List of top Mathematics Questions

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

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 \(f(x) = x^2\) 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 \(sin^{-1}(tan\frac{π}{4})-sin^{-1}(\sqrt{\frac{3}{x}}) = \frac{π}{6}\) then \(x\) is a root of the equation

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 \(cot\frac{A}{2}:cot\frac{B}{2}:cot\frac{C}{2} =\)

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 ...

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 \(\text{adj}(A) = \ldots\) ..

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 ...

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 ...

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

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 value of \(cos(\frac{π}{5})\) is ...

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

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 ....

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 ....

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 .....

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 ...

The maximum value of \(z = 4x+y\) subject to the constraints \(x+y\leq 5,2x+y\leq 7,3x+2y\leq 11,x\geq 0,y\geq 0\) is \(\ldots\)

In an entrance test, there are multiple choice questions. There are four possible answers to each question, only one of which is correct. The probability that a student knows the answer to a question is 90%. If he gets the correct answer to a question, then the probability that he was guessing is

A fair die is thrown 4 times. If getting a prime number on the die is considered as a success, then the probability of getting no success at all is \(\ldots\)

If the p. d. f. of a continuous random variable X is given by \(f(x) = \{\begin{array}{cc}k(9+8x-x^2), & \text{for }-1\leq x\leq 4 \\ 0, & \text{otherwise}\end{array}\) then the value of \(k\) is \(\ldots\)