# Class 12 Maths Sample paper 2021-22: best sample paper for practice.

## Maths Sample paper : Most expected sample paper for Board exams.

Maths sample paper: This is an MCQ-based Maths sample paper. The exam for the Mathematics Class 12  CBSE board is going to be held on 30 November. Attempt this quiz to check your preparation and practice for the exam.

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This quiz contains a lot of MCQs and is made on the latest CBSE pattern. The quiz is made up of all the chapter-wise MCQs.

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Class 12 Mathematics sample paper

This sample paper is one of the most expected for the upcoming exam and contains the most important of all questions complete this entire quiz to test your preparations. All the best students!

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A) Let $\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}$ be defined by $f(x)=\left\{\begin{array}{l}2 x: x>3 \\ x^{2}: 1<x \leq 3 \\ 3 x: x \leq 1\end{array}\right.$
Then $f(-1)+f(2)+f(4)$ is

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B) Corner points of the feasible region for an LPP are (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5). Let F = 4x
+ 6y be the objective function. Maximum of F – Minimum of F =

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C) 3. Find the value of b for which the function $f(x)=\left\{\begin{array}{ll}5 x-4 & , 0<x \leq 1 \\ 4 x^{2}+3 b x & , 1<x<2\end{array}\right.$ is continuous at every point of its domain, is

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D) Let A be a non-singular square matrix of order 3 × 3. Then |adj A| is equal to

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E) A fruit grower can use two types of fertilizer in his garden, brand P and brand Q. The amounts
(in kg) of nitrogen, phosphoric acid, potash, and chlorine in a bag of each brand are given in
the table. Tests indicate that the garden needs at least 240 kg of phosphoric acid, at least 270 kg
of potash, and at most 310 kg of chlorine.

If the grower wants to maximize the amount of nitrogen added to the garden, how many bags
of each brand should be added? What is the maximum amount of nitrogen added?

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F) The equation of normal to the curve
$3 x^{2}-y^{2}=8$
= 8 which is parallel to the line x + 3y = 8 is

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G) If $\omega$ is a complex cube root of unity then the value of $\left|\begin{array}{ccc}1 & \omega & 1+\omega \\ 1+\omega & 1 & \omega \\ \omega & 1+\omega & 1\end{array}\right|$

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H) If $\mathrm{y}=\mathrm{x}^{2} \sin \frac{1}{x}$ then $\frac{d y}{d x}=$ ?

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I) Determine the maximum value of $\mathrm{Z}=11 \mathrm{x}+7 \mathrm{y}$ subject to the constraints : $2 \mathrm{x}+\mathrm{y} \leq 6, \mathrm{x} \leq 2, \mathrm{x} \geq 0$, $y \geq 0$.

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J) If $A=\left[\begin{array}{ccc}0 & 2 & -3 \\ -2 & 0 & -1 \\ 3 & 1 & 0\end{array}\right]$ then $\mathrm{A}$ is a

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K) If $f(x)=\left\{\begin{array}{ll}m x+1, & \text { if } x \leq \frac{\pi}{2} \\ \sin x+n, & \text { if } x>\frac{\pi}{2}\end{array}\right.$ is continuous at $x=\frac{\pi}{2}$ then

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L) The feasible region for an LPP is shown in the Figure. Let F = 3x - 4y be the objective function.
Maximum value of F is.

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M) The value of $\mathrm{k}$ for which \mathrm{f}(\mathrm{x})=\left\{\begin{aligned} \frac{\sin 5 x}{3 x}, & \text { if } x \neq 0 \\ k, & \text { if } x=0 \end{aligned}\right. is continuous at x=0 is

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N) The function $f(x)=\frac{4-x^{2}}{4 x-x^{3}}$ is

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O) If $y=x^{\mathrm{n}-1} \log x$ then $x^{2} y_{2}+(3-2 n) x y_{1}$ is equal to

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P) The function f(x) = tanx - x

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Q) The point on the curve y2
= 4x which is nearest to the point (2,1) is

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R) $\sin ^{-1}\left(\frac{-1}{2}\right)+2 \cos ^{-1}\left(\frac{-\sqrt{3}}{2}\right)=$ ?

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S) If $\mathrm{x}^{\mathrm{y}}=\mathrm{e}^{\mathrm{x}-\mathrm{y}}$, then $\frac{d y}{d x}$ is

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T) The curves x= y2
and xy = k cut orthogonally when

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U) Attempt any 16 questions
Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as aRb if a is congruent to $\mathrm{b} \mathrm{a}, \mathrm{b} \in \mathrm{T}$. Then $\mathrm{R}$ is

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V) f(x) = sin x $\sqrt{3}$ cos x is maximum when x =

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W) The feasible region for an LPP is shown in Figure. Evaluate Z = 4x + y at each of the corner
points of this region. Find the minimum value of Z, if it exists

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X) 24. The slope of the tangent to the curve $x=3 t^{2}+1, y=t^{3}-1$ at x=1 is

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Y) If $y=\frac{1}{1+x^{a-b}+x^{c-b}}+\frac{1}{1+x^{b-c}+x^{a-c}}+\frac{1}{1+x^{b-a}+x^{c-a}}$ , then $\frac{d y}{d x}$ is equal to

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Z) $\cot \left(\tan ^{-1} \mathrm{x}+\cot ^{-1} \mathrm{x}\right)$

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AA) If the set A contains 5 elements and the set B contains 6 elements, then the number of one one and onto mappings from A to B is

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AB) $\tan \left[2 \tan ^{-1} \frac{1}{5}-\frac{\pi}{4}\right]=?$

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AC) If $\mathrm{y}=\tan ^{-1}\left(\frac{\sqrt{a}+\sqrt{x}}{1-\sqrt{a x}}\right)$ then $\frac{d y}{d x}=$?

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AD) If A’ is the transpose of a square matrix A, then

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AE) If $\sqrt{1-x^{6}}+\sqrt{1-y^{6}}=\mathrm{a}^{3}\left(\mathrm{x}^{3}-\mathrm{y}^{3}\right)$ then $\frac{d y}{d x}$ is equal to

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AF) If $y=\frac{e^{x}-e^{-x}}{e^{x}+e^{-x}}$ , then $\frac{d y}{d x}$ is equal to

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AG) If the function $f(x)=2 x^{2}-k x+5$ is increasing on (1,2), then  k lies in the interval

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AH) $\operatorname{Sin}\left(\tan ^{-1} x\right),|x|<1$ is equal to

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AI) $\left|\begin{array}{ccc}b+c & a & a \\ b & c+a & b \\ c & c & a+b\end{array}\right|=?$

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AJ) The feasible region (shaded) for an LPP is shown in the Figure. Minimum of Z = 4x + 3y occurs at
the point

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AK) If A is an invertible matrix of order 2 , then $\operatorname{det}\left(\mathrm{A}^{-1}\right)$ is equal to

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AL) Let $\mathrm{f}(\mathrm{x})=\mathrm{x}^{3}$, then $\mathrm{f}(\mathrm{x})$ has a

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AM) If $f(x)=\sqrt{1-\sqrt{1-x^{2}}}$, then $\mathrm{f}(\mathrm{x})$ is

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AN) Which of the following functions from Z into Z are bijections?

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AO) If $\tan ^{-1}\left\{\frac{\sqrt{1+x^{2}}-\sqrt{1-x^{2}}}{\sqrt{1+x^{2}}+\sqrt{1-x^{2}}}\right\}=\alpha$ , then $\mathrm{x}^{2}=$

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AP) Maximize $\mathrm{Z}=-\mathrm{x}+2 \mathrm{y}$ , subject to the constraints : $\mathrm{x} \geq 3, \mathrm{x}+\mathrm{y} \geq 5, \mathrm{x}+2 \mathrm{y} \geq 6, \mathrm{y} \geq 0$

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AQ) If f is derivable at x = a , then $\operatorname{Lt}_{x \rightarrow a} \frac{x f(a)-a f(x)}{x-a}$ is equal to

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AR) If A, B are two n × n non - singular matrices, then what can you infer about AB?

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AS) Let S be the set of all real numbers and let R be a relation on S, defined by $\mathrm{a} \mathrm{Rb} \Leftrightarrow(1+\mathrm{ab})>0$ Then , R is

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AT) Question No. 46 to 50 are based on the given text. Read the text carefully and answer the
questions:
Consider 2 families A and B. Suppose there are 4 men, 4 women and 4 children in family A and 2 men, 2
women and 2 children in family B. The recommended daily amount of calories is 2400 for a man, 1900
for a woman, 1800 for children and 45 grams of proteins for a man, 55 grams for a woman and 33
grams for children.

The requirement of calories and proteins for each person in matrix form can be represented
as

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AU) The requirement of calories of family A is

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AV) The requirement of proteins for family B is

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AW) If A and B are two matrices such that $\mathrm{AB}=\mathrm{B}$ and $\mathrm{BA}=\mathrm{A}$ , then $\mathrm{A}^{2}+\mathrm{B}^{2}$ equals

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AX) If $\mathrm{A}=\left(\mathrm{a}_{\mathrm{ij}}\right)_{\mathrm{m}} \times \mathrm{n}, \mathrm{B}=\left(\mathrm{b}_{\mathrm{ij}}\right)_{\mathrm{n}} \times \mathrm{p}$ and $\mathrm{C}=\left(\mathrm{c}_{\mathrm{ij}}\right) \mathrm{p} \times \mathrm{q}$ , then the product  (BC)A is possible only when