List of top Questions asked in MHT CET

The coordinates of the point on the curve \(y=\sin \left(\frac{\pi x}{2}\right)\) at which the normal is parallel to the Y- axis are:

If \(A^{-1}=\begin{bmatrix} 1 & 0 & -4 \\ 0 & -1 & 2 \\ -1 & 2 & 1 \end{bmatrix}=\frac{\text{adj}(A)}{k}\), then \(k\) is a root of the equation...

If \(A=\begin{bmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & a & 1 \end{bmatrix}\) and \(A^{-1}=\begin{bmatrix} \frac{1}{2} & -\frac{1}{2} & \frac{1}{2} \\ -4 & 3 & c \\ \frac{5}{2} & -\frac{3}{2} & \frac{1}{2} \end{bmatrix}\), then ...

If the planes \(ax=y+z\), \(by=z+x\), \(cz=x+y\) pass through a common line, then the value of \((a+b+c-abc)=\cdots\)

If \(x\in [0,1)\) then the value of \(\tan \left\{\frac{1}{2}\sin ^{-1}\left(\frac{2x}{1+x^{2}}\right)+\frac{1}{2}\cos ^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right)\right\}\) is:

If \(f'\left(\frac{1}{2}\right)=\sqrt{3}\) and \(g'\left(\frac{\sqrt{3}}{2}\right)=-2\), then the derivative of \(f(\sin x)\) with respect to \(g(\cos x)\) at \(x=\frac{\pi }{6}\) is:

If \(y=\tan ^{-1}\left(\frac{2x^{5/2}}{1-x^{5}}\right)\), then \(\frac{dy}{dx}\) is equal to ....

If the compound statement \((p\wedge \sim q)\rightarrow (q\vee \sim r)\) is false then which of the following statements is a true ?

If \(k>5\) and \(\lim _{x\rightarrow 0}\frac{k^{2x}+25^{x}-2\cdot (5k)^{x}}{\tan 3x\cdot \ln (1+3x)}=\lim _{n\rightarrow \infty }\frac{(n+1)!+n!}{(n+1)!-n!}\), then value of \(k\) is...

Let \(f(x)\) be a function continuous at \(x=0\), defined for \(x\neq 0\) as \(f(x)=\frac{1-\cos (1-\cos (6x))}{x^{2}\sin ^{2}(3x)}\). Then the value of \(f(0)\) is...

Let \(A=\{1,2,3,\ldots ,10\}\). Consider the following statements:
\(p:\forall x\in A,x^{2}-x>0\)
\(q:\exists x\in A\), such that \(x+10=20\)
Then the truth values of \(p\) and \(q\) are respectively ____

The statement \((p\wedge (\sim q))\vee ((\sim p)\wedge q)\vee ((\sim p)\wedge (\sim q))\) is equivalent to :

The equations of the lines passing through the center of circle \(x^{2}+y^{2}-4x-10y-7=0\) and intersecting the line \(3x-y-1=0\) at an angle \(\frac{\pi }{4}\) is...

The equation of the directrix of the parabola \(x^{2}-4x-5y-1=0\) is...

If \(\lim _{x\rightarrow 0}\left(\frac{f(x)}{x^{2}}\right)\) exists finitely and \(\lim _{x\rightarrow 0}\left(1+x+\frac{f(x)}{x}\right)^{1/x}=e^{3}\), then \(\int f(x)\cdot \log xdx\) is equal to:

The angle between the tangents drawn from the point \((1,1)\) to the circle \(2x^{2}+2y^{2}-8x+4y+5=0\) is …………

The coordinates of the point on the curve \(x^{2}+y^{2}=8\) which are nearest to the point \((2,0)\) are:

If \(\theta _{1}\) and \(\theta _{2}\) are the acute angles between the lines \(3x^{2}-7xy+4y^{2}=0\) and \(6x^{2}-5xy+y^{2}=0\) respectively, then ...

If all permutations of the letters of the word THREE are arranged as in dictionary, then \(47^{th}\) word is...

If \(x\in (0,2\pi )\) satisfies the equation \(\cos x+\sin x=\frac{1}{2}\), then the sum of all distinct values of \(\tan x\) is...

In a triangle, the lengths of the two largest sides are \(10\) cm. and \(9\) cm. If the angles of the triangle are in arithmatic progression (A. P.), then the length of the third side (in cm.) is...

In a triangular plot \(ABC\), the side lengths are \(BC=7m\), \(CA=8m\), and \(AB=9m\). A vertical lamp post is located at the midpoint \(E\) of side \(AC\). If the angle of elevation of the top of the lamp post from point \(B\) is \(\tan ^{-1}(4)\), then the height of the lamp post is...

If \(\omega\) is a complex cube root of unity, then the value of the expression \((1-\omega +\omega ^{2})^{7}+(1+\omega -\omega ^{2})^{7}\) is equal to...

Which of the following forms of proteins is used for transport of cholesterol in our body?

Which of the following is constituents of ribonucleoside ?