List of top Questions asked in MHT CET

The radius of a spherical soap bubble is increasing at a constant rate of \(0.5\) cm/sec. At the instant when the radius is \(5\) cm, the rate at which its volume is increasing is...

Let \(f(x)\) be the cubic polynomial having one of its roots as \(x=-1\). If \(f(0)=4,f'(0)=0,f^{''}(1)=0\), then...

If \(f(x)=2^{2x-1}\) and \(\phi (x)=-2^{x}+x\log 4\), such that \(f'(x)>\phi '(x)\), then the set of all possible values of \(x\) is...

If \(\sqrt{1-x^{6}}+\sqrt{1-y^{6}}=a^{3}(x^{3}-y^{3})\), then \(\frac{dy}{dx}=\) ...

If \(y=x-e^{x}\), then \(\frac{d^{2}x}{dy^{2}}=\) ...

Let \(A^{T}=\begin{bmatrix} 1 & 1 & 2 \\ 1 & -1 & 1 \\ 1 & 2 & -1 \end{bmatrix}\), \(B^{T}=[\begin{matrix} 6 & 5 & 1 \end{matrix}]\) and \(X=\begin{bmatrix} x \\ y \\ z \end{bmatrix}\). If \(AX=B\), then the values of \(x,y,z\) are..........

If \(A=\begin{bmatrix} 1 & 3 \\ 2 & 1 \end{bmatrix}\), then the determinant of \((A^{2}-2A)^{-1}\) is...

If \(\sin ^{-1}\left(\frac{x}{5}\right)+\csc ^{-1}\left(\frac{5}{4}\right)=\frac{\pi }{2}\), then the value of \(x\) is

If the statement pattern \((p\vee \sim q)\wedge (\sim p\vee q)\) is true, then which of the following is true?

Consider the following statements:
(i) \(\sim (p\wedge \sim q)\)
(ii) \((p\rightarrow q)\leftrightarrow (\sim q\rightarrow \sim p)\)
Result 1 : (i) and (ii) are logically equivalent
Result 2 : (ii) is a contradiction
then which of the following is correct?

The number of points of discontinuity of the function \(f(x)=\frac{1}{\log |x^{2}-1|}\) (where \(|\cdot |\) denotes the modulus function) is:

In an ellipse with semi-minor axis OB, S and S' are its foci, \(a>b\) and \(\angle SBS'\) is a right angle, then the eccentricity of the ellipse is..

The Cartesian coordinates of a point P with parameter \(\theta =\frac{5\pi }{6}\) on the circle \(x^{2}+y^{2}-2x+4y+1=0\) are...

The equation of a circle passing through the foci of the ellipse \(\frac{x^{2}}{25}+\frac{y^{2}}{16}=1\) and having a center at \((0,-4)\) is :

The dual of the statement pattern \(\sim p\rightarrow \sim (\sim p\rightarrow q)\) is...

If the equation \(x^{2}-y^{2}-x+\lambda y-2=0\) (where \(\lambda >0\)) represents a pair of lines, then the coordinates of their point of intersection are:

The value of \(\lim _{x\rightarrow \infty }\left(\sqrt[3]{x^{3}+6x^{2}+1}-x\right)\) is:

In \(\triangle ABC\) with usual notations, if \(a,c,b\) are in Arithmetic Progression (A.P.), then the value of \(\frac{a\cos B-b\cos A}{a-b}\) is:

A straight line passes through the point \((3,3)\) and intersects the positive \(x\) and \(y\) axes at the points \(A(h,0)\) and \(B(0,k)\) respectively. If O is the origin, then the minimum area of \(\triangle OAB\) is:

A teacher has 2 different books on English, 3 different books on physics, and 4 different books on mathematics. These books are to be placed on the shelf so that all books of the same subjects are together. The number of different ways this can be done is:

The minimum value of \(e^{2x}+e^{-2x}\) is .......

If \(z=\frac{\sqrt{3}+i}{2}\), then the value of \(z^{69}\) is

With usual notations, if the perimeter of a triangle is \(2s\), then its maximum area is:

If \(f(x)=\frac{2}{x+5}\) and \(g(x)=x^{2}-1\), then the positive value of \(x\) satisfying \((f\circ g)(x)=\frac{1}{10}\) is

If \(\frac{\cos A+\sin A}{\cos A-\sin A}=\cot (2A)\), where \(A\in \left(0,\frac{\pi }{2}\right)-\left\{\frac{\pi }{4}\right\}\), then the value of \(A\) (in degrees) is...