List of top Mathematics Questions asked in MHT CET

If \(y=\cos ^{-1}x\), then \(\frac{d^{2}y}{dx^{2}}=\)
If \(f(x)=\begin{vmatrix} \sin x+\sin 2x+\sin 3x & \sin 2x & \sin 3x \\ 3+4\,\sin x & 3 & 4\,\sin x \\ 1+\sin x & \sin x & 1 \end{vmatrix}\), then \(\int _{0}^{\frac{\pi }{2}}f(x)dx=\)
If \(x=\frac{e^{m}+e^{-m}}{2}\) and \(y=\frac{e^{m}-e^{-m}}{2}\) then \(\frac{dy}{dx}=\)
If \(y=4^{\log _{4}(x+2)-\log _{4}(x-2)}\), then \(\frac{dy}{dx}=\)
If \(y=x^{\sqrt{x}}\), then \(\frac{dy}{dx}=\)
The value of \(c\) for which the function \(f(x)=\log \left(\frac{x^{2}+6}{5x}\right)\) satisfies Rolle's theorem in the interval \([2,3]\) is ____
If \(p\wedge q\) is F and \(p\rightarrow q\) is F, then the truth values of \(p\) and \(q\) respectively are
\(2\sin ^{-1}\left(\frac{3}{5}\right)+\tan ^{-1}\left(\frac{1}{5}\right)+\tan ^{-1}\left(\frac{1}{7}\right)=\)
If \(\sin ^{-1}(1-x)-2\sin ^{-1}x=\frac{\pi }{2}\), then the value of \(x\) is
The truth values of logical statements \(p,q,r\) are T, T and F respectively. If \(\*\) and \(\#\) are symbolic logical connectives such that \((p\#r)\rightarrow (\sim q\#r)\) is false and \((\sim p\* q)\leftrightarrow (\sim q\#r)\) is true, then \(\*\) and \(\#\) are respectively ____
If \(A=\begin{bmatrix} 4 & 5 \\ 2 & 1 \end{bmatrix}\), then \(A^{-1}=\)
If \(A^{-1}=\begin{bmatrix} 3 & -1 & 1 \\ -15 & 6 & -5 \\ 5 & -2 & 2 \end{bmatrix}\) and \(B=\begin{bmatrix} 1 & 2 & -2 \\ -1 & 3 & 0 \\ 0 & -2 & 1 \end{bmatrix}\), then \((AB)^{-1}=\)
A statement logically equivalent to the statement pattern \(\sim [(p\rightarrow \sim q)\wedge (\sim q\vee p)]\) is
The joint equation of pair of lines passing through origin and perpendicular to the lines given by \(3x^{2}+4xy-5y^{2}=0\) is
If \(f(x)=\frac{ax-3}{5x+7}\) and \(\lim _{x\rightarrow 0}f(x)\cdot \lim _{x\rightarrow \infty }f(x)=3\) then \(a=\ldots\)
The equation of a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length \(3a\) is
If the line \(12x-5y+k=0\) is tangent to the hyperbola \(x^{2}-4y^{2}=100\), then \(k=\)
If the function \(f(x)\) is defined as below
\(f(x)=\begin{cases} \frac{(3^{x}+3^{-x}-2)\log (1+4x)}{(1-\cos 4x)\tan (2x)}, & x\neq 0 \\ \frac{(\log p)^{r}}{q}, & x=0 \end{cases}\)
is continuous at \(x=0\) then \(p+q-r=\ldots\)
If \(x=\frac{25}{3-4i}\) then \(2x^{3}-11x^{2}+44x+27=\)
\(\cos (4A)=\)
In a polygon, the number of diagonals is \(54\). Then the number of sides of the polygon is
The general solution of the equation \(\tan x+\sec x=2\,\cos x\) is
In \(\Delta ABC\) with the usual notations, angles \(A,B,C\) of are in A.P. and \(b:c=\sqrt{3}:\sqrt{2}\). The ratio of the largest and the smallest angle of the triangle will be
If \(P(a,b)\) is the midpoint of a line segment intercepted between the coordinate axes, then the equation of the line is
If \([\cdot ]\) represents the greatest integer function of less than or equal to type then the solution set of the equation \([x]^{2}-5[x]+6=0\) is