CBSE 12th Math (Term 1) Paper 2021-22

Paper was held on
Sun, Dec 5, 2021 11:30 AM

## Mathematics

Differential of $$\log [\log (\log {x^5})]$$ w.r.t. x is

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The number of all possible matrices of order 2 $$\times$$ 3 with each entry 1 or 2 is

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A function f : R $$\to$$ R is defined as f(x) = x3 + 1. Then the function has

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If $$\sin y = x\cos (a + y)$$, then $${{dx} \over {dy}}$$ is

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The points on the curve $${{{x^2}} \over 9} + {{{y^2}} \over {25}} = 1$$, where tangent is parallel to x-axis are

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Three points P(2x, x + 3), Q(0, x) and R(x + 3, x + 6) are collinear, then x is equal to

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The principal value of $${\cos ^{ - 1}}\left( {{1 \over 2}} \right) + {\sin ^{ - 1}}\left( { - {1 \over {\sqrt 2 }}} \ri

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If $${({x^2} + {y^2})^2} = xy$$, then $${{dy} \over {dx}}$$ is

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If a matrix A is both symmetric and skew symmetric, then A is necessarily a

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Let set X = {1, 2, 3} and a relation R is defined in X as : R = {(1, 3), (2, 2), (3, 2)}, then minimum ordered pairs whi

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A Linear Programming Problem is as follows:Minimize z = 2x + ysubject to the constraints x $$\ge$$ 3, x $$\le$$ 9, y $$\

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The function $$f(x) = \left\{ {\matrix{
{{{{e^{3x}} - {e^{ - 5x}}} \over x},} & {if\,x \ne 0} \cr
{k,} & {if\,x

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If Cij denotes the cofactor of element pij of the matrix $$P = \left[ {\matrix{
1 & { - 1} & 2 \cr
0 & 2 & { - 3

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The function $$y = {x^2}{e^{ - x}}$$ is decreasing in the interval

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If R = {(x, y); x, y $$\in$$ Z, x2 + y2 $$\le$$ 4} is a relation in set Z, then domain of R is

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The system of linear equations5x + ky = 5,3x + 3y = 5; will be consistent if

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The equation of the tangent to the curve y (1 + x2) = 2 $$-$$ x, where it crosses the x-axis is

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If $$\left[ {\matrix{
{3c + 6} & {a - d} \cr
{a + d} & {2 - 3b} \cr
} } \right] = \left[ {\matrix{
{12} &

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The principal value of $${\tan ^{ - 1}}\left( {\tan {{9\pi } \over 8}} \right)$$ is

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For two matrices $$P = \left[ {\matrix{
3 & 4 \cr
{ - 1} & 2 \cr
0 & 1 \cr
} } \right]$$ and $${Q^T} =

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The function $$f(x) = 2{x^3} - 15{x^2} + 36x + 6$$ is increasing in the interval

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If $$x = 2\cos \theta - \cos 2\theta $$ and $$y = 2\sin \theta - \sin 2\theta $$, then $${{dy} \over {dx}}$$ is

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What is the domain of the function $${\cos ^{ - 1}}(2x - 3)$$ ?

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A matrix $$A = {[{a_{ij}}]_{3 \times 3}}$$ is defined by $${a_{ij}} = \left\{ {\matrix{
{2i + 3j} & , & {i j} \cr

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If a function f defined by $$f(x) = \left\{ {\matrix{
{{{k\cos x} \over {\pi - 2x}}} & , & {if\,x \ne {\pi \over 2}

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For the matrix $$X = \left[ {\matrix{
0 & 1 & 1 \cr
1 & 0 & 1 \cr
1 & 1 & 0 \cr
} } \right]$$, (X2 $$-$

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Let X = {x2 : x $$\in$$ N} and the function f : N $$\to$$ X is defined by f(x) = x2, x $$\in$$ N. Then this function is

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The corner points of the feasible region for a Linear Programming problem are P(0, 5), Q(1, 5), R(4, 2) and S(12, 0). Th

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The equation of the normal to the curve ay2 = x3 at the point (am2, am3) is

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If A is a square matrix of order 3 and |A| = $$-$$ 5, then |adj A| is

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The simplest form of $${\tan ^{ - 1}}\left[ {{{\sqrt {1 + x} - \sqrt {1 - x} } \over {\sqrt {1 + x} + \sqrt {1 - x} }}

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If for the matrix $$A = \left[ {\matrix{
\alpha & { - 2} \cr
{ - 2} & \alpha \cr
} } \right]$$, | A3 | = 1

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If $$y = \sin (m{\sin ^{ - 1}}x)$$, then which one of the following equations is true?

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The principal value of $$[{\tan ^{ - 1}}\sqrt 3 - {\cot ^{ - 1}}( - \sqrt 3 )]$$ is

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The maximum value of $${\left( {{1 \over x}} \right)^{x}}$$ is

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Let matrix $$X = [{x_{ij}}]$$ is given by $$X = \left[ {\matrix{
1 & { - 1} & 2 \cr
3 & 4 & { - 5} \cr
2 &

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A function f : R $$\to$$ R defined by f(x) = 2 + x2 is

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A Linear Programming Problem is as follows:Maximize/Minimize objective function Z = 2x $$-$$ y + 5Subject to the constra

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If x = $$-$$4 is a root of $$\left| {\matrix{
x & 2 & 3 \cr
1 & x & 1 \cr
3 & 2 & x \cr
} } \right| = 0

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The absolute maximum value of the function $$f(x) = 4x - {1 \over 2}{x^2}$$ in the interval $$\left[ { - 2,{9 \over 2}}

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In a sphere of radius r, a right circular cone of height h having maximum curved surface area is inscribed. The expressi

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The corner points of the feasible region determined by a set of constraints (linear inequalities) are P(0, 5), Q(3, 5),

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If curves y2 = 4x and xy = c cut at right angles, then the value of c is

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The inverse of the matrix $$X = \left[ {\matrix{
2 & 0 & 0 \cr
0 & 3 & 0 \cr
0 & 0 & 4 \cr
} } \right]$

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For an L.P.P. the objective function is Z = 4x + 3y, and the feasible region determined by a set of constraints (linear

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In a residential society comprising of 100 houses, there were 60 children between the ages of 10-15 years. They were ins

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In a residential society comprising of 100 houses, there were 60 children between the ages of 10-15 years. They were ins

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In a residential society comprising of 100 houses, there were 60 children between the ages of 10-15 years. They were ins

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