List of top Mathematics Questions

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. ?
 

For a scalar function \(\vec{F}(x, y, z) = x^2 + 3y^2 + 2z^2\), the directional derivative at the point P( 1, 2, -1) is the direction of a vector \((\hat{i} + \hat{j} + 2\hat{k})\) is
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:
If \( (b - c)\cos \frac{A}{2} = k \sin \frac{B - C}{2} \), then \( \frac{k}{\sin A} = \) :
If \(P(A)=\frac{3}{8}\), \(P(\overline{A}\mid B)=\frac{3}{5}\), \(P(\overline{B}\mid A)=\frac{3}{5}\), then \(P(A \cap B) + P(B)=\) :

If \(S = \{(x,y)\;|\; x = 2\cos t + 3\sin t,\; y = 3\cos t + 2\sin t,\; t \in \mathbb{R}\}\), then the points of \(S\) lie on the curve: 

\([y]\) represents the greatest integer less than or equal to \(y\) and \(\{y\}\) represents the fractional part of \(y\). If \[ \lim_{x \to 0^{+}} \left( [1-x] + \frac{a^{2[1-x] + \{1-x\} - 1}}{2[1-x] + \{1-x\}^{2}} \right) = 11, \] then \(a =\) ?

If \[ y=(e^{2x}-4)(6e^{2x}-5e^{x}+1), \] then \[ \left(\frac{dy}{dx}\right)_{x=0} - \left(\frac{d^{2}y}{dx^{2}}\right)_{x=0} = \ ? \]