List of top Mathematics Questions

The set of all \(x\) satisfying the inequality \(8 + 3x > 4(x - 3) + 2\) is

\(\sin 15^\circ \sin 45^\circ \sin 75^\circ =\)

The value of \(\sin(x + \frac{7\pi}{4}) + \sin(x - \frac{7\pi}{4})\) is equal to

If \(\sin \theta = \frac{3}{5}\) and \(\cos \theta < 0\), then the value of \(\tan \theta\) is

Let \(A\) and \(B\) be two square matrices each of order 3. If \(|AB| = 21\) and \(|A^{-1}| = -7\), then the value of \(|B|\) is equal to

If the homogeneous system of simultaneous equations \(AX=0\) where \(A = \begin{bmatrix} 9 & 2 & k \\ 1 & -1 & -3 \\ k-1 & 1 & 3 \end{bmatrix}\) has a nontrivial solution, then the possible values of \(k\) are

If \(^n P_5 = 360360\), then \(^n C_5 = \)

If the coefficient of \(x^4\) in the binomial expansion of \((4x + a)^7\) is -1120, then the value of \(a\) is equal to

Let \(A = \begin{bmatrix} 3 & 5\\ -2 & -3 \end{bmatrix}\). If \(BA^2 = A\), where \(B\) is a \(2 \times 2\) matrix, then \(B = \)

In a business meeting, each person shakes hands with each other person once. A person arrives after 5 people have left and he shakes hands only with those present. If the total number of handshakes is exactly 100, then the initial number of people in the party, is

The number of 3-digit numbers greater than 500, that can be formed using the digits 3, 4, 5, and 7, with repetition, is

If \(k\), 6 and \(k+5\) are the first three terms of a geometric series, then the possible values of the common ratio are

The first and the twentieth terms of a G.P. are 512 and \(\frac{1}{1024}\) respectively. Then the common ratio is

Let \(z = \frac{a - \frac{i}{2}}{i - 2}\), where \(a\) is a real number and \(i = \sqrt{-1}\). If \(\text{Im}(z) = 0\), then the value of \(a\) is equal to

In a complex plane, if two vertices of an equilateral triangle are at \(-3(1+i)\) and \(3(1-i)\), then the area of the triangle (in sq.units) is equal to

If \(z |z| = 24 + 7i\), where \(z\) is a complex number, then the value of \(|z|\) is equal to

A geometric series has common ratio \(\frac{1}{3}\). If the sum of first four terms is 200, then the first term is

The sum of the second and third terms of a G.P. is 8 and the fourth term is 4. The common ratio \(r \neq 1\) is

Let A and B denote the sets of students in a school who play cricket and football respectively. If \(n(A) = 45, n(B) = 35\) and \(n(A \cap B) = 13\), then \(n((A \cap B)' \cap (A \cup B))\) =

Let \(f : [-\frac{\pi}{2}, \frac{\pi}{2}] \rightarrow (-\infty, \infty)\) be given by \(f(x) = \tan(x)\sin(x)\). Then \(f(x)\) is

Find the total area of the region bounded between the curve \( y = x^3 \), the x-axis, and the vertical lines \( x = -1 \) and \( x = 1 \).

The integral of \(f(x)=1+x^2+x^4\) with respect to \(x^2\) is

A bag contains 6 blue and 6 green balls. Pairs of balls are drawn without replacement until the bag is empty. The probability that each drawn pair consists of one blue ball and one green ball is:

Consider the following statements:
Statement I : If $A$ is a non-singular matrix, then $A^{-1}$ exists.
Statement II : If $A$ and $B$ are symmetric matrices of same order, then $(AB - BA)$ is a skew symmetric matrix.
Choose the correct option.

In Linear Programming Problem (LPP), the objective function $Z = ax + by$ has the same maximum value at two corner points. The number of points at which $Z_{max}$ occurs is