Home UP BOARD Question Papers NCERT Solutions CBSE Papers CBSE Notes NCERT Books CBSE Syllabus

CBSE Class 12 Previous Year Question Papers With Solutions Pdf Maths

Here we are providing CBSE Previous Year Question Papers Class 6 to 12 solved with soutions CBSE Class 12 Previous Year Question Papers With Solutions pdf Maths Maths sample paper class 12, Maths previous year question paper class 12, cbse class 12 Maths sample paper, cbse class 12 Maths sample paper 2020, Maths sample paper class 12 2020, cbse sample paper 2020 class 12 Maths, class 12 Maths sample paper 20 Practice of previous year question papers and sample papers protects each and every student to score bad marks in exams.If any student of CBSE Board continuously practices last year question paper student will easily score high marks in tests. Fortunately earlier year question papers can assist the understudies with scoring great in the tests. Unraveling previous year question paper class 12 Maths is significant for understudies who will show up for Class 12 Board tests.

Class 12 Subject Maths Paper Set 2 with Solutions

SECTION A

Question numbers 1 to 20 carry 1 mark each.

Question numbers 1 to 10 are multiple choice type questions. Select the correct option.


Question 1: (Marks 1)

The relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1), (1, 1)} is

(A) symmetric and transitive, but not reflexive

(B) reflexive and symmetric, but not transitive

(C) symmetric, but neither reflexive nor transitive

(D) an equivalence relation


Answer :

(C) symmetric, but neither reflexive nor transitive


Question 2: (Marks 1)


ncert solution class 12th math Question 2









Answer :

ncert solution class 12th math Answer 2





Question 3: (Marks 1)

If A is a non-singular square matrix of order 3 such that A2 = 3A, then value of |A| is

(A) – 3

(B) 3

(C) 9

(D) 27


Answer :

(D) 27


Question 4: (Marks 1)

The function f : R → R given by f(x) = – |x – 1| is

(A) continuous as well as differentiable at x = 1

(B) not continuous but differentiable at x = 1

(C) continuous but not differentiable at x = 1

(D) neither continuous nor differentiable at x = 1


Answer :

(C) continuous but not differentiable at x = 1


Question 5: (Marks 1)

Let A = {1, 3, 5}. Then the number of equivalence relations in A containing (1, 3) is

(A) 1

(B) 2

(C) 3

(D) 4


Answer :

(B) 2


Question 6: (Marks 1)

The interval in which the function f given by 2 x f(x) x e− = is strictly increasing, is

(A) (–∞, ∞)

(B) (–∞, 0)

(C) (2, ∞)

(D) (0, 2)


Answer :


(D) (0, 2)


Question 7: (Marks 1)

ncert solution class 12th math Question 7






Answer :

(A) [0, 12]


Question 8: (Marks 1)


ncert solution class 12th math Question 8






Answer :

(A) –2


Question 9: (Marks 1)


ncert solution class 12th math Question 9







Answer :

(A) 35 sq. units


Question 10: (Marks 1)

The coordinates of the foot of the perpendicular drawn from the point (2, – 3, 4) on the y-axis is

(A) (2, 3, 4)

(B) (– 2, – 3, – 4)

(C) (0, – 3, 0)

(D) (2, 0, 4)


Answer :

(C) (0, –3, 0)

Fill in the blanks in question numbers 11 to 15.


Question 11: (Marks 1)

ncert solution class 12th math Question 11





Answer :


ncert solution class 12th math Answer 11






Question 12: (Marks 1)

ncert solution class 12th math Question 12





Answer :

0


Question 13: (Marks 1)

The distance between parallel planes 2x + y – 2z – 6 = 0 and 4x + 2y – 4z = 0 is ___________ units.

OR

If P(1, 0, – 3) is the foot of the perpendicular from the origin to the plane, then the cartesian equation of the plane is _____________ .


Answer :

2

OR

x – 3z = 10


Question 14: (Marks 1)

If the radius of the circle is increasing at the rate of 0·5 cm/s, then the rate of increase of its circumference is _____________.

Answer :

π cm/s


Question 15: (Marks 1)

The corner points of the feasible region of an LPP are (0,0), (0,8), (2,7), (5,4) and (6,0). The maximum profit P 3x 2y = + occurs at the point ________


Answer :

(5, 4)

Question numbers 16 to 20 are very short answer type questions.


Question 16: (Marks 1)

ncert solution class 12th math Question 16






Answer :

ncert solution class 12th math Answer 16






Question 17: (Marks 1)

ncert solution class 12th math Question 17





Answer :

L.H.L. is k + 5

getting k = –3


Question 18: (Marks 1)

ncert solution class 12th math Question 18






Answer :

ncert solution class 12th math Answer 18





Question 19: (Marks 1)

ncert solution class 12th math Question 19




Answer :

Given differential equation is ey dy = ex dx

Integrating to get ey = ex + C


Question 20: (Marks 1)


ncert solution class 12th math Question 20




Answer :

ncert solution class 12th math Answer 20




SECTION B

Question numbers 21 to 26 carry 2 marks each.


Question 21: (Marks 2)

ncert solution class 12th math Question 21



Answer :

ncert solution class 12th math Answer 21




Question 22: (Marks 2)

ncert solution class 12th math Question 22





Answer :
ncert solution class 12th math Answer 22












Question 23: (Marks 2)

ncert solution class 12th math Question 23





Answer :

ncert solution class 12th math Answer 23

Question 24: (Marks 2)

ncert solution class 12th math Question 24





Answer :

ncert solution class 12th math Answer 24










Question 25: (Marks 2)

ncert solution class 12th math Question 25



Answer :

Any point on line is (2 + 3λ, - 1 + 4λ ,2 + 2λ)

Putting in equation of plane to get λ = 0

Thus point of intersection is (2, –1, 2)


Question 26: (Marks 2)

A purse contains 3 silver and 6 copper coins and a second purse contains 4 silver and 3 copper coins. If a coin is drawn at random from one of the two purses, find the probability that it is a silver coin.

Answer :

ncert solution class 12th math Answer 26







SECTION C


Question numbers 27 to 32 carry 4 marks each.


Question 27: (Marks 4)

ncert solution class 12th math Question 27



Answer :

Let a ∈ N clearly a divides a ∴ (a, a) ∈ R

∴ R is reflexive

For symmetric

(1, 2) ∈ R but (2, 1) ∉ R

∴ R is not symmetric

For transitive

Let (a, b) , (b, c) ∈ R

∴ a divides b and b divides c

⇒ a divides c ∴ (a, c) ∈ R

R is transitive

As R is not symmetric ∴ It is not an equivalence relation

OR

ncert solution class 12th math Answer 27









Question 28: (Marks 4)

ncert solution class 12th math Question 28



Answer :

ncert solution class 12th math Answer 28



Question 29: (Marks 4)

ncert solution class 12th math Question 29




Answer :

ncert solution class 12th math Answer 29



Question 30: (Marks 4)

ncert solution class 12th math Question 30



Answer :

ncert solution class 12th math Answer 30



Question 31: (Marks 4)

ncert solution class 12th math Question 31


Answer :

ncert solution class 12th math Answer 31









Question 32: (Marks 4)

ncert solution class 12th math Question 32


Answer :

ncert solution class 12th math Answer 32













SECTION-D

Question numbers 33 to 36 carry 6 marks each.


Question 33: (Marks 6)

ncert solution class 12th math Question 33


Answer :

ncert solution class 12th math Answer 33




























Question 34: (Marks 6)

Amongst all open (from the top) right circular cylindrical boxes of volume 125π cm3, find the dimensions of the box which has the least surface area.

Answer :

ncert solution class 12th math Answer 34












Question 35: (Marks 6)

Using integration, find the area lying above x-axis and included between the circle x2 + y2 = 8x and inside the parabola y2 = 4x.

OR

Using the method of integration, find the area of the triangle ABC, coordinates of whose vertices are A(2, 0), B(4, 5) and C(6, 3).


Answer :

ncert solution class 12th math Answer 35






























Question 36: (Marks 6)

Find the probability distribution of the random variable X, which denotes the number of doublets in four throws of a pair of dice. Hence, find the mean of the number of doublets (X).


Answer :

ncert solution class 12th math Answer 36


CBSE Class 12 Previous Year Question Papers With Solutions pdf Maths

Maths sample paper class 12, Maths previous year question paper class 12, cbse class 12 Maths sample paper, cbse class 12 Maths sample paper 2020, Maths sample paper class 12 2020, cbse sample paper 2020 class 12 Maths, class 12 Maths sample paper 2020, class 12 important questions Maths, cbse class 12 board exam Maths paper, Maths previous year question papers class 12 with solutions, Maths sample paper class 12 2019, cbse class 12 Maths question paper 2017 solved pdf, cbse class 12 Maths question paper 2018, class 12 Maths paper 2019, Maths question paper for class 12, cbse class 12 Maths paper 2019

Ncert Solution for class 6 to 12 download in pdf

CBSE Model test papars Download in pdf

NCERT Books Free Pdf Download for Class 5, 6, 7, 8, 9, 10 , 11, 12 Hindi and English Medium

Mathematics Biology Psychology
Chemistry English Economics
Sociology Hindi Business Studies
Geography Science Political Science
Statistics Physics Accountancy

CBSE Syllabus Class 6 to 9, 10, 11, 12 Maths, Science, Hindi, English ...

Last year CBSE Question paper for Class 6 to 9, 10, 11, 12 Maths, Science, Hindi, English ...

Important Links

Follow Us On

Face book page ncerthelp twitter page youtube page linkdin page

Revised Syllabus for Class 12

Please Share this webpage on facebook, whatsapp, linkdin and twitter.

Facebook Twitter whatsapp Linkdin

Copyright @ ncerthelp.com A free educational website for CBSE, ICSE and UP board.