Date: March 2018

Find the magnitude of each of two vectors `veca` and `vecb` having the same magnitude such that the angle between them is 60° and their scalar product is `9/2`

Chapter: [0.1] Vectors

Find the value of `tan^(-1) sqrt3 - cot^(-1) (-sqrt3)`

Chapter: [0.02] Inverse Trigonometric Functions

If a * b denotes the larger of 'a' and 'b' and if a∘b = (a * b) + 3, then write the value of (5)∘(10), where * and ∘ are binary operations.

Chapter: [0.01] Relations and Functions

if the matrix A =`[(0,a,-3),(2,0,-1),(b,1,0)]` is skew symmetric, Find the value of 'a' and 'b'

Chapter: [0.03] Matrices

A black and a red dice are rolled. Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.

Chapter: [0.13] Probability

If *θ* is the angle between two vectors `hati - 2hatj + 3hatk and 3hati - 2hatj + hatk` find `sin theta`

Chapter: [0.1] Vectors

Find the differential equation representing the family of curves `y = ae^(bx + 5)`. where *a* and *b* are arbitrary constants.

Chapter: [0.09] Differential Equations

Evaluate `int (cos 2x + 2sin^2x)/(cos^2x) dx`

Chapter: [0.07] Integrals

The total cost C(x) in Rupees associated with the production of x units of an item is given by

C(x) = 0.007x^{3} – 0.003x^{2} + 15x + 4000.

Find the marginal cost when 17 units are produced

Chapter: [0.06] Applications of Derivatives

Differentiate `tan^(-1) ((1+cosx)/(sin x))` with respect to x

Chapter: [0.05] Continuity and Differentiability

Given `A = [(2,-3),(-4,7)]` compute `A^(-1)` and show that `2A^(-1) = 9I - A`

Chapter: [0.03] Matrices

Prove that `3sin^(-1)x = sin^(-1) (3x - 4x^3)`, `x in [-1/2, 1/2]`

Chapter: [0.02] Inverse Trigonometric Functions

Two numbers are selected at random (without replacement) from the first five positive integers. Let X denote the larger of the two numbers obtained. Find the mean and variance of X

Chapter: [0.13] Probability

An open tank with a square base and vertical sides is to be constructed from a metal sheet so as to hold a given quantity of water. Show that the cost of material will be least when the depth of the tank is half of its width. If the cost is to be borne by nearby settled lower-income families, for whom water will be provided, what kind of value is hidden in this question?

Chapter: [0.06] Applications of Derivatives

Find the equations of the tangent and the normal, to the curve 16x^{2} + 9y^{2} = 145 at the point (x_{1}, y_{1}), where x_{1} = 2 and y_{1} > 0.

Chapter: [0.06] Applications of Derivatives

Find the intervals in which the function `f(x) = x^4/4 - x^3 - 5x^2 + 24x + 12` is (a) strictly increasing, (b) strictly decreasing

Chapter: [0.06] Applications of Derivatives

if `(x^2 + y^2)^2 = xy` find `(dy)/(dx)`

Chapter: [0.05] Continuity and Differentiability

If x = a (2θ – sin 2θ) and y = a (1 – cos 2θ), find `dy/dx` when `theta = pi/3`

Chapter: [0.05] Continuity and Differentiability

If *y* = sin (sin *x*), prove that `(d^2y)/(dx^2) + tan x dy/dx + y cos^2 x = 0`

Chapter: [0.05] Continuity and Differentiability

Find the particular solution of the differential equation e^{x} tan y dx + (2 – e^{x}) sec^{2} y dy = 0, give that `y = pi/4` when x = 0

Chapter: [0.09] Differential Equations

Find the particular solution of the differential equation `dy/dx + 2y tan x = sin x` given that y = 0 when x = `pi/3`

Chapter: [0.09] Differential Equations

Find the shortest distance between the lines `vecr = (4hati - hatj) + lambda(hati+2hatj-3hatk)` and `vecr = (hati - hatj + 2hatk) + mu(2hati + 4hatj - 5hatk)`

Chapter: [0.11] Three - Dimensional Geometry

Find `int (2cos x)/((1-sinx)(1+sin^2 x)) dx`

Chapter: [0.07] Integrals

Suppose a girl throws a die. If she gets 1 or 2 she tosses a coin three times and notes the number of tails. If she gets 3,4,5 or 6, she tosses a coin once and notes whether a ‘head’ or ‘tail’ is obtained. If she obtained exactly one ‘tail’, what is the probability that she threw 3,4,5 or 6 with the die ?

Chapter: [0.13] Probability

Let `veca = 4hati + 5hatj - hatk`, `vecb = hati - 4hatj + 5hatk` and `vecc = 3hati + hatj - hatk`. Find a vector `vecd` which is perpendicular to both `vecc` and `vecb and vecd.veca = 21`

Chapter: [0.1] Vectors

Using properties of determinants, prove that `|(1,1,1+3x),(1+3y, 1,1),(1,1+3z,1)| = 9(3xyz + xy + yz+ zx)`

Chapter: [0.04] Determinants

Find the area of the region in the first quadrant enclosed by the *x*-axis, the line *y* = *x* and the circle *x*^{2} + *y*^{2} = 32.

Chapter: [0.08] Applications of the Integrals

Let A = {*x* ∈ Z : 0 ≤ *x* ≤ 12}. Show that R = {(*a*, *b*) : *a*, *b *∈ A, |*a* – *b*| is divisible by 4}is an equivalence relation. Find the set of all elements related to 1. Also write the equivalence class [2]

Chapter: [0.01] Relations and Functions

Show that the function f: ℝ → ℝ defined by f(x) = `x/(x^2 + 1), ∀x in R`is neither one-one nor onto. Also, if g: ℝ → ℝ is defined as g(x) = 2x - 1. Find fog(x)

Chapter: [0.01] Relations and Functions

Find the distance of the point (−1, −5, −10) from the point of intersection of the line `vecr=2hati-hatj+2hatk+lambda(3hati+4hatj+2hatk) ` and the plane `vec r (hati-hatj+hatk)=5`

Chapter: [0.11] Three - Dimensional Geometry

A factory manufactures two types of screws A and B, each type requiring the use of two machines, an automatic and a hand-operated. It takes 4 minutes on the automatic and 6 minutes on the hand-operated machines to manufacture a packet of screws 'A' while it takes 6 minutes on the automatic and 3 minutes on the hand-operated machine to manufacture a packet of screws 'B'. Each machine is available for at most 4 hours on any day. The manufacturer can sell a packet of screws 'A' at a profit of 70 paise and screws 'B' at a profit of Rs 1. Assuming that he can sell all the screws he manufactures, how many packets of each type should the factory owner produce in a day in order to maximize his profit? Formulate the above LPP and solve it graphically and find the maximum profit.

Chapter: [0.12] Linear Programming

Evaluate `int_0^(pi/4) (sinx + cosx)/(16 + 9sin2x) dx`

Chapter: [0.07] Integrals

Evaluate : `int_1^3 (x^2 + 3x + e^x) dx` as the limit of the sum.

Chapter: [0.07] Integrals

If A = `[(2,-3,5),(3,2,-4),(1,1,-2)]` find *A*^{−1}. Using A^{−1} solve the system of equations

2x – 3y + 5z = 11

3x + 2y – 4z = – 5

x + y – 2z = – 3

Chapter: [0.04] Determinants

Using elementary row transformations, find the inverse of the matrix A = `[(1,2,3),(2,5,7),(-2,-4,-5)]`

Chapter: [0.03] Matrices [0.04] Determinants

#### Other Solutions

#### Submit Question Paper

Help us maintain new question papers on Shaalaa.com, so we can continue to help studentsonly jpg, png and pdf files

## CBSE previous year question papers Class 12 Mathematics with solutions 2017 - 2018

Previous year Question paper for CBSE Class 12 Maths-2018 is solved by experts. Solved question papers gives you the chance to check yourself after your mock test.

By referring the question paper Solutions for Mathematics, you can scale your preparation level and work on your weak areas. It will also help the candidates in developing the time-management skills. Practice makes perfect, and there is no better way to practice than to attempt previous year question paper solutions of CBSE Class 12.

How CBSE Class 12 Question Paper solutions Help Students ?

• Question paper solutions for Mathematics will helps students to prepare for exam.

• Question paper with answer will boost students confidence in exam time and also give you an idea About the important questions and topics to be prepared for the board exam.

• For finding solution of question papers no need to refer so multiple sources like textbook or guides.