List of top Mathematics Questions asked in MHT CET

The value of the integral \(\int _{1/e}^e\frac{|logx|}{x^2}dx\) is

\(\int \frac{1}{\sqrt{2x-x^2}}dx =\)

\(\int \frac{logx}{(1+logx)^2}dx =\)

\(\int (x^{21}+x^6+x^3)(2x^{18}+7x^3+14)^{\frac{1}{3}} dx =\)

If \(\int _{-π/2}^{π/2}(sin^2x+sin^3x)dx = k\), then the value of \(k\)

If \(\int f(x)dx = g(x)+c\) then \(\int f^{-1}(x)dx =\)

An aeroplane at an altitude of 1 km is flying horizontally at 600 km / hr, passes directly over an observer. Then the rate at which it is approaching the observer when it is 1250 meters away from him is........

The line \(x+y = 0\) touches the curve \(y^2 = ax^3+b\) at \((1,-1)\) then values of \(a\) and \(b\) respectively are ...........

The function \(f(x) = x(x+3)e^{-(\frac{1}{2})x}\) satisfies all the conditions of Rolle's theorem in \([-3,0]\), then \(c =\)

If \(f(x),g(x)\) be twice differentiable functions, satisfying \(f^{''}(x) = g^{''}(x),f^'(1) = 2g^'(1) = 4\) and \(f(2) = 3g(2) = 9\) then \(f(x)-g(x)\) at \(x = 4\) is equal to

If \(\sqrt{\frac{x}{y}}+\sqrt{\frac{y}{x}} = 6\), then \(\frac{dy}{dx} =\)

If \(x = asin^3t\) and \(y = acos^3t\), then the value of \(\frac{d^2y}{dx^2}\) at \(t = \frac{π}{3}\) is equal to

If \(x = 4t^3+3,y = 3t^4+4\) and \(\frac{\frac{d^2x}{dy^2}}{(\frac{dx}{dy})^n}\) is constant then the value of \(n\) is

If the function \(f(x)\) defined by \(f(x) = \{\begin{array}{cc}ax+1 & \text{if }x\leq 3 \\ bx+3 & \text{if }x > 3\end{array}\) is continuous at \(x = 3\), then \((a-b) =\) ..........

If \(f(x) = \frac{2x-1}{x+5}\), \(x\neq -5\) then \(f^{-1}(x)\) is equal to

Let \(A = \left[ \begin{array}{ccc}3 & 1 & 2 \\ 1 & 2 & 0 \\ 1 & 1 & 4\end{array} \right]\) and \(pC_{11}+4C_{21}-5C_{32} = -2\), where \(C_{ij}\) denotes the cofactor of an element \(a_{ij}\) of matrix \(A\), then the value of \(p\) is :

If \(3sin^{-1}(\frac{2x}{1+x^2})-4cos^{-1}(\frac{1-x^2}{1+x^2})+2tan^{-1}(\frac{2x}{1-x^2}) = \frac{π}{3}\) then \(x = ?\)

If \(2sin^{-1}x-3cos^{-1}x = 4\), then \(2sin^{-1}x+3cos^{-1}x =\)

The contrapositive of \(\sim q\rightarrow p\) is equivalent to

The value of \(\underset{n\rightarrow \infty }{lim}[\frac{1}{1-n^2}+\frac{2}{1-n^2}+\ldots +\frac{n}{1-n^2}]^3\) is

With the usual notations, if the lengths of the sides of the triangle are 3 units, 5 units and 7 units, then the largest angle of the triangle is

The angles of \(△ABC\) are in A.P. and \(b:c = \sqrt{3}:\sqrt{2}\) then \(\angle A =\)

If \(\sim p∨q\) is false then which of the following is correct?

If \(A = [\begin{array}{cc}1 & -5 \\ -2 & 4\end{array}]\), then \(A^{-1} =\)

If \(x+y = \frac{π}{4}\), then \((1+tanx)(1+tany) =\)