List of top Mathematics Questions asked in MHT CET

If \(\int \sin ^{3}x\cdot \cos ^{3}xdx=\frac{1}{32}\left[\frac{3}{2}f(x)+\frac{1}{6}g(x)\right]+C\), then \(f(x)\) and \(g(x)\) are respectively...

If Rolle's theorem holds for the function \(f(x)=x^{3}+px^{2}+qx+5,x\in [1,3]\) with \(c=2+\frac{1}{\sqrt{3}}\), then the values of \(p\) and \(q\) are respectively...

If the matrix \(A=\begin{bmatrix} 3 & -5 \\ 4 & -7 \end{bmatrix}\) and \(A^{-1}=\begin{bmatrix} 7 & -5 \\ 4 & a \end{bmatrix}\), then the value of \(a\) is...

If \(f(x)=\begin{vmatrix} x^{2} & \sin x & e^{x} \\ 2 & 1 & -1 \\ p & p^{2} & 1 \end{vmatrix}\) then \(f^{''}(0)=\)

If \(f(x)=\begin{cases} \frac{\tan x-\cot x}{x-\frac{\pi }{4}}, & x\neq \frac{\pi }{4} \\ a, & x=\frac{\pi }{4} \end{cases}\), then the value of \({}'a'\) so that \(f(x)\) is continuous at \(x=\pi /4\) is...

The second derivative of \(a\sin ^{3}t\) with respect to \(a\cos ^{3}t\) at \(t=\frac{\pi }{4}\) is...

If \(y=\left(\sqrt{x}+\frac{1}{\sqrt{x}}\right)^{2}\) and \(\frac{dy}{dx}=\frac{3}{4}\), then the value of \(x\) is...

If \(\frac{d}{dx}\left(\frac{1+x^{4}+x^{8}}{1+x^{2}+x^{4}}\right)=ax^{3}+bx\), then the values of \(a\) and \(b\) are respectively...

If \(\cot ^{-1}2\) and \(\cot ^{-1}3\) are the angles of a triangle, then the third angle is ...

If \(A=\begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1 \end{bmatrix}\) and \(A^{-1}=xA+yI\), then the values of \(x\) and \(y\) are...

Consider the function: \(f(x)=\begin{cases} x^{2}+1 & \text{if }x\lt 2 \\ 5 & \text{if }x=2 \\ 3x-1 & \text{if }x>2 \end{cases}\)
Which of the following statements is correct ?

The inverse of a statement \((p\vee q)\rightarrow r\) is

The negation of the statement "She will earn money if she works" is...

The switching circuit for the logical expression \((p\wedge q)\vee \sim (p\wedge q)\) is simplified and found to be equivalent to a circuit with:

How many different five digit numbers which are divisible by \(4\) can be formed using the digits in the number \(22457\) ?

The equation \(16x^{2}-3y^{2}-32x+12y-44=0\) represents a hyperbola whose...

The modulus and argument of \((1+i\sqrt{3})^{8}\) are respectively...

The length of the tangent segment drawn from point \(P\) to the circle, \(x^{2}+y^{2}-2x-2y-2=0\) is \(4\sqrt{2}\) units. If \(\lambda _{max}\) and \(\lambda _{min}\) are the maximum and minimum distances of point \(P\) from the circle, then \(\lambda _{max}+\lambda _{min}\) is equal to....

The product of the lengths of the perpendiculars drawn from the point \((3,4)\) to the lines represented by \(3x^{2}-5xy+2y^{2}=0\) is...

If \((2,8)\) is one vertex and \(x-y+3=0\) is one diagonal of a square, then the equation of the other diagonal is

If \(\sin x,1,\,\cos 2x\) are in G.P., then the general solution for \(x\) is ...

In \(\triangle ABC\), if \(l(AB)=8,l(BC)=5,l(AC)=7\), then \(\cot \frac{A}{2}+\cot \frac{B}{2}+\cot \frac{C}{2}\) is equal to......

If \(f(x)=\sin x+\cos x\), then which of the following is true?

If \(\sin ^{4}\theta +\cos ^{4}\theta =\frac{5}{8},0\lt \theta \lt \frac{\pi }{2}\), then \(\sin 2\theta =...\)

Given \(\log _{10}2=0.3010\). Then the number of digits in the number \(20^{10}\) is...