Mathematics 2025 Question Paper Online Test (12th Standard)

Q1

Subtraction is not a binary operation in :

A.\(\mathbb{N}\) B.\(\mathbb{R}\) C.\(\mathbb{Q}\) D.\(\mathbb{Z}\)

Q2

Suppose that X takes on one of the values 0, 1 and 2. If for some constant k, \(P(X=i)=k\,P(X=i-1)\) for \(i=1, 2\) and \(P(X=0)=\frac{1}{7}\), then the value of k is :

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

Q3

If A is a non-singular matrix of order \(3\times 3\) and \(|A|=5\) then \(|A^{-1}|\) is :

A.\(5^2\) B.5 C.\(\frac{1}{5^2}\) D.\(\frac{1}{5}\)

Q4

A stone is thrown up vertically. The height it reaches at time t seconds is given by \(x=80t-16t^2\). The stone reaches the maximum height in time t seconds is given by :

A.3 B.2 C.3.5 D.2.5

Q5

The order and degree of the differential equation \(\sqrt{\frac{dy}{dx}}-4\frac{dy}{dx}-7x=0\) are respectively :

A.1, 2 B.2, 1 C.2, 2 D.1, 1

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

The slope at any point of a curve \(y=f(x)\) is given by \(\frac{dy}{dx}=3x^2\) and it passes through \((-1, 1)\). Then the equation of the curve is :

A.\(y=3x^3+4\) B.\(y=x^3+2\) C.\(y=x^3+5\) D.\(y=3x^2+4\)

Q8

The domain of the function defined by \(f(x)=\sin^{-1}\sqrt{x-1}\) is :

A.\([0, 1]\) B.\([1, 2]\) C.\([-1, 0]\) D.\([-1, 1]\)

Q9

If \(u(x, y)=e^{x^2+y^2}\), then \(\frac{\partial u}{\partial x}\) is equal to :

A.\(x^2u\) B.\(e^{x^2+y^2}\) C.\(y^2u\) D.\(2xu\)

Q10

The number of real numbers in \([0, 2\pi]\) satisfying \(\sin^4x-2\sin^2x+1\) is :

A.1 B.2 C.\(\infty\) D.4

Q11

The square root of i are :

A.\(\pm\frac{1}{2}(1+i)\) B.\(\pm\frac{1}{\sqrt{2}}(1+i)\) C.\(\pm\frac{1}{2}(1-i)\) D.\(\pm\frac{1}{\sqrt{2}}(1-i)\)

Q12

The value of \(\sum_{n=1}^{13}(i^n+i^{n-1})\) is :

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

Q13

If in 6 trials, X is a binomial variable which follows the relation \(9P(X=4)=P(X=2)\), then the probability of success is :

A.0.375 B.0.125 C.0.75 D.0.25

Q14

The angle between the lines \(\frac{x-2}{3}=\frac{y+1}{-2}, z=2\) and \(\frac{x-1}{1}=\frac{2y+3}{3}=\frac{z+5}{2}\) is :

A.\(\frac{\pi}{3}\) B.\(\frac{\pi}{6}\) C.\(\frac{\pi}{2}\) D.\(\frac{\pi}{4}\)

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 value of \(\int_0^{\frac{2}{3}}\frac{dx}{\sqrt{4-9x^2}}\) is :

A.\(\frac{\pi}{4}\) B.\(\frac{\pi}{6}\) C.\(\pi\) D.\(\frac{\pi}{2}\)

Q17

The volume of solid of revolution of the region bounded by \(y^2=x(a-x)\) about x-axis is :

A.\(\frac{\pi a^3}{5}\) B.\(\pi a^3\) C.\(\frac{\pi a^3}{6}\) D.\(\frac{\pi a^3}{4}\)

Q18

An ellipse has OB as semi minor axes, F and F' its foci and the angle FBF' is a right angle. Then the eccentricity of the ellipse is :

A.\(\frac{1}{4}\) B.\(\frac{1}{\sqrt{2}}\) C.\(\frac{1}{\sqrt{3}}\) D.\(\frac{1}{2}\)

Q19

The volume of the parallelepiped with its edges represented by the vectors \(\hat{i}+\hat{j}, \hat{i}+2\hat{j}, \hat{i}+\hat{j}+\pi\hat{k}\) is :

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

Q20

If \(f(x)>0\) for all x and \(g(x)=\log(f(x))\), then dg is :

A.\(\frac{1}{f(x)}\,dx\) B.\(\frac{1}{f(x)}f'(x)\,dx\) C.\(\frac{1}{x}\,dx\) D.\(\frac{1}{x}f(x)\,dx\)

12th Standard Mathematics March 2025: Online Practice Test

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