List of top Questions asked in MHT CET

For \(x\neq 0\), the value of \(I=\int \frac{x^{2}-1}{(x^{4}+3x^{2}+1)\tan ^{-1}\left(x+\frac{1}{x}\right)}dx\) is ...

For which of the following functions is Rolle's theorem not applicable?

If \(I_{1}=\int \frac{e^{x}}{e^{2x}+e^{x}+1}dx\) and \(I_{2}=\int \frac{1}{e^{-2x}+e^{-x}+1}dx\), then \(I_{1}-I_{2}=\)

If \(y=(x-1)(x-2)(x-3)\cdots (x-100)\) and the value of \(\frac{dy}{dx}\) at \(x=5\) is equal to \(\lambda \left(\frac{100!}{{}^{100}C_{5}}\right)\), then \(\lambda =\) ...

Let \(f(x)\) be a function defined by \(f(x)=\begin{cases} \int _{0}^{x}(|t-2|+3)dt, & x>4 \\ 2x+8, & x\leq 4 \end{cases}\) then \(f(x)\) is ...

Let \(A\) be an invertible matrix. Identify the correct statement(s) from the following.
(I) \(A(\text{adj }A^{-1})=\frac{1}{|A|}A^{2}\) (II) \((\text{adj }A^{-1})^{-1}=\frac{1}{|A|}A^{-1}\) (III) \((\text{adj }A)=\frac{1}{|A|}A^{-1}\)

If \(A=\begin{bmatrix} \sin \alpha & -\cos \alpha \\ \cos \alpha & \sin \alpha \end{bmatrix}\) and \(S=\left\{\alpha :\alpha \in \left(\frac{\pi }{2},\frac{3\pi }{2}\right),A+A^{-1}=I\right\}\), then \(\alpha =\) ...

If the truth values of \(p,q,r,s\) are respectively \(T,F,F,T\) then the truth values of the compound statements \(\sim (p\rightarrow \sim q)\) and \((\sim r\wedge s)\rightarrow (p\wedge \sim q)\) are respectively ... and .....

If \(x=at^{2}\) and \(y=2at,t\neq 0\) then ...

\(\lim _{x\rightarrow 1}\left[\frac{2^{2x-2}-2^{x}+1}{\sin ^{2}(x-1)}\right]=\)

The area of the triangle formed by the vertex and the endpoints of the latus rectum of the parabola \(x^{2}=-18y\) is ...

If the sum of the slopes of the line represented by \(x^{2}+kxy-3y^{2}=0\) is twice their product, then the acute angle between the lines \(x^{2}+kxy\cos ec\alpha +y^{2}=0\) is ...

The standard parametric equations of the circle \(x^{2}+y^{2}-4x-6y-12=0\) are ...

Symbolic form of the circuit

is equivalent to .........

The dual statement of "\(x=1\) only if \(x^{2}=x\)" is

In \(\Delta ABC\), with usual notations, if \(1-\tan \frac{A}{2}\cdot \tan \frac{C}{2}=\frac{b}{k}\), then \(k=\) ...

In \(\Delta ABC\), with usual notations, if \(\sin B-\cos C=\cos A\), then

The coordinates of the foot of the perpendicular from the point \((2,3)\) on the line \(x+y-11=0\) are ...

If \(\frac{(n+3)!}{(n^{2}-4)(n+1)!}=\frac{11}{6}\), for \(n\in N,n\neq 2\), then the value of \(3n-20\) is equal to ...

A line passes through the points \(O(0,0),A(3,3)\). Then the polar coordinates of point A are ...

If \(n\in Z\), then the expression \(\frac{2^{n}}{(1-i)^{2n}}+\frac{(1+i)^{2n}}{2^{n}}\) is equal to ...

The Range of the function \(y=\log (\sin x)\), defined for all \(x\) such that \(\sin x>0\) is ...

If \(\tan \theta +\tan 2\theta +\tan 3\theta =\tan \theta \tan 2\theta \tan 3\theta\), then the most general value of \(\theta\) for which all terms in the equation are defined is ...

If \(\sin x\cos x=\frac{1}{4}\), then the general solution of the equation is ...