List of top Mathematics Questions

The derivative of \(log_{10}x\) with respect to \(log_x10\) is

The value of integral \(\int \frac{dx}{sin^2x+tan^2x}\) is...

If \(y = sin(2sin^{-1}x)\) then \(\frac{dy}{dx} =\)..

If \(sin^{-1}(tan\frac{π}{4})-sin^{-1}(\sqrt{\frac{3}{x}}) = \frac{π}{6}\) then \(x\) is a root of the equation

Let \(x = at^2-1\), where \(a > 0\) and \(y = t^3+1\). If at \(t = 1\), \(\frac{d^2y}{dx^2} = \frac{3}{16}\), then the value of \(a\) is...

If \(y = cot^{-1}(\frac{1+sin5x}{cos5x})\), then the value of \(\frac{dy}{dx}\) is

\(\sum _{k = 1}^{2026}sin^{-1}(cos\frac{kπ}{4}) =\)

If \(f(x) = x^2\) and \(g(x) = [x^2]\) where \([\cdot ]\) represents the greatest integer function then, \((f\circ g)(\frac{3}{2})+(g\circ f)(\frac{3}{2})\) is equal to ...

If \(A = [a_{ij}]_{3\times 3}\), where \(a_{ij} = \{\begin{array}{cc}1, & \text{if }i+j\text{ is even} \\ 0, & \text{if }i+j\text{ is odd}\end{array}\), then \(\text{adj}(A) = \ldots\) ..

Which of the following logical statements is a tautology?

The inverse of matrix \(\left[ \begin{array}{ccc}1+pq & p & 0 \\ q & 1+pq & p \\ 0 & q & 1\end{array} \right]\) is ...

The logical statement \((p∨q)∧[(\sim p∧q)∨(p∧\sim q)]∧\sim q\) is logically equivalent to ...

In \(△ABC\), with usual notations, if the sides \(a\), \(b\) and \(c\) are in the ratio \(18:17:7\), then \(cot\frac{A}{2}:cot\frac{B}{2}:cot\frac{C}{2} =\)

If the function \(f(x) = \frac{2\sqrt{2}-(cosx+sinx)^3}{1-sin2x}\) is continuous at \(x = \frac{π}{4}\), then the value of \(f(\frac{π}{4})\) is ...

The value of \(\underset{x\rightarrow 0}{lim}(\frac{8}{x^8})[1-cos\frac{x^2}{2}-cos\frac{x^2}{4}+cos\frac{x^2}{2}\cdot cos\frac{x^2}{4}]\) is equal to ...

The simplified switching circuit for the following circuit is

A tangent having slope \(-\frac{1}{2}\) to the ellipse \(3x^2+4y^2 = 12\) intersects the X-axis and Y-axis at the points A and B respectively. if O is the origin, then the area of \(△AOB\) is ...

If the combined equation of angle bisectors of the lines \(x^2-2pxy-y^2 = 0\) is \(x^2-2qxy-y^2 = 0\), then which of the following is true?

The smallest positive integer \(n\) for which \(\frac{(1+i)^n}{(1-i)^{n-2}}\) is a real number, is ...

Let \(x\in [0,6π]\) satisfy the equation \(cosx-sinx = -1\). If \(x = k(\frac{π}{3})\) where \(k\in N\), then find the number of possible values of \(k\) is .....

A straight line L passes through the point of intersection of the lines \(x-y+1 = 0\) and \(2x+y-7 = 0\). If L intersects the positive x-axis at \(A(a,0)\) and the positive y-axis at \(B(0,b)\), then the minimum area of the triangle \(OAB\) (where \(O\) is the origin) is ....

The value of \(cos(\frac{π}{5})\) is ...

Four men and three women are to be arranged at a round table. The number of arrangements in which no two women are together is ....

A line making equal intercepts on coordinate axes and is tangent to the circle \(x^2+y^2 = 4\). The length of each intercept made by line on the coordinate axes is ...

Let \(a\) be an integer selected at random from the set \(\{0,1,2,3,\ldots ,9\}\). The probability that the equation \(ax^2-ax+1 = 0\) has real roots is ...