List of top Mathematics Questions asked in MHT CET

If \(\int x^2\cdot e^xdx = e^xf(x)+c\), then the minimum value of \(f(x)\) is ...

If Rolle's theorem is applicable for the function \(f(x) = log(\frac{x^2+a}{x})\) on \([3,4]\) with \(c\in (3,4)\) such that \(f^'(c) = 0\), then the value of \(f^{''}(c)\) is

Let \(f(x)\) be the differentiable function for all \(x\) such that \(f^'(x)\leq 5\) and \(f(1) = 4\). The maximum value of \(f(5)\) is...

If \(\sqrt{y+x}+\sqrt{y-x} = c\) such that \(\frac{dy}{dx} = f(x)-\sqrt{[f(x)]^2-1}\), then \(f(x) =\) ____

\(\frac{d}{dx}[sin^2\{cot^{-1}\sqrt{\frac{1-x}{1+x}}\}] =\) ...

If \(g(x)\) is the inverse function of \(f(x)\), where \(f(x) = \frac{5x+3}{4x-1}\), then \(g(1) =\)

If \(f(x) = \sqrt{x^2+1},g(x) = \frac{x+1}{x^2+1},h(x) = 2x-3\), then \(f^'(h^'(g^'(x))) =\)

If \(f(x)\) is continuous at \(x = 0\), where \(f(x) = \frac{8^x-2^x}{k^x-1}\), for \(x\neq 0\) and \(f(0) = 2\), then the value of \(k\) is ...

The element in 1st row and 2nd column of the inverse of the matrix \(\left[ \begin{array}{ccc}1 & 3 & -2 \\ -3 & 0 & -5 \\ 2 & 5 & 0\end{array} \right]\) is ...

Let \(f(x) = (sin^{-1}x)^2+(cos^{-1}x)^2\) be a real-valued function defined on its domain. Then the sum of the greatest and the least values of \(f(x)\) is

The value of \(\frac{tan^{-1}(1)+cos^{-1}(\frac{1}{2})+sin^{-1}(\frac{1}{2})}{tan^{-1}(\sqrt{3})-sec^{-1}(-2)}\) is equal to

If \(y = tan^{-1}(\frac{1}{x^2+x+1})+tan^{-1}(\frac{1}{x^2+3x+3})+tan^{-1}(\frac{1}{x^2+5x+7})+\ldots\) upto \(n\) terms, then \(y^'(0) =\)

If \(A = [\begin{array}{cc}secθ & -tanθ \\ -tanθ & secθ\end{array}]\), \(θ\in (0,\frac{π}{2})\) such that \(A+adj\,A = 4I\), then \(θ =\)

If the truth value of the compound statement
\([(p∨q)∧(q\rightarrow r)∧(\sim r)]\rightarrow (p∧q)\) is false, then the truth values of \(p\rightarrow q\) and \(q\rightarrow p\) are respectively...

The distance of the focus of the parabola \(y^2 = 16x\) from its directrix is...

Which of the following statements is logically equivalent to \(\sim (p\leftrightarrow q)\) ?

The value of \(\underset{n\rightarrow \infty }{lim}\frac{(n+2)!+(n+1)!}{(n+2)!-(n+1)!}\) is ____

The equation of the circle concentric with circle \(x^2+y^2-6x+7 = 0\) and which touches the line \(x+y+3 = 0\) is ....

The pair of straight lines represented by the equation \(\sqrt{3}x^2-4xy+\sqrt{3}y^2 = 0\) are

If the equation \(kx^2-5xy+6y^2+x-3y = 0\) represents a pair of straight lines, then the co-ordinates of their point of intersection are

If \(sin3α = 4sinα\cdot sin(x+α)\cdot sin(x-α)\) where \(α\neq nπ,n\in Z\), then all possible values of \(x\) are given as

The equation of the straight line passing through the point \((-5,3)\) such that the portion of the line intercepted between the axes is divided by the point in the ratio \(4:3\) (from the X-axis to the Y-axis) is...

The general solution of \(cosθ-sinθ = 1\) is

If \(cos(θ-α) = a\) and \(sin(θ-β) = b\), then the value of \(cos^2(α-β)+2absin(α-β)+cos^2(θ-α)\) is...

The quadratic polynomial \(p(x)\) has roots \(1\) and \(α\), while quadratic polynomial \(q(x)\) has roots \(1\) and \(β\). Let \(α\) and \(β\) be the roots of \(r(x) = p(x)+q(x)\). Then \(\underset{x\rightarrow \infty }{lim}[\sqrt{p(x)}-\sqrt{q(x)}] =\)