List of top Mathematics Questions asked in MHT CET

If \(\int f(x)\,dx = g(x)\) then \(\int x^3f(x^2)\,dx\) is equal to

The equation of the tangent to the curve \(y = \sqrt{9-3x^2}\) at the point where the ordinate and abscissa equal is...

If \(\int \frac{sinx}{sin4x}\,dx = αlog\frac{1+sinx}{1-sinx}+βlog\frac{1+\sqrt{2}sinx}{1-\sqrt{2}sinx}+c\), then the value of \(32(α+β^2) =\)

If the line \(y = 4x-5\) is tangent to the curve \(y^2 = ax^3+b\) at the point \((2,3)\), then the value of \(7a-2b\) is...

If \(\int \frac{3x+7}{x^2-3x+2}\,dx = mlog(\frac{x-2}{x-1})+nlog(x-2)+c\), where \(m,n\in R\) and \(c\) is an integration constant, then \(m+n =\)

The derivative of \(tan^{-1}(\frac{\sqrt{1+x^2}-1}{x})\) with respect to \(tan^{-1}(\frac{x}{\sqrt{1-x^2}})\) at \(x = \frac{1}{2}\) is

If \(y = \frac{1}{3x+5}\), then the value of \(\frac{d^9y}{dx^9}\) is..

If \(f(x) = cot^{-1}(\frac{3x-x^3}{1-3x^2})\) and \(g(x) = cos^{-1}(\frac{1-x^2}{1+x^2})\), then \(\underset{x\rightarrow a}{lim}\frac{f(x)-f(a)}{g(x)-g(a)}\), \((0 < a < \frac{1}{2})\) is

If \(f(x) = cosx\,cos2x\,cos4x\,cos8x\,cos16x\), then \(f^'(\frac{π}{4}) =\)

If \(y = \sqrt{cosx^2+\sqrt{cosx^2+\sqrt{cosx^2+\ldots \infty }}}\) and \(\frac{dy}{dx} = \frac{f(x)}{2y-1}\) then, \(\int f(x)\,dx = \ldots\)

If the function \(f(x) = \frac{4\sqrt{2}(sin3x+sinx)}{2sin2xsin\frac{3x}{2}+cos\frac{5x}{2}-cos\frac{3x}{2}}\) for \(x\neq \frac{π}{2}\) is continuous at \(x = \frac{π}{2}\), then the value of \(f(\frac{π}{2})\) is equal to

\(sin(3sin^{-1}(\frac{1}{5})) =\)

\(cos^{-1}(cos\frac{4π}{3})+sin^{-1}(sin\frac{4π}{3}) = \ldots\)

If \(A = \left[ \begin{array}{ccc}3 & 0 & 0 \\ 0 & -5 & 0 \\ 0 & 0 & 7\end{array} \right]\); \(B = \left[ \begin{array}{ccc}-1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4\end{array} \right]\) then, \((2A+3B)^{-1} =\) _______

If \(sin^{-1}(x-2)+cos^{-1}(x)+tan^{-1}(x+2)+cot^{-1}(x+4) = sec^{-1}(\sqrt{k})-\frac{π}{2}\), then \(cos(2\,\text{cosec}^{-1}\sqrt{k-1}) = \ldots\)

If \(f(x) = \frac{1-x}{1+x}\), then \(f(f(cosx)) =\)

The statement pattern \([(p∧q)\rightarrow (\sim p∨r)]∨[(\sim p∨r)\rightarrow (p∧q)]\) is

In \(△ABC\), with usual notation, if cot A, cot B, cot C are in arithmetic progression, then

If \(A = \left[ \begin{array}{cc}1 & -tan\frac{θ}{2} \\ tan\frac{θ}{2} & 1\end{array} \right]\) and \(B = \left[ \begin{array}{cc}1 & tan\frac{θ}{2} \\ -tan\frac{θ}{2} & 1\end{array} \right]\) then \(A^{-1}B\) is equal to

Which of the following statements is/are False?
\(S_1:\exists \,n\in N\), such that \(n^2+n+2\) is divisible by 4.
\(S_2:\exists \,x\in N\), such that \(x-17 < 20\).
\(S_3:\forall \,n\in N,\,x^2+3x-10 = 0\).
\(S_4:\forall \,n\in N,\,n^2\geq 1\).

The negation of \((p∧q)\rightarrow ((p∨r)\rightarrow \,\sim q)\) is equivalent to ...

If the line \(3x+4y+k = 0\) touches the ellipse \(9x^2+16y^2 = 144\), then the value of k is.

If the circles \(x^2+y^2 = 16\) and \(x^2+y^2+2ax+4y+4 = 0\) touch each other internally then \(a =\)

The line \(y = 2x+c\) passes through a point that is equidistant from both the axes and lies in the first quadrant \((x > 0,y > 0)\). Then the value of c is...

\(\frac{(cos2θ+isin2θ)^7}{(cos4θ+isin4θ)^3} =\)