 12 - Introduction to Three-dimensional Geometry

Chapter 13 - Limits & derivatives

Chapter 14 - Mathematical Reasoning

Chapter 15 - Statistics

Chapter 16 - Probability

Some Basic Concepts to Revise:

Number System

Mensuration Results

Quadratic Equations

Solution of Polynomial Inequality - Wavy Curve Method

Probability__Revision of the Topics studied in Earlier Classes  

Result Sheets

Trigonometric Identities

• NCERT Solutions
• NCERT Class 11
• NCERT 11 Maths
• Chapter 3: Trigonometric Functions
• Chapter 3 Trigonometric Functions Miscellaneous Ex

NCERT Solutions for Class 11 Maths Chapter 3 - Trigonometric Functions Miscellaneous Exercise

Chapter 3, Trigonometric Functions of Class 11 Maths, is categorised under the CBSE Syllabus for 2023-24. The miscellaneous exercise contains questions covering the entire topics present in the chapter. The last exercise of NCERT Solutions for Class 11 Maths Chapter 3 – Trigonometric Functions is based on the following topics:

• Trigonometric Functions
• Trigonometric Functions of Sum and Difference of Two Angles
• Trigonometric Equations

The solutions provided here are based on the latest guidelines of the syllabus prescribed by the CBSE. The NCERT Solutions for Class 11 can help the students in preparing well for the board examination.

NCERT Solutions for Class 11 Maths Chapter 3 – Trigonometric Functions Miscellaneous Exercise

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Access other exercise solutions of Class 11 Maths Chapter 3 – Trigonometric Functions

The NCERT Class 11 Maths Solutions for Chapter 3 can be referred to in PDF format by checking the links below.

Exercise 3.1 Solutions 7 Questions

Exercise 3.2 Solutions 10 Questions

Exercise 3.3 Solutions 25 Questions

Exercise 3.4 Solutions 9 Questions

Access Solutions for Class 11 Maths Chapter 3 Miscellaneous Exercise

Prove that:

2. (sin 3 x  + sin  x ) sin  x  + (cos 3 x  – cos  x ) cos  x  = 0

LHS = (sin 3x + sin x) sin x + (cos 3x – cos x) cos x

By further calculation,

= sin 3x sin x + sin 2 x + cos 3x cos x – cos 2 x

Taking out the common terms,

= cos 3x cos x + sin 3x sin x – (cos 2 x – sin 2 x)

Using the formula

cos (A – B) = cos A cos B + sin A sin B

= cos (3x – x) – cos 2x

= cos 2x – cos 2x

LHS = (cos x + cos y) 2 + (sin x – sin y) 2

By expanding using the formula, we get

= cos 2 x + cos 2 y + 2 cos x cos y + sin 2 x + sin 2 y – 2 sin x sin y

Grouping the terms,

= (cos 2 x + sin 2 x) + (cos 2 y + sin 2 y) + 2 (cos x cos y – sin x sin y)

Using the formula cos (A + B) = (cos A cos B – sin A sin B)

= 1 + 1 + 2 cos (x + y)

= 2 + 2 cos (x + y)

Taking 2 as common

= 2 [1 + cos (x + y)]

From the formula cos 2A = 2 cos 2 A – 1

LHS = (cos x – cos y) 2 + (sin x – sin y) 2

By expanding using the formula,

= cos 2 x + cos 2 y – 2 cos x cos y + sin 2 x + sin 2 y – 2 sin x sin y

= (cos 2 x + sin 2 x) + (cos 2 y + sin 2 y) – 2 (cos x cos y + sin x sin y)

Using the formula cos (A – B) = cos A cos B + sin A sin B

= 1 + 1 – 2 [cos (x – y)]

= 2 [1 – cos (x – y)]

From formula cos 2A = 1 – 2 sin 2 A

5. sin x + sin 3x + sin 5x + sin 7x = 4 cos x cos 2x sin 4x

8. Find sin x/2, cos x/2 and tan x/2 in each of the following.

cos x = -3/5

From the formula,

9. cos x = -1/3, x in quadrant III

10. sin x = 1/4, x in quadrant II

Class 11 Maths NCERT supplementary or miscellaneous exercise solutions PDFs are provided here.

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• Important Questions for CBSE Class 11 Maths (2024-25)

CBSE Class 11 Maths Chapter wise Important Questions - Free PDF Download

One of the most important subjects that students attempt in the science stream is Mathematics. For those taking exams in their eleventh grade, having the important questions for class 11 maths beforehand can help prepare better. We at Vedantu provide you with the opportunity to gain a lot of advantages when it comes to studying before the exam:

We provide the important questions for class 11 maths laid out chapter wise with solutions. Students can accordingly set their schedule

All the questions for the examination are available in a free PDF download any time of the year so you can choose when you want to include it in your study schedule

The questions are all prepared in the latest CBSE syllabus of the latest year of the CBSE board and are updated every annual academic year

Solving these questions will give students the advantage of preparing themselves better before their class 11 examinations

The NCERT important questions for class 11 Maths with answers are present for all chapters from Sets to Probability

There are a whole host of other advantages that come when you want to download the class 11 Maths NCERT important questions available as a free PDF download

Download CBSE Class 11 Maths Important Questions 2024-25 PDF

Also, check CBSE Class 11 Maths Important Questions for All chapters:

Chapter wise Important Questions for CBSE Class 11 Maths

Important Questions for Class 11 Maths CBSE Board

There are a lot of advantages that come with our different services for education. We provide private tutors for students that will help them understand the important questions for class 11 Maths that come chapter wise with free PDF solutions better. Here, they can solve problems at their own pace and also clear their doubts with the tutor online.

Our tutors are experienced and will be able to streamline themselves to the student's schedule. Students can also decide a schedule that works for them so that they can study at a pace that suits them. Our teachers will be able to guide you better when it comes to how you must pace your answers, tackling the right questions and practising well so you can perform better.

CBSE Class 11 Maths Weightage 2024-25

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At Vedantu, you will be able to also tap into various that we can provide to you such as CBSE Important question papers , revision notes , CBSE syllabus and so much more.

Students must enjoy their studies, and we want to help them understand their lessons better instead of just studying by rote.

We provide students with personal teachers for subjects such as Maths, Physics, Chemistry and Biology . They know exactly what sort of questions appear in exams due to their vast years of experience and this can be very helpful for students who are slow learners.

Parents can also breathe easy knowing that their kids are studying in a safe environment and can also contact these teachers to address their concerns. The overall goal is the same, and with us, the extra incentive of enjoying studying is always a bonus.

Other CBSE Class 11 Important Questions Links

Important related links for cbse class 11.

FAQs on Important Questions for CBSE Class 11 Maths (2024-25)

Q 1: How Vedantu’s answers assist us in scoring good marks in the exam?

All our solutions are framed with the aid of our subject matter specialists of maths and that they have given every part of the bankruptcy at the side of the exercise questions which might be referred to at the give up of the bankruptcy. Our Solutions for Class 11 Maths will provide an explanation for to you all the essential major points of the chapter. This will basically help you in building up a sturdy basis of the challenge and eventually you can also enhance your grades with it. The answers supplied through us will help in revision before the examination. These paintings as last-minute have a look at notes for your exam which could be visible just earlier than the examination to memorise all the key factors.

Q 2: What are the important concepts in chapter 11 conic sections?

The chapter covers topics like parts of a cone which teaches about circle, ellipse, parabola, hyperbola and degenerate conic sections . You will also learn about Relationship between the semi-major axis, semi-minor axis and the distance of the focus from the centre of the ellipse, Standard equations of an ellipse, Standard equations of a parabola and Special cases of an ellipse .

The chapter also discusses on Eccentricity, Latus rectum, Standard equation of Hyperbola and minor axis of the distance . This is one of the important chapters of class 11 maths which also explains about the equilateral triangle and equations of the hyperbola.

Q 3: What are the principal topics in relation and functions?

The chapter introduces you to the relations and features. You will particularly encounter the Cartesian Product of Sets and Relations . Here, you may, in particular, realize approximately the real-life model of cartesian products which are explained with the assist of Lindt chocolates are available in 5 shapes, three flavours and in six colours.

You can also be taught of functions which encompass Some capabilities and their graphs along with Identity feature, Constant function, Polynomial feature, Rational features, The Modulus function, Signum feature and Greatest integer characteristic. You will also study about the Algebra of real functions which incorporates Addition of two actual features, Subtraction of a real character from another, Multiplication with the aid of a scalar, Multiplication of two real capabilities and The quotient of two real capabilities.

Q 4: What will I learn in chapter four Mathematical Induction?

Mathematical Induction is a specific technique that is primarily used to prove a given statement or a theorem. The important section of this method is that the theorem should always be true for every natural number given. It is one of the useful methods as you do not have to solve an equation or a statement for every possible value it could take.

You will get familiar with the following pointers while studying Mathematical Induction:

Proving the given illustration or statement is the primary motive.

The proof should always stand true for all the values consisting of natural numbers.

The statement should be true for the initial value as well.

The statement should be true for all other values till nth iteration.

Every step involved in the proof must be justified and has to be true.

Q5. Name the important concepts discussed in Chapter 11 Conic Sections of NCERT Solutions for Class 11 Maths.

Chapter 11 "Conic Sections" deals with various conic sections like circles, ellipses, parabolas, and hyperbolas. The important topics of this chapter are as follows:

a) Sections of a cone

b) Circles

c) Ellipses

d) Special cases of an ellipse

e) Parabolas

f) Standard equations of a parabola

g) Hyperbolas

h) Degenerated Conic Sections

i) Latus rectum

j) Eccentricity 

k) Standard equation of an ellipse

Important questions on all these topics are available here.

These solutions are available on Vedantu's official website( vedantu.com ) and mobile app free of cost.

Q6. What are the main topics covered in important questions of “Relations and Functions” for Class 11 Maths?

"Relations and Functions" is Chapter 2 in the NCERT textbook for Class 11. This is an important chapter and includes the following topics:

Cartesian products of sets

Functions and their graphs

   i) Identity function

            ii) Polynomial function

            iii) Constant function

            iv) Rational function

            v) Modulus function

            vi) Signum function

            vii) Greatest integer function

Algebra of real functions

Students can find all the important questions from this chapter here.

Q7. Which book is best for Class 11 Maths?

Ans: The most important book for Class 11 Mathematics is the main NCERT textbook. Almost all questions in the CBSE exam are directly asked from the NCERT textbook. For this very reason, it is extremely important to understand the concepts mentioned in the NCERT textbook well and practice the NCERT example, and practice questions thoroughly.

Apart from this, students can also practice Vedantu's important questions, NCERT Solutions, sample papers, and previous years' question papers for thorough practice.

Q8 . How many chapters are there in Class 11 Maths?

Ans:   Class 11 CBSE Maths curriculum consists of a total of 16 chapters.  Vedantu has carefully enlisted the important questions from all these chapters. Vedantu's Important Questions for Class 11 Mathematics will allow the students to practice questions that are significant from the exam point of view. It will also teach them the right way to compose step-by-step answers to these questions so they do not lose important marks in exams due to incomplete answers.

Q9. Is Class 11 Maths tough?

Ans: Class 11 Mathematics is definitely not a child's play. It has some complicated topics as well. However, this does not mean that with proper guidance, planning, and effort you cannot ace this subject. You can even top in Class 11 Maths if you follow the following steps:

a) Understand and practice NCERT Solutions and example questions thoroughly.

b) Refer to Vedantu's Important questions and practice

c) Solve loads of sample papers and previous years' question papers.

d) Practice over and over again.

Important Questions for CBSE Class 11

Cbse class 11 study materials, home tuitions in india.

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