CBSE Class 12 Maths Answer Key 2021-2022

CBSE Class 12th Maths Answer Key 2021-22 – CBSE has conducted the class 12 mathematics exam on December 6, 2021, from 11:30 AM to 1:00 PM. Students can check CBSE Class 12 Maths question paper with answers from this page.

Ques. A relation R is defined on N Which of the following is the reflexive relation?
Ans. Correct option is (c)

Ques. A function f R ——> R defined by f(x) = 4x+3 cosx is
Ans. Neither one-one nor onto

Ques. If y = cot^-1x, x<0, then
Ans. x/2 <y<x

Ques. The number of function defined from (1,2,3,4,5) —> (a,b) which are one-one is:
Ans. 0

Ques. If A = [4,2 x -1,1], then (A-2I) (A-3I) is equal to
Ans. 0

Ques. If P is a 3×3 matrix such that P = 2P+1, where P is the transpose of P, then
Ans. P = -I

Ques. If order of matrix A is 2×3, of matrix B is 3×2, and matrix C is 3×3, then which one of the following is not defined?
Ans. C(A+B’)

Ques. If A = [a,2 x 2,a] and |A³| = 27, then the value of a is
Ans. ±√7

Ques. The function f(x) = (x) is the greatest integer function that is less than or equal to x, is continuous at
Ans. 15

Ques. If y = tan^-1(e^2x), then dy/dx is equal to
Ans. 2e^2x / 1+e^4x

Ques. If y²(2-x) = x³, then (dy/dx)_(1,1) is equal to
Ans. 2

Ques. The angle between the tangents to the curve y=x2-5x+6 at the points (2,0) and (3,0)
Ans. 2

Ques. The interval in which function y=x3+6×2+6 is increasing, is:
Ans. (-,-4)(0,)

Ques. The value of x for which (x-x2) is maximum, is:
Ans. ½

Ques. If the corner points of the feasible region of LPP are (0,3), (3,2) and (0,5), then the minimum value of Z=11x+7y is:
Ans. 21

Ques. The number of solutions of the system of inequations x+2y3, 3x+4y12, x0, y1 is:
Ans. 0

Ques. The number of equivalence relations in the set {1,2,3} containing the elements (1,2) and (2,1) is:
Ans. 2

Ques. Let f: RR be defined by f(x)=1x, for all xR. Then, f is:
Ans. not defined

Ques. The function f:NN is defined by f(n)=n+12, if n is odd and n2, if n is evenThe function f is:
Ans. onto but not one-one.

Ques. The value of sin-1cos 135 is:
Ans. -10

Ques. If sin-1x>cos-1x, then x should lie in the interval:
Ans. 12,1

Ques. If A=cos -sin    sin    cos and A+A’=I, then the value of is:
Ans. 3

Ques. The determinant y+k, y, y, y, y+k, y, y,y,y+k is equal to:

Ques. If A=[1,-2,4,2,-1,3,4,2,0] is the adjoint of a square matrix B, the B-1 is equal to:
Ans. 12A

Ques. If A=[1,-1,1,1,-1,1,1,-1,1], then A5-A4-A3+A2 is equal to:
Ans. 0

Ques. If y=e-x, then d2ydx2 is equal to:
Ans. y

Ques. If x=t2+1,y=2at, then d2ydx2 at t=a is:
Ans. -12a2

Ques. The function f(x)={x2 for x<1 and 2-x for x1} is:
Ans. not differentiable at x=1

Ques. The curve x2-xy+y=27 has tangents parallel to x-axis at:
Ans. (3,6) and (-3,-6)

Ques. A wire of length 20 cm is bent in the form of a sector of a circle. The maximum area that can be enclosed by the wire is:
Ans. 25 sq cm

Ques. The function (x-sinx) decreases for:
Ans. no value of x

Ques. If is the angle of intersection between the curves y2=4ax and ay=2x2at (a,2a), the the value of tan is:
Ans. 3/5

Ques. The maximum value of Z=3x+4y subject to the constraints x0,
Ans. 4

Ques. The feasible region of an LPP is given in the following figure. Then, the constraints of the LPP are x0, y0 and
Ans. 2x+y104 and x+2y76

Ques. If the minimum value of an objective function Z=ax+by occurs at two points (3,4) and (4,3) then:
Ans. a=b

Ques. For the following LPP, Maximise Z=3x+4y subject to constraints x-y-1, x3, x0, y0
Ans. 25

Ques. A relation r is defined on Z as: aRb if and only a2-7ab+6b2=0. Then, R is:
Ans. Reflexive but not symmetric

Ques. The value of 1!,2!,3*3!, 2*2!, 3*3!,4*4!,3!,4!,5! is :
Ans. -24

Ques. If 1, -tan, tan, 1[1, tan, -tan, 1]-1=[a,-b,b,a], then:
Ans. a=cos 2,b=sin 2

Ques. The normal to the curve 3y=6x-5×3 at the point (1,⅓) passes through the point:
Ans. (3,1)

Ques. If y=sin (2sin-1x), then (1-x2)y2 is equal to:
Ans. -xy1-4y

Ques. The volume (V) of the casted half cylinder will be:
Ans. 12r2h

Ques. The total surface area (S) of the casted half cylinder will be:
Ans. rh+r2+2rh

Ques. The volume (V) of the casted half cylinder will be:
Ans. 12r2h

Ques. The total surface area (S) of the casted half cylinder will be:
Ans. rh+r2+2rh

Ques. The total surface area S can be expressed in terms V and r as:
Ans. r+2V(+2)r

Ques. For the given half cylinder of volume V, the total surface area S is minimum, when:
Ans. (+2)V=2r3

Ques. The ratio of h:2r for S to be minimum will be equal to:
Ans. :+2

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