List of top Questions asked in MHT CET

A man of height \(1.2\) m is moving away from the lamp post at the rate \(0.6\) m/sec. If the height of the lamp post is \(4.8\) m, then the rate at which the shadow of the man is lengthening is:

\(\int \frac{2x}{4-3x-x^{2}}\ dx=\ldots\)

The approximate surface area of a sphere of radius \(2.01\) cm is

If \(\begin{bmatrix} 1 & 1 & 1 \\ 2 & -1 & 7 \\ 3 & 1 & 2 \end{bmatrix}\begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} 1 \\ 7 \\ 2 \end{bmatrix}\) then \(\begin{bmatrix} x \\ y \\ z \end{bmatrix}=\)

If \(\cos ^{-1}x+\cos ^{-1}y+\cos ^{-1}z=3\pi\), then \(xy+yz+zx\) is equal to

If \(A=\begin{bmatrix} 1 & -1 & 1 \\ 0 & 2 & -3 \\ 2 & 1 & 0 \end{bmatrix}\), \(B=\text{adj}\ A\) and \(C=5A\), then the value of \(\frac{|\text{adj}\ B|}{|C|}\) is:

Let \(f(x)=\frac{12^{x}-4^{x}-3^{x}+1}{1-\cos 2x}\), for \(x\neq 0\). If \(f(x)\) is continuous at \(x=0\) and \(f(0)=\frac{(\log a)\cdot (\log 3)}{4k}\), then the value of \(a\) in terms of \(k\) is:

If \(f(x)=\sin (\tan ^{-1}x)\), then \(\int _{0}^{1}xf^{''}(x)dx\) is:

If \(\sin ^{-1}\left(\frac{y}{2}\right)=\tan ^{-1}\left(\frac{x}{2}\right),\ |y|\lt 2\), such that \(\frac{dx}{dy}=k(4+x^{2})\), then \(k=\ldots\)

If \(\tan ^{-1}\left[\frac{\sqrt{5+2\sqrt{6}}}{1-\sqrt{6}}\right]=a+\tan ^{-1}(\sqrt{2})\), then \(\csc (a)=\ldots\)

The solutions of the equation \(\sin [2\cos ^{-1}\{\cot (2\tan ^{-1}x)\}]=0\) are

The logical expression \([\sim (p\rightarrow q)\wedge (q\rightarrow p)]\vee \sim (p\leftrightarrow q)\) is equivalent to:

If \(p\rightarrow (\sim p\vee q)\) is false, then the truth values of \(p,q\) are:

Let \(p\): switch \(S_{1}\) is closed, \(q\): switch \(S_{2}\) is closed.
Then, the equivalent symbolic form for the following circuit is:

One of the tangents at the end of the latus rectum of the parabola \(y^{2}=12x\) is

\(\lim _{h\rightarrow 0}\frac{\log _{e}(1+2h)-2\log _{e}(1+h)}{h^{2}}\)

The sum of the ordinates of the points on the line \(4x+3y=10\) whose distance from the line \(x+y-4=0\) is \(\sqrt{2}\) is equal to ...

The tangent to the parabola \(x^{2}=2y\) at point P makes an angle of \(45^{\circ }\) with the X-axis, then the coordinates of P are:

The equation of a circle whose center is at \((3,-4)\) and the line \(12x-5y-17=0\) cuts the circle at \(A\) and \(B\), where \(l(AB)=6\) is ...

How many numbers (without repetition) between \(400\) and \(1000\) can be made with the digits \(2,3,4,5,6,\) and \(0\)?

If the equation \(mx^{2}-y^{2}+2y+n=3\) represents a pair of perpendicular lines, then the values of \(m\) and \(n\) respectively are...

Find monomers of PHBV.

Which of the following elements is not present in salvarsan?

In \(\triangle ABC\), if \(b=\sqrt{3}+1\), \(c=\sqrt{3}-1\) and \(A=\frac{\pi }{3}\), then \(B-C=\ldots\)

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