List of top Mathematics Questions asked in MHT CET

If \(x^{y}\cdot y^{x}=1\) then the value of \(\frac{dy}{dx}\) is

The approximate value of \(\sin ^{-1}(0.51)\) is .......
[Given \(\pi =3.1416\), \(\frac{2}{\sqrt{3}}=1.1547\)]

If matrix \(\begin{pmatrix} x & 1 & 2 \\ 2 & 4 & x \\ -3 & 3 & 2 \end{pmatrix}\) is non-invertible matrix and distinct values of \(x\) are \(a\) and \(b\) then \(9(a^{2}+b^{2})=\cdots \cdots \cdots\)

Let \(y=\frac{1}{3x-5}\) and if \(\frac{d^{4}y}{dx^{4}}=1944\), then the value of \(x\) is

If \(y=\sin (2\sin ^{-1}x)\), then \(\frac{dy}{dx}=\) ______

If \(y=2^{x}+(\sin x)^{x}\), then \(\frac{dy}{dx}=\)

Let \(A=\begin{bmatrix} 2 & 1 \\ 3 & 2 \end{bmatrix}\) and \(B=\begin{bmatrix} -1 & -1 \\ 1 & 1 \end{bmatrix}\). If the variables \(x\) and \(y\) satisfy the matrix equation \((A^{-1}+B)\begin{bmatrix} x \\ y \end{bmatrix}=\begin{bmatrix} 0 \\ -2 \end{bmatrix}\), then the value of \(x+3y\) is......

The compound statement \([\sim (p\rightarrow q)\vee \sim (p\wedge r)]\wedge p\) is logically equivalent to:

The negation of the contrapositive of the statement \((p\vee q)\rightarrow r\) is logically equivalent to..

The dual of the statement pattern \((p\wedge q)\wedge \sim (p\vee q)\) is a:

If the tangent to the circle \(x^{2}+y^{2}=5\) at point \((1,-2)\) also touches the circle \(x^{2}+y^{2}-8x+6y+k=0\), then \(\frac{k}{5}=\cdots \cdots \cdots\)

The equation of the hyperbola formed by the locus of the point of intersection of the lines \(\sqrt{5}x-y-2\sqrt{5}\mu =0\), and \(\sqrt{5}\mu x+\mu y-2\sqrt{5}=0\), where \(\mu\) is a variable parameter, is...

\(\lim _{x\rightarrow 0}\frac{1-\cos (1-\cos x)}{x^{4}}=\)

The polar coordinates of point \(P\) are \(\left(\sqrt{2},\frac{\pi }{4}\right)\). If \(Q\) is the image of \(P\) about \(y\) axis, then the polar coordinates of \(Q\) are ______

If two lines represented by the equation \(x^{2}+bcy^{2}=(b+c)xy\) are coincident, then ____

The coordinates of the foot of the perpendicular from the point \((2,3)\) on the line \(y=3x+4\) is given by ...

The sum of the greatest values of \({}^{15}C_{r}\) and \({}^{12}C_{r}\) is equal to

If \(z_{1}=3\cdot e^{\frac{5\pi }{12}i}\) and \(z_{2}=4\cdot e^{\frac{\pi }{12}i}\) then \(z_{1}\cdot z_{2}=\cdots \cdots\)

The points on the line \(x+y-4=0\) which are at one unit distance from the line \(4x+3y-10=0\) are...

If \(f(x)=\sin ^{-1}\left[\log _{1/2}\left(\frac{x^{2}}{2}\right)\right]\), then the domain of the function \(f(x)\) is:

The value of expression \(\tan 9^{\circ }-\tan 27^{\circ }-\tan 63^{\circ }+\tan 81^{\circ }\) is....

In \(\triangle ABC\), with usual notations, the value of \(\text{cosec}\left(\frac{A}{2}\right)\text{cosec}\left(\frac{B}{2}\right)\text{cosec}\left(\frac{C}{2}\right)\) is:

If in a triangle \(ABC\), \(\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}\) and the side \(a=2\), then the area of the triangle is:

The general solution of the equation \(2\sin ^{2}x+\sin ^{2}2x=2\) is \(x=(2n+1)\alpha\) or \(x=m\pi \pm \beta\), \(m,n\in \mathbb{Z}\), then \(\alpha\) and \(\beta\) are the roots of the quadratic equation _______

If \(f(x)=\frac{1}{\sqrt{x}},g(x)=3-2x-x^{2}\) then \(\int [(f\circ g)(e^{x})]\cdot e^{x}dx=\cdots \cdots \cdots\)