List of top Mathematics Questions

If a real valued function \(f:A\rightarrow B\) defined by \[ f(x)=\sin^{-1}\!\left(\sqrt{x^{2}-4x+5}\right) \] is a bijection, then \(A\cup B=\)
If \(a\) is a real root of the equation \[ x^{3}-2x^{2}-2x-3=0 \] and \[ A= \begin{bmatrix} 1& 2& a\\ 2& a& 1\\ a& 1& 2 \end{bmatrix}, \] then \(A^{2}-A=\)
Consider the following Assertion (A): \[ 5^{2n}-3^{2n-1} \] is divisible by 2 for all \(n\in\mathbb N\). Reason (R): \[ 5^{2n}+3^{2n-1} \] is divisible by 7 for all \(n\in\mathbb N\).
If the statement \( (p \land q) \rightarrow (r \lor \neg s) \) is False (F), what are the truth values of \(p, q, r,\) and \(s\) respectively?
LCM of the numbers 12 and 20 will be :
If $P = \begin{pmatrix} 1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{pmatrix}$ is the adjoint of a $3 \times 3$ matrix A and $det(A) = 4$, then $\alpha =$
Let \( A = \begin{bmatrix} 1 & 2 2 & 1 \end{bmatrix} \) and \( B = \begin{bmatrix} x & y 1 & 2 \end{bmatrix} \) be two matrices such that \( (A + B)(A - B) = A^2 - B^2 \).
If \( C = \begin{bmatrix} x & 2 1 & y \end{bmatrix} \), then trace \((C) = \)
An equilateral triangle OAB is inscribed in the parabola $y^2 = 4x$ with the vertex O at the vertex of the parabola. Then the minimum distance of the circle having AB as a diameter from the origin is
A square matrix P satisfies \(P^2 = I - P\). If \(P^n = 5I - 8P\) then n is equal to
Two numbers P and Q are selected from Set {1,2,3,.....,100\,then find the probability of P.Q is divisible by 5.}
The mean of some observations is 54. If each observation is increased by 8 and its sum is divided by 2, then what is the mean of the resulting observations?
If the sum of the first four terms of an A.P. is 6 and the sum of its first six terms is 4 , then the sum of its first twelve terms is
Out of 8 students in Section Alpha, 10 students in Section Beta and 12 students in Section Gamma, a teacher wants to create a team of three to represent the school in inter-school quiz competition. In how many ways the team can be formed such that all the members of the team are not from the same section ?
Let \(n(A) = m\) and \(n(B) = n\), if the number of subsets of A is 56 more than of subsets of B, then \(m + n\) is equal to

Which of the following sequence is \(\textit{not }\)an A.P. ?
 

In a class test, Veer scored 6 more than twice as many marks as Kevin scored. If one of them had scored 4 more marks, their total score would have been 40. Find the marks obtained by Veer and Kevin.
Aarush bought 2 pencils and 3 chocolates for Rs 11 and Tanish bought 1 pencil and 2 chocolates for Rs 7 from the same shop. Represent this situation in the form of a pair of linear equations. Find the price of 1 pencil and 1 chocolate, graphically.
How many elements of order 5 are there in a cyclic group of order 25?
What is the total number of terms in the expansion of \( (x+y)^{15} \)?
What is the value of \( ^nC_{n-1} \)?
What is the value of \( i^{4k+2} \) where \( k \) is an integer?
Let \([t]\) represent the greatest integer less than or equal to \(t\). If \[ x = (7\sqrt{5} + 15)^9 \quad \text{and} \quad y = (5\sqrt{7} + 13)^{11}, \] then \([x]\) and \([y]\) are:

If \(\alpha_n\) is the coefficient of \(x^n\) in the expansion of \((1-x)^{-5}\) and \(\beta_n\) is the coefficient of \(x^n\) in the expansion of \((1-x)^{-4}\), then \(\alpha_{12} + \beta_{13}\) is equal to: 

The number of values of \(\theta\) lying in \([0, 2\pi]\) for which \(\sin 3\theta\) attains its maximum when \[ \left|\sin\theta \cdot \sin\left(\frac{\pi}{3} - \theta\right)\cdot \sin\left(\frac{\pi}{3} + \theta\right)\right| \le \frac{1}{8} \] is: 

The number of real solutions of the equation \[ \sin^{-1}(2-x) - 2\sin^{-1}x = \pm \frac{\pi}{2} \] is: