The Central Board of Secondary Education, CBSE has scheduled the CBSE Class 12th Mathematics Examination 2020 on March 17, 2020. The students who will be appearing for the upcoming examination can go through the list of chapter-wise important questions and answers. These questions are strictly based on the latest CBSE pattern prescribed by the Board for Class 12th Mathematics Examination 2020.

**CBSE Class 12th Mathematics Chapter 1- Relations and Functions **

**Question 1- ** If * be binary operation defined on R by:

What will the operation * be?

**Answer: **Operation * is communicative but not associative.

**Question 2- **Let * be the binary operation defined on Q. Find which of the following binary operations are commutative.

**Answer:** (i) * is not commutative.

(ii) * is commutative.

(iii) * is not commutative.

(iv) * is commutative.

**Question 3-**Functions f ,g :R →R are defined, respectively, by f(x) = x^{2} + 3x +1, g(x) = 2x − 3, find

(i) *fog*

(ii) *gof*

(iii) *fof*

(iv) *gog*

**Answer: **(i) *fog = 4x ^{2} - 6x + 1*

(ii) *gof = 2x ^{2} + 6x - 1*

(iii) *fof = x ^{4} + 6x^{3} + 14x^{2} + 15x + 5*

(iv) *gog = 4x - 9 *

**For more questions on Relations and Functions, check the link below: **

**CBSE Class 12th Mathematics Chapter 2-**** ****Inverse Trigonometric Functions**

**Question 4- **If a_{1}, a_{2 }, a_{3}, ....., an is an arithmetic progression with common difference d, then evaluate the following expression.

**Answer: **

**Question 5- **** **Find the value of:

**Answer:** π / 4.

**Question 6-**Find the simplified form of:

**Answer: **

**For more questions on Inverse Trigonometric Functions, check the link below: **

**CBSE Class 12th Mathematics Chapter 3- Matrices**

**Question 7-** Find x, y and z, if the below-mentioned matrix, satisfies A’ = A^{-1}

**Answer:**

**Question 8-** Express the given matrix as the sum of a symmetric and a skew-symmetric matrix.

**Answer: **

**Question 9-** If possible, using elementary row transformations, find the inverse of the following matrices.

**Answer:** (i)

(ii) The second row of matrix *A* on LHS contains all zeroes, so, the inverse of matrix *A *does not exist.

(iii)

**For more questions on Matrices, check the link below: **

**CBSE 12th Mathematics Board Exam 2020: Important Questions & Answers from Chapter 3 - Matrices**

**CBSE Class 12th Mathematics Chapter 4 - Determinants**

**Question 10- **Find the value of A^{-1} if:

Using A^{-1}, solve the system of linear equations x - 2y = 10, 2x - y - z = 8 and - 2y + z = 7.

**Answer:** * x* = 0, *y* = - 5 and *z* = - 3

**Question 11- **Using matrix method, solve the system of equations 3*x* + 2*y* - 2*z* = 3, *x* + 2*y* + 3*z* = 6 and 2*x* - *y* + *z* = 2.

**Answer:*** x *= 1, *y* = 1 and *z* = 1

**Question 12- **Find *BA* and use this to solve the system of equations *y* + 2*z* = 7, *x* - y = 3 and 2*x* + 3*y* + 4*z* = 17.

**Answer: ***x* = 2, *y* = - 1 and *z* = 4

**For more questions on Determinants, check the link below: **

**CBSE 12th Mathematics Board Exam 2020: Important Questions & Answers from Chapter 4 - Determinants**

**CBSE Class 12th Mathematics Chapter 5 - Continuity and Differentiability**

**Question 13- **Find the values of p and q, so that the given equation is differentiable at *x* = 1.

**Answer:** p = 3 and q = 5

**Question 14-**

**Answer:**

**Question 15-** Find a point on the curve y = (x - 3)^{2}, where the tangent is parallel to the chord joining the points (3, 0) and (4, 1).

**Answer: **(7/2, 1/4)

**For more questions on Continuity and Differentiability, check the link below: **

**CBSE Class 12th Mathematics Chapter 6 - Application of Derivatives**

**Question 16- **If the sum of lengths of the hypotenuse and a side of a right-angled triangle is given, then show that the area of the triangle is maximum when the angle between them is π / 3.

**Answer: **Area of the right-angled triangle is maximum when the angle between them is π / 3

**Question 17- **Find the points of local maxima, local minima and the points of inflexion of the function f(x) = x^{5}^{ }- 5x^{4}^{ }+ 5x^{3}^{ }- 1. Also, find the corresponding local maximum and local minimum values.

**Answer: **Maximum value of y is given by 0 and the minimum value is given by - 298.

**Question 18- **A telephone company in a town has 500 subscribers on its list and collects fixed charges of 300 per subscriber per year. The company proposes to increase the annual subscription and it is believed that for every increase of 1 per one subscriber will discontinue the service. Find what increase will bring maximum profit?

**Answer: **The company should increase the subscription fee by 100 so that it has a maximum profit.

**For more questions on Application of Derivatives, check the link below: **

**CBSE Class 12th Mathematics Chapter 7 - Integrals**

**Question 19-**

**Answer: **

**Question 20- **

**Answer: ***I = π*

**Question 21- **

**Answer: **xe^{ tan -1x} + C

**For more questions on Integrals, check the link below: **

**CBSE 12th Mathematics Board Exam 2020: Important Questions & Answers from Chapter 7 - Integrals**

**CBSE Class 12th Mathematics Chapter 8 - Application of Integrals**

**Question 22- ** ** **Draw a rough sketch of the given curve *y* = 1 *+*|*x *+ l|, *x* = - 3, *x* = 3, *y* = 0 and find the area of the region bounded by them, using integration.

**Answer:** 16 sq units

**Question 23- **Compute the area bounded by the lines x + 2y =2, y - x =1 and 2x + y = 7.

**Answer:** 6 sq units

**Question 24-** Draw a rough sketch of the region {(x, y): y^{2 } ≤ 6 ax and x^{2} + y^{2 } ≤ 16a^{2}}. Also, find the area of the region sketched using the method of integration.

**Answer: Area of the region is: **

**For more questions on Application of Integrals, check the link below: **

**CBSE Class 12th Mathematics Chapter 9 - Differential Equations**

**Question 25-** State the equation of a curve which passes through the point (1, 1) if the tangent drawn at any point say *P *(*x, y*)* *on the curve meets the coordinate axes at *A *and *B *such that *P *is the mid-point of *AB.*

**Answer:** xy = 1

**Question 26-** Solve the given differential equation:

(x + y) (dx - dy) = dx + dy.

**Answer: **x + y = Ke^{x - y}

**Question 27- **Form a differential equation of all the circles which pass through the origin and whose centres lie on *Y*-axis.

**Answer:**

**For more questions on Differential Equations, check the link below: **

**CBSE Class 12th Mathematics Chapter 10 - Vector Algebra**

**Question 28- **Using vectors, find the area of the △ABC with vertices A(1, 2, 3), B(2, –1, 4)

and C(4, 5, –1).

**Answer: **The area of the △ABC is 1/2**√**274sq. units.

**Question 29- **Using vectors, find the value of *k, *such that the points *(k, –*10, 3), (1, –1, 3) and (3, 5, 3) are collinear.

**Answer:** *k *= -2

**Question 30- **

**Answer: **Area of the parallelogram is 1/2√62 sq. units.

**For more questions on Vector Algebra, check the link below: **

**CBSE Class 12th Mathematics Chapter 11 - Three Dimensional Geometry**

**Question 31- **Find the length and the foot of the perpendicular from the point to the given plane: 2x - 2y + 4z + 5 = 0.

**Answer:** The foot of the perpendicular is (0, 5/2, 0) and the perpendicular distance is **√**6 units.

**Question 32- **Find the equation of the plane which is perpendicular to the plane 5x + 3y + 6z + 8 = 0 and contains the Line of intersection of the planes x + 2y + 3z - 4 = 0 and 2x + y - z+ 5 = 0.

**Answer: **The equation of the plane: 51x + 15y - 50z + 173 = 0.

**Question 33- **Show that the straight lines whose direction cosines are given by 2l + 2m - n = 0 and mn + nl + lm = 0 are at right angles.

**Answer: ** θ = π/2

**For more questions on Three Dimensional Geometry, check the link below: **

**CBSE Class 12th Mathematics Chapter 12 - Linear Programming**

**Question 34- **Solve the following problem graphically: Minimise and Maximise Z = 3x + 9y. subject to the constraints:

x + 3y ≤ 60

x + y ≥ 10

x ≤ y

x ≥ 0, y ≥ 0

**Answer: **The minimum value of Z is 60 at point B (5, 5) of the feasible region. The maximum value of Z on the feasible region occurs at the two corner points C (15, 15) and D (0, 20) and it is 180 in each case.

**Question 35- **A company manufactures two types of sweaters A and B. It costs Rs 360 to make a sweater A and Rs 120 to make a sweater B. The company can make at most 300 sweaters and spend at most Rs 72,000 a day. The number of sweaters B cannot exceed the number of sweaters A by more than 100. The company makes a profit of Rs 200 for each sweater A and Rs 120 for every sweater B. Express this problem as an LPP to maximise the profit to the company.

**Answer: **Required LPP to** **Maximise profit is Z = 200x + 120y is subject to constraints.

3x + y ≤ 600

x + y ≤ 300

x – y ≥ -100

x ≥ 0, y ≥ 0

**Question 36- **One kind of cake requires 200g of flour and 25g of fat, and another kind of cake requires 100g of flour and 50g of fat. Find the maximum number of cakes which can be made from 5kg of flour and 1 kg of fat assuming that there is no shortage of the other ingredients used in making the cakes.

**Answer:** Maximum number of cakes = 30 of kind one and 10 cakes of another kind.

**For more questions on Linear Programming, check the link below: **

**CBSE Class 12th Mathematics ****Chapter 13 - Probability**

**Question 37- **A bag contains 5 red marbles and 3 black marbles. Three marbles are drawn one by one without replacement. What is the probability that at least one of the three marbles drawn be black if the first marble is red?

**Answer: **P(E) = 25/56

**Question 38-** If X is the number of tails in three tosses of a coin, then determine the standard deviation of X.

**Answer: **standard deviation of X = **√**3 / 2.

**Question 39-** There are 5 cards numbered 1 to 5, one number on one card. Two cards are drawn at random without replacement. Let *X *denotes the sum of the numbers on two cards drawn. Find the mean and variance of *X.*

**Answer:** Mean, E (*X*) = 6 and var (*X*) = 3

**For more questions on Probability, check the link below: **

**CBSE 12th Mathematics Board Exam 2020: Important Questions & Answers from Chapter 13 - Probability**

The above-mentioned questions are based on the NCERT textbook, previous year papers and sample papers. This article will help the students in the last minute preparation before the examination. The students appearing for the CBSE Class 12th Mathematics Examination can also go through the link mentioned below:

**CBSE 12th Maths Board Exam 2020: Important Multiple Choice Questions (MCQs) with Answers**