List of top Questions asked in MHT CET

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

A water tank in the house of an inverted cone is being emptied at the rate of \(2\) cubic feet per second. The height of the cone is \(8\) feet and the radius is \(4\) feet, then the rate of change of the water level when the depth is \(6\) feet.

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 \(A=\begin{bmatrix} 2 & 1 \\ 3 & 2 \end{bmatrix}\) 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......

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

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

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

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...

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

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

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

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 \(\frac{k}{5}=\cdots \cdots \cdots\)

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

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

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

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

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 ______

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

Which of the following medicinal plants is used to extract antimocrobial substance for cold?