Mathematics 2024 Question Paper Online Test (12th Standard)

Q1

The area between \(y^2=4x\) and its latus rectum is :

A.\(\frac{8}{3}\) B.\(\frac{2}{3}\) C.\(\frac{5}{3}\) D.\(\frac{4}{3}\)

Q2

The value of \(\int_0^a \left(\sqrt{a^2-x^2}\right)^3 dx\) is :

A.\(\frac{3\pi a^2}{8}\) B.\(\frac{\pi a^3}{16}\) C.\(\frac{3\pi a^4}{8}\) D.\(\frac{3\pi a^4}{16}\)

Q3

If \(P(x, y)\) be any point on \(16x^2+25y^2=400\) with foci \(F_1(3, 0)\) and \(F_2(-3, 0)\), then \(PF_1+PF_2\) is :

A.10 B.8 C.12 D.6

Q4

If \(|z_1|=1, |z_2|=2, |z_3|=3\) and \(|9z_1z_2+4z_1z_3+z_2z_3|=12\) then the value of \(|z_1+z_2+z_3|\) is :

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

Q5

The number of rows in the truth table of \((p\vee q)\wedge(p\vee r)\) is :

A.6 B.9 C.3 D.8

Q6

If a vector \(\vec{\alpha}\) lies in the plane of \(\vec{\beta}\) and \(\vec{\gamma}\), then :

A.\([\vec{\alpha},\vec{\beta},\vec{\gamma}]=0\) B.\([\vec{\alpha},\vec{\beta},\vec{\gamma}]=1\) C.\([\vec{\alpha},\vec{\beta},\vec{\gamma}]=2\) D.\([\vec{\alpha},\vec{\beta},\vec{\gamma}]=-1\)

Q7

The differential equation of the family of curves \(y=Ae^x+Be^{-x}\), where A and B are arbitrary constants is :

A.\(\frac{dy}{dx}+y=0\) B.\(\frac{d^2y}{dx^2}+y=0\) C.\(\frac{dy}{dx}-y=0\) D.\(\frac{d^2y}{dx^2}-y=0\)

Q8

The horizontal asymptote of \(f(x)=\frac{1}{x}\) is :

A.\(x=c\) B.\(y=0\) C.\(y=c\) D.\(x=0\)

Q9

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

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

Q10

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

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

Q11

The number given by the Rolle's theorem for the function \(x^3-3x^2, x\in[0, 3]\) is :

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

Q12

The type of conic section for \(x^2-3=5x+3y\) is :

A.hyperbola B.ellipse C.circle D.parabola

Q13

If A is a non-singular matrix such that \(A^{-1}=\begin{bmatrix}5 & 3\\ -2 & -1\end{bmatrix}\), then \((A^T)^{-1}=\)

A.\(\begin{bmatrix}-1 & -3\\ 2 & 5\end{bmatrix}\) B.\(\begin{bmatrix}-5 & 3\\ 2 & 1\end{bmatrix}\) C.\(\begin{bmatrix}5 & -2\\ 3 & -1\end{bmatrix}\) D.\(\begin{bmatrix}5 & 3\\ -2 & -1\end{bmatrix}\)

Q14

The angle between the line \(\vec{r}=(\vec{i}+2\vec{j}-3\vec{k})+t(2\vec{i}+\vec{j}-2\vec{k})\) and the plane \(\vec{r}\cdot(\vec{i}+\vec{j})+4=0\) is :

A.\(45^\circ\) B.\(0^\circ\) C.\(90^\circ\) D.\(30^\circ\)

Q15

If \(\sin^{-1}x+\cot^{-1}\left(\frac{1}{2}\right)=\frac{\pi}{2}\), then x is equal to :

A.\(\frac{2}{\sqrt{5}}\) B.\(\frac{1}{2}\) C.\(\frac{\sqrt{3}}{2}\) D.\(\frac{1}{\sqrt{5}}\)

Q16

If \(\alpha, \beta\) and \(\gamma\) are 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.\(-\frac{p}{r}\)

Q17

The value of Var(3) is :

A.0 B.3 C.Var(3) D.9

Q18

The random variable X has binomial distribution with n = 25 and p = 0.8 then standard deviation of X is :

A.3 B.6 C.2 D.4

Q19

If A, B and C are invertible matrices of some order, then which one of the following is not true ?

A.\(\det A^{-1}=(\det A)^{-1}\) B.\(\text{adj } A=|A|A^{-1}\) C.\((ABC)^{-1}=C^{-1}B^{-1}A^{-1}\) D.\(\text{adj }(AB)=(\text{adj } A)(\text{adj } B)\)

Q20

A zero of \(x^3+64\) is :

A.\(4i\) B.0 C.−4 D.4

12th Standard Mathematics March 2024: Online Practice Test

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