# CBSE Class 12 Maths Board Exam 2018: Important 4 marks questions

Important questions for CBSE Class 12 Maths 2018 board exam are available here. These are basically 4 marks’ questions. According to the latest blueprint of CBSE Class 12 Maths, students will get eleven 4 marks question in CBSE Class 12 Maths 2018 board exam’s question paper.

In order to score well in CBSE Class 12 Maths board exam 2018 students are advised to go prepare these questions well.

Besides going through 4 marks students should also learn about **important 2 marks questions **and** important 1 mark questions.**

**Important 4 marks’ questions are given below:**

**Question:**

(i) Is the binary operation defined on set N, given by a*b = (a + b)/2 for all *a*, *b* ϵ *N*, commutative?

(ii) Is the above binary operation associative?

**Question:**

Find the equation of tangent to the curve *x* = sin 3*t*, *y* = cos 2*t* at *t* = π/4.

**CBSE Class 12 Maths Sample Paper: 2018**

**Question:**

Solve the following differential equation: (x^{2} - y^{2}) dx + 2xy dy = 0 given that y = 1 when x = 1.

**Question:**

Solve the following differential equation: cos^{2}x (dy/dx)+ y = tan x.

**Question:**

Solve the following differential equation:

*x* (*dy*/*dx*) + *y* = *x *log*x*; *x* ≠ 0

**Question:**

Form the differential equation representing the parabolas having vertex at the origin and axis along positive direction of x-axis.

**Question:**

Solve the following differential equation: (3xy + y^{2})dx + (x^{2} + xy)dy = 0.

**Question:**

Solve the following differential equation: dy/dx + y = cos x ‒ sin x.

**Question:**

Find the particular solution of the differential equation satisfying the given conditions: x^{2}dy + (xy + y^{2}) dx = 0; y = 1 when x = 1.

**Question:**

Solve the differential equation dy/dx + y cot x = 2 cos x, given that y = 0, when x = π/2.

**Question:**

Find the particular solution of the differential equation: *y* *e ^{y}*

*dx*= (

*y*

^{3}+ 2

*xe*) d

^{y}*y*,

*y*(0) = 1

Show that (*x* ‒ *y*) *dy* = (x + 2y) is a homogenous differential equation. Also, find the general solution of the given differential equation.

**Question:** Differentiate the following function w.r.t. x:

x^{sin }^{x} + (sin x) ^{cos }^{x}

**Question:**

If y = log (√x + 1/√x)^{2}, then prove that *x*(*x* +1)^{2} *y*_{2} +(*x* + 1)^{2} *y*_{1} = 2 .

**Question:**

If x^{m} y^{n} = (x + y)^{(}^{m} ^{+} ^{n}^{)}, prove that dy/dx = y/x.

**Question:**

Find dy/dx, if yx + xy = ab, where a, b are constants.

**Question:**

Find dy/dx if (x^{2} + y^{2})^{2} = xy.

**Question:**

Bag I contains 1 white, 2 black and 3 red balls; Bag II contains 2 white, 1 black and 1 red balls; Bag III contains 4 white, 3 black and 2 red balls. A bag is chosen at random and two balls are drawn from it with replacement. They happen to be one white and one red. What is the probability that they came from Bag III.

**Question:**

Four bad oranges are accidentally mixed with 16 good ones. Find the probability distribution of the number of bad oranges when two oranges are drawn at random from this lot. Find the mean and variance of the distribution.

**Question:**

On a multiple choice examination with three possible answers (out of which only one is correct) for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing?

**Question:**

Three cards are drawn at random (without replacement) from a well shuffled pack of 52 playing cards. Find the probability distribution of number of red cards. Hence find the mean of the distribution.

**Question:**

The probability that A hits a target is 1/3 and the probability that B hits it is 2/5. If each one of A and B shoots at the target, what is the probability that

(i) the target is hit?

(ii) exactly one-of-them-hits the target?

**Question:** A die is thrown again and again until three sixes are obtained. Find the probability of obtaining the third six in the sixth throw of the die.

**Question:**

A and B throw a pair of die turn by turn. The first to throw 9 is awarded a prize. If A starts the game, show that the probability of A getting the prize is 9/17.

**Question:**

(i) Is the binary operation defined on set N, given by a*b = (a + b)/2 for all *a*, *b* ϵ *N*, commutative?

(ii) Is the above binary operation associative?

**Question:**

Prove that the relation R on the set A = {1, 2, 3, 4, 5} given by R = {(a, b) :|a - b| is even }, is an equivalence relation.

**Question:**

Prove that the relation R on the set A = {1, 2, 3, 4, 5} given by R = {(a, b) :|a - b| is even }, is an equivalence relation.

**Question:**

Find the equation(s) of the tangent(s) to the curve y = (*x*^{3} ‒ 1) (*x* ‒ 2) at the points where the curve intersects the x –axis.

**Question:**

Find the intervals in which the function *f* (*x*) = ‒3 log (1 + *x*) + 4 log (2 + *x*) ‒ 4/(2+*x*) is strictly increasing or strictly decreasing.

**Question:**

Find the approximate value of f (3.02), upto 2 places of decimal, where f (x) = 3x^{2} + 5x + 3

**Question:**

Find the points on the curve y = x^{3} at which the slope of the tangent is equal to the y-coordinate of the point.

**Question:**

Find the intervals in which the function f given by f(x) = sin x + cos x, 0 ≤ x ≤ 2π, is strictly increasing or strictly decreasing.

**Question:**

The length *x *of a rectangle is decreasing at the rate of 5 cm/minute and the width *y *is increasing at the rate of 4 cm/minute. When *x *= 8 cm and *y *= 6 cm, find the rate of change of (*a*) the perimeter, (*b*) the area of the rectangle.

**Question:**

Find the intervals in which the function f given by f (x) = x^{3} + 1/*x*^{3}, *x* ≠ 0 is (i) increasing (ii) decreasing.

**Question:**

A person wants to plant some trees in his community park. The local nursery has to perform this task. It charges the cost of planting trees by the following formula:

*C* (*x*) = *x*^{3} ‒ 45 *x*^{2} + 600*x*, where *x* is the number of trees and* C*(*x*) is the cost of planting x trees in rupees. The local authority has imposed a restriction that it can plant 10 to 20 trees in one community park for a fair distribution. For how many trees should the person place the order so that he has to spend the least amount?

How much is the least amount? Use calculus to answer these questions. Which value is being exhibited by the person?

**Question:**

Prove that the curves *x* = *y*^{2} and *xy* = *k* intersect at right angles if 8*k* ^{2} = 1.

**Question:**

**
**

**Question:**

**
**

**Question:**

Let

Express A as sum of two matrices such that one is symmetric and the other is skew symmetric.

**Question:**

If

verify that A^{2} - 4A - 5I = 0.

**Question:**

Differentiate the following with respect to x:

**Question:**

**
**

Then find the value of

**
**

**Question:**

Find ‘*a*’ and ‘*b*’, if the function given by

is differentiable at x = 1.

**CBSE Class 12 Sample Paper 2018: All Subjects**