List of top Mathematics Questions

The area of the smaller region bounded by the circle \(x^2+y^2 = 4\) and the line \(x = 1\) is...

The value of the integral \(\int _{-π/2}^{π/2}(\frac{x^2cosx}{1+e^x})dx\) is equal to \((\frac{π^2}{A})-B\). Then \((\frac{A}{B}) =\)

If an antiderivative of \(f(x)\) is \(e^x\) and an antiderivative of \(g(x)\) is \(cosx\), then \(\int f(x)cosx\,dx+\int g(x)e^x\,dx =\)

If the area bounded by the curve \(x^2 = by\) and the lines \(y = 1,y = 4\) in the first quadrant is \(28\) sq. units, then the value of b is...

\(\int _0^{log10}[\frac{e^x\sqrt{e^x-1}}{e^x+8}]dx =\)

If the function \(f(x) = ax^3-bx^2-8x-4\) satisfies Roll's theorem in \([1,3]\), if \(f^'(2) = 0\) then \(a-b\) is equal to...

If \(\int \frac{1}{cos^3x\sqrt{sin2x}}\,dx = p(tan^2x+q)\sqrt{tanx}+c\), then the values of \(p\) and \(q\) respectively are

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

Let \(f(x) = 3x^3+4e^{\frac{x}{2}}\) and \(g(x) = f^{-1}(x)\). Then the value of \(g^'(4)\) is equal to...

The co-ordinates of the point on the curve \(y = xlogx\) at which the normal is parallel to the line \(2x-2y = 3\) are...

If \(\int \sqrt{2}\sqrt{1+sinx}\,dx = -4cos(ax+b)+c\), then the value of \(a,b\) respectively are...

If the function f is continuous at \(x = 1\), where \(f(x) = \frac{1+cos(πx)}{π(1-x)^2}\), for \(x\neq 1\), then the value of \(f(1)\) is....

If \(f(x-y)+f(x+y) = 2f(x)f(y)\) for all \(x,y\in R\), then \(f(x)\) is .....

If \(y = logx^x\), then the value of \((\frac{dy}{dx})^2\) at \(x = e^2\) is

If \(y = cos^{-1}(sinx)\), where \(\frac{π}{2} < x < π\), then \(\frac{dy}{dx} = ...\)

If \(tan^{-1}[\frac{\sqrt{5-2\sqrt{6}}}{1+\sqrt{6}}] = \frac{π}{3}-tan^{-1}(k)\), then \(sec^{-1}(k) = ...\)

If \(y = (\frac{ax+b}{cx+d})\), then \(2\frac{dy}{dx}\cdot \frac{d^3y}{dx^3}\) is equal to

If \(A = [\begin{array}{cc}cosθ & -sinθ \\ sinθ & cosθ\end{array}]\), then the matrix \(A^{-3}\) when \(θ = \frac{π}{6}\) is equal to...

Let \(A = \left[ \begin{array}{ccc}2k-1 & 1 & 1 \\ 0 & 2k-1 & 1 \\ 0 & 0 & 2k-1\end{array} \right]\) and \(B = \left[ \begin{array}{ccc}0 & 2k-1 & 1 \\ 1-2k & 0 & k \\ -1 & -k & 0\end{array} \right]\) where k is a real number. If \(det(\text{adj}A)+det(\text{adj}B) = 11^6\), then the value of \(k-5\) is equal to...

In \(△ABC\) with usual notations, if \(1+tan(\frac{A}{2})tan(\frac{B}{2}) = \frac{k}{s}\) (where \(s\) is the semi-perimeter), then the value of \(k\) is...

The dual of the converse of the inverse of the logical statement \(p\rightarrow (q\rightarrow r)\) is equivalent to...

If \(\underset{x\rightarrow 0}{lim}\frac{(4^x-1)^3}{tan(\frac{x}{4})log(1+\frac{x^2}{3})} = 96(loga)^b\), then \((a+b) =\)

The statements p, q and r have truth values True, False and False respectively. The truth values of a logical statement \([\sim (p∧\sim q)∨(q∨\sim r)]\) and its dual are, respectively.....

If a triangle \(ABC\) has vertices \(A(1,-6),B(2,-3)\) and \(C(3,-2)\), then the coordinates of its orthocenter are....

The triangle formed by the lines \(2x^2-3xy-2y^2 = 0\) and \(3x-y = 7\) is...