List of top Mathematics Questions

If \[ \begin{vmatrix} 0 & 3 & 2b \\ 2 & 0 & 1 \\ 4 & -1 & 6 \end{vmatrix} \] is singular, then the value of \(b\) is

The value of \( x \) satisfying the relation \( 11\binom{x}{3} = 24\binom{x+1}{2} \) is

The number of 5-digit numbers (no digit is repeated) that can be formed by using the digits \(0,1,2,\ldots,7\) is

If \( a, b, c \) are in A.P. and their squares in same order form a G.P., then \( (a+c)^4 = \)

If the roots of the equation \( (x-a)(x-b) + (x-b)(x-c) + (x-c)(x-a) = 0 \) are equal, then \( a^2 + b^2 + c^2 = \)

If one root of a quadratic equation is \( \frac{1}{1+\sqrt{3}} \), then the quadratic equation is

Let \( S(n) \) denote the sum of the digits of a positive integer \(n\). Then the value of \( S(1)+S(2)+\cdots+S(99) \) is

An A.P. consists of 23 terms. If the sum of the 3 terms in the middle is 141 and the sum of the last 3 terms is 261, then the first term is

The 5th and 8th terms of a G.P. are 1458 and 54 respectively. The common ratio of the G.P. is

If 4th term of a G.P. is 32 whose common ratio is half of the first term, then the 15th term is

If the difference between the roots of \( x^2 + 2px + q = 0 \) is two times the difference between the roots of \( x^2 + qx + \frac{p}{4} = 0 \), where \( p \neq q \), then

Sum of the roots of the equation \( |x-3|^2 + |x-3| - 2 = 0 \) is equal to

The quadratic equation whose roots are three times the roots of the equation \( 2x^2 + 3x + 5 = 0 \), is

If \(x\) is real number, then \( \frac{x}{x^2 - 5x + 9} \) must lie between

If \( z = 1 + i \), then the argument of \( z^2 e^{z-i} \) is

If \( \mathrm{Re}(1+iy)^3 = -26 \), where \(y\) is a real number, then the value of \( |y| \) is

If \( z = x + iy \) is a complex number such that \( |z| = \mathrm{Re}(z) + 1 \), then the locus of \(z\) is

Let \( i^2 = -1 \). Then \( \left(i^{10} - \frac{1}{i^{11}}\right) + \left(i^{11} - \frac{1}{i^{12}}\right) + \left(i^{12} - \frac{1}{i^{13}}\right) + \left(i^{13} - \frac{1}{i^{14}}\right) + \left(i^{14} + \frac{1}{i^{15}}\right) \) is equal to

The set \( (A \setminus B) \cup (B \setminus A) \) is equal to

In a class of 80 students numbered 1 to 80, all odd numbered students opt for Cricket, students divisible by 5 opt for Football, and those divisible by 7 opt for Hockey. The number of students who do not opt any of the three games is

Let the six numbers \( a_1, a_2, a_3, a_4, a_5, a_6 \) be in A.P., and \( a_1 + a_3 = 10 \). If the mean of these six numbers is \( \frac{19}{2} \) and their variance is \( \sigma^2 \), then \( 8\sigma^2 \) is equal to:

Let \( X \) and \( Y \) be two non-empty sets such that \( X \cap A = Y \cap A = \emptyset \) and \( X \cup A = Y \cup A \) for some non-empty set \( A \). Then

If \( f(1)=1 \), \( f(2n)=f(n) \) and \( f(2n+1)=(f(n))^2 - 2 \) for \( n=1,2,3,\ldots \), then the value of \( f(1)+f(2)+\cdots+f(25) \) is equal to

The sum of coefficients of integral powers of $x$ in the binomial expansion $(1-2\sqrt x)^{50}$ is

If the mean and the variance of a binomial variate $X$ are $2$ and $1$ respectively, then the probability that $X$ takes a value greater than or equal to one is :