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

Exam Held on Sun Dec 05 2021 11:30:00 GMT+0000 (Coordinated Universal Time)
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## Mathematics

Differential of $$\log [\log (\log {x^5})]$$ w.r.t. x is
The number of all possible matrices of order 2 $$\times$$ 3 with each entry 1 or...
A function f : R $$\to$$ R is defined as f(x) = x<sup>3</sup> + 1. Then the func...
If $$\sin y = x\cos (a + y)$$, then $${{dx} \over {dy}}$$ is
The points on the curve $${{{x^2}} \over 9} + {{{y^2}} \over {25}} = 1$$, where ...
Three points P(2x, x + 3), Q(0, x) and R(x + 3, x + 6) are collinear, then x is ...
The principal value of $${\cos ^{ - 1}}\left( {{1 \over 2}} \right) + {\sin ^{ -... If$${({x^2} + {y^2})^2} = xy$$, then$${{dy} \over {dx}}$$is If a matrix A is both symmetric and skew symmetric, then A is necessarily a Let set X = {1, 2, 3} and a relation R is defined in X as : R = {(1, 3), (2, 2),... A Linear Programming Problem is as follows:<br/><br/>Minimize z = 2x + y<br/><br... The function$$f(x) = \left\{ {\matrix{ {{{{e^{3x}} - {e^{ - 5x}}} \over x},}...
If C<sub>ij</sub> denotes the cofactor of element p<sub>ij</sub> of the matrix \$...
The function $$y = {x^2}{e^{ - x}}$$ is decreasing in the interval
If R = {(x, y); x, y $$\in$$ Z, x<sup>2</sup> + y<sup>2</sup> $$\le$$ 4} is a re...
The system of linear equations<br/><br/>5x + ky = 5,<br/><br/>3x + 3y = 5; will ...
The equation of the tangent to the curve y (1 + x<sup>2</sup>) = 2 $$-$$ x, wher...
If $$\left[ {\matrix{ {3c + 6} & {a - d} \cr {a + d} & {2 - 3b} \cr ... The principal value of$${\tan ^{ - 1}}\left( {\tan {{9\pi } \over 8}} \right)$$... For two matrices$$P = \left[ {\matrix{ 3 & 4 \cr { - 1} & 2 \cr 0 ...
The function $$f(x) = 2{x^3} - 15{x^2} + 36x + 6$$ is increasing in the interval...
If $$x = 2\cos \theta - \cos 2\theta$$ and $$y = 2\sin \theta - \sin 2\theta ... What is the domain of the function$${\cos ^{ - 1}}(2x - 3)$$? A matrix$$A = {[{a_{ij}}]_{3 \times 3}}$$is defined by$${a_{ij}} = \left\{ {\...
If a function f defined by $$f(x) = \left\{ {\matrix{ {{{k\cos x} \over {\pi ... For the matrix$$X = \left[ {\matrix{ 0 & 1 & 1 \cr 1 & 0 & 1 \cr 1...
Let X = {x<sup>2</sup> : x $$\in$$ N} and the function f : N $$\to$$ X is define...
The corner points of the feasible region for a Linear Programming problem are P(...
The equation of the normal to the curve ay<sup>2</sup> = x<sup>3</sup> at the po...
If A is a square matrix of order 3 and |A| = $$-$$ 5, then |adj A| is
The simplest form of $${\tan ^{ - 1}}\left[ {{{\sqrt {1 + x} - \sqrt {1 - x} } ... If for the matrix$$A = \left[ {\matrix{ \alpha & { - 2} \cr { - 2} & \...
If $$y = \sin (m{\sin ^{ - 1}}x)$$, then which one of the following equations is...
The principal value of $$[{\tan ^{ - 1}}\sqrt 3 - {\cot ^{ - 1}}( - \sqrt 3 )]... The maximum value of$${\left( {{1 \over x}} \right)^{x}}$$is Let matrix$$X = [{x_{ij}}]$$is given by$$X = \left[ {\matrix{ 1 & { - 1} &...
A function f : R $$\to$$ R defined by f(x) = 2 + x<sup>2</sup> is
A Linear Programming Problem is as follows:<br/><br/>Maximize/Minimize objective...
If x = $$-$$4 is a root of $$\left| {\matrix{ x & 2 & 3 \cr 1 & x & 1 \... The absolute maximum value of the function$$f(x) = 4x - {1 \over 2}{x^2}$$in t... In a sphere of radius r, a right circular cone of height h having maximum curved... The corner points of the feasible region determined by a set of constraints (lin... If curves y<sup>2</sup> = 4x and xy = c cut at right angles, then the value of c... The inverse of the matrix$$X = \left[ {\matrix{ 2 & 0 & 0 \cr 0 & 3 & 0...
For an L.P.P. the objective function is Z = 4x + 3y, and the feasible region de...
<p>In a residential society comprising of 100 houses, there were 60 children bet...
<p>In a residential society comprising of 100 houses, there were 60 children bet...
<p>In a residential society comprising of 100 houses, there were 60 children bet...
<p>In a residential society comprising of 100 houses, there were 60 children bet...
<p>In a residential society comprising of 100 houses, there were 60 children bet...

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