Mathematics 2022 Question Paper Online Test (12th Standard)

Q1

If \(f(x)=\begin{cases}2x & 0\le x\le a\\ 0 & \text{otherwise}\end{cases}\) is a probability density function of a random variable, then the value of a is :

A.3 B.1 C.4 D.2

Q2

Which one of the following is not true in the case of discrete random variable X ?

A.\(\lim_{x\to\infty}F(x)=F(\infty)=1\) B.\(0\le F(x)\le 1\) for all \(x\in\mathbb{R}\) C.\(F(x)\) is real valued decreasing function. D.\(\lim_{x\to-\infty}F(x)=F(-\infty)=0\)

Q3

If \(f(x)=\frac{x}{x+1}\), then its differential is :

A.\(\frac{1}{x+1}\,dx\) B.\(\frac{-1}{(x+1)^2}\,dx\) C.\(\frac{-1}{x+1}\,dx\) D.\(\frac{1}{(x+1)^2}\,dx\)

Q4

The value of \(\int_0^1 x(1-x)^{99}\,dx\) is :

A.\(\frac{1}{10010}\) B.\(\frac{1}{11000}\) C.\(\frac{1}{10001}\) D.\(\frac{1}{10100}\)

Q5

The principal value of \(\cos^{-1}\left(\frac{\sqrt{3}}{2}\right)\) is :

A.\(\frac{\pi}{2}\) B.\(\frac{\pi}{3}\) C.\(\frac{5\pi}{6}\) D.\(\frac{\pi}{6}\)

Q6

If \(A=\begin{bmatrix}2&3\\5&-2\end{bmatrix}\) be such that \(\lambda A^{-1}=A\), then \(\lambda\) is :

A.19 B.17 C.21 D.14

Q7

If \(\alpha,\beta\) and \(\gamma\) are the zeros of \(x^3+px^2+qx+r\), then \(\sum\frac{1}{\alpha}\) is :

A.\(\frac{q}{r}\) B.\(-\frac{q}{r}\) C.\(-\frac{q}{p}\) D.\(-\frac{p}{r}\)

Q8

If \((1+i)(1+2i)(1+3i)\cdots(1+ni)=x+iy\) then the value \(2\cdot5\cdot10\cdots(1+n^2)\) is :

A.\(x^2+y^2\) B.1 C.\(1+n^2\) D.\(i\)

Q9

The minimum value of the function \(|3-x|+9\) is :

A.6 B.0 C.9 D.3

Q10

The value of \(\sum_{n=1}^{12} i^n\) is :

A.0 B.1 C.-1 D.\(i\)

Q11

If the vectors \(2\hat{i}-\hat{j}+3\hat{k},\ 3\hat{i}+2\hat{j}+\hat{k},\ \hat{i}+m\hat{j}+4\hat{k}\) are coplanar, then the value of m is :

A.2 B.3 C.-2 D.-3

Q12

The general equation of a circle with centre \((-3,-4)\) and radius 3 units is :

A.\(x^2+y^2-6x+8y-16=0\) B.\(x^2+y^2-6x-8y+16=0\) C.\(x^2+y^2+6x-8y+16=0\) D.\(x^2+y^2+6x+8y+16=0\)

Q13

The solution of \(\frac{dy}{dx}+p(x)y=0\) is :

A.\(x=ce^{-\int p\,dy}\) B.\(y=ce^{\int p\,dx}\) C.\(x=ce^{\int p\,dy}\) D.\(y=ce^{-\int p\,dx}\)

Q14

The value of \(\int_0^\infty e^{-3x}x^2\,dx\) is :

A.\(\frac{4}{27}\) B.\(\frac{7}{27}\) C.\(\frac{2}{27}\) D.\(\frac{5}{27}\)

Q15

The point of inflection of the curve \(y=(x-1)^3\) is :

A.\((1,0)\) B.\((0,0)\) C.\((1,1)\) D.\((0,1)\)

Q16

The angle between the lines \(\frac{x-4}{2}=\frac{y}{1}=\frac{z+1}{-2}\) and \(\frac{x-1}{4}=\frac{y+1}{-4}=\frac{z-2}{2}\) is :

A.\(\frac{\pi}{2}\) B.\(\frac{\pi}{4}\) C.\(\frac{2\pi}{3}\) D.\(\frac{\pi}{3}\)

Q17

Which one of the following is a binary operation on N ?

A.Multiplication B.Division C.Subtraction D.All the above

Q18

Which one of the following is incorrect ?

A.If A is a square matrix of order n, and \(\lambda\) is a scalar, then \(\text{Adj}(\lambda A)=\lambda^n(\text{Adj}\,A)\). B.Adjoint of a symmetric matrix is also a symmetric matrix. C.\(A(\text{Adj}\,A)=(\text{Adj}\,A)A=|A|I\). D.Adjoint of a diagonal matrix is also a diagonal matrix.

Q19

If \(\sin x\) is the integrating factor of the linear differential equation \(\frac{dy}{dx}+Py=Q\), then P is :

A.\(\tan x\) B.\(\log\sin x\) C.\(\cot x\) D.\(\cos x\)

Q20

The length of the latus rectum of the parabola \(x^2=24y\) is :

A.8 B.24 C.6 D.12

12th Standard Mathematics May 2022: Online Practice Test

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