List of top Questions asked in MHT CET

\(\int \frac{5x^{12}+6x^{11}}{(x^{6}+x+1)^{3}}dx=\)
If \(f(x)=\sqrt{1+\cos ^{2}(x^{2})}\), then \(f'\left(\frac{\sqrt{\pi }}{2}\right)=\ldots\)
If \(f(x)=\begin{cases} \frac{x-e^{x}+\cos 2x}{x^{2}}, & \text{if }x\neq 0 \\ k, & \text{if }x=0 \end{cases}\) is continuous at \(x=0\), then the value of \(k\) is...
The maximum volume (in cubic units) of a right circular cylinder for which the sum of the square of its height and the square of its radius of base \(48\), is
If \(f(x)=\log \left(\frac{1+x}{1-x}\right)\) and \(g(x)=\left(\frac{3x+x^{3}}{1+3x^{2}}\right)\), then \(\frac{d}{dx}(f(g(x)))=\)
If \(x=\frac{1-\sqrt{y}}{1+\sqrt{y}}\), then \(\frac{dy}{dx}=\)
If \(\sqrt{1-x^{6}}+\sqrt{1-y^{6}}=a^{3}(x^{3}-y^{3})\), then \(\frac{dy}{dx}=\ldots\)
\(\sin ^{-1}(\cos (\sin ^{-1}x))+\cos ^{-1}(\sin (\cos ^{-1}x))=\ldots\)
If \(a\) and \(b\) are respectively the minimum and maximum values of the expression \(f(x)=(\sin ^{-1}x+2\cos ^{-1}x)\), then \(a+b\) is equal to...
The sum of the matrix \(\begin{bmatrix} 2 & -3 \\ 5 & -7 \end{bmatrix}\) and its multiplicative inverse is
The value of \(\cot \left(\operatorname{cosec}^{-1}\frac{5}{3}+\tan ^{-1}\frac{2}{3}\right)\) is ...
If \(A+I=\begin{pmatrix} 3 & -2 \\ 1 & -1 \end{pmatrix}\), then the inverse of the matrix \((A-I)\) is:
If \(\tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\left(\frac{1}{5}\right)+\tan ^{-1}\left(\frac{1}{7}\right)=\frac{\pi }{4}-\tan ^{-1}\left(\frac{1}{k}\right)\) then the value of \(k\) is
If \(\sin ^{-1}x+\sin ^{-1}y+\sin ^{-1}z=\pi\), then \(x^{4}+y^{4}+z^{4}+4x^{2}y^{2}z^{2}=\)
The value of \(\lim _{x\rightarrow \frac{\pi }{4}}\left[\frac{4-(\cos x+\sin x)^{4}}{1-\sin 2x}\right]\) is equal to
The statement pattern \([p\wedge (q\vee r)]\vee [\sim r\wedge \sim q\wedge p]\) is equivalent to _____
The equation of the common tangent to the parabolas \(y^{2}=4x\) and \(x^{2}=32y\) is ...
The point on the ellipse \(\frac{x^{2}}{25}+\frac{y^{2}}{9}=1\) which is equidistant from its foci can be
Consider the following statements -
(i) If a person is social, then he is happy.
(ii) If a person is not social, then he is not happy.
(iii) If a person is not happy, then he is not social.
(iv) If a person is happy, then he is social.
Which of the above statements are equivalent?
The negation of the statement \((p\wedge \sim q)\rightarrow (\sim p\vee r)\) is equivalent to:
If the slopes of the lines given by \(ax^{2}+2hxy+by^{2}=0\) are in the ratio \(2:3\), then \(h^{2}=\)
If \(|z-5i|=|z+3|\), where \(z\) is a complex number, then the equation of the locus of \(z\) in Cartesian coordinates is ...
The domain of the function \(f(x)=\frac{1}{\sqrt{|x|-x}}\) is
The equation of the line \(\sqrt{3}x-y+4=0\) in the normal form is _____
The maximum number of points of intersection between \(4\) circles and \(4\) straight lines is: