List of practice Questions

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

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

If \(^n P_5 = 360360\), 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 \(A\) 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

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

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

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

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

When was the first Jute Mill established in India?

Which of the following is NOT a Kharif crop?

What is the main problem in the present industrialization of India?

Which transportation mode reduces trans-shipment losses and delays?

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 numbers \(17.0145\) and \(21.0235\) were rounded to three figures after the decimal point. The resulting numbers, respectively, are

Which of the following is a benefit of Free and Open Source Software (FOSS)?