List of top Mathematics Questions

There are rooms numbered from 1 to 99 in an apartment. A mathematician notices that the sum of all room numbers before his room is equal to the sum of all room numbers after his room. Find his room number.
Number of all possible ways of distributing eight identical apples among three persons is

In a group of 50 family members, three medicines are given to fight a virus.
• 40 members received medicine A 
• 30 received medicine B 
• 20 received medicine C 
• 10 received all three medicines How many members received at least two medicines?

When \(|x|<1/2\), the coefficient of \(x^6\) in the expansion of \((\frac{2-x^2}{1+2x})^6\) is
If A and B are skew-symmetric matrices, then which one of the following is NOT true?
Let \( A = \{1, 2, 3, 4\} \) and \( B = \{1, 4, 9, 16\} \). Then the number of many-one functions \( f: A \to B \) such that \( 1 \in f(A) \) is equal to:
$(\sqrt{3}+i)^{10} + (\sqrt{3}-i)^{10} =$
In a triangle with one of the angles \( 120^\circ \), the lengths of the sides form an A.P. If the length of the greatest side is 7 m, then the area of the triangle is
If A and B are independent events such that \( P(A \cap B') = \frac{3}{25} \) and \( P(A' \cap B) = \frac{8}{25} \), then \( P(A) = \)}
If \( \bar{a} = \frac{1}{\sqrt{10}}(3\hat{i} + \hat{k}) \) and \( \bar{b} = \frac{1}{7}(2\hat{i} + 3\hat{j} - 6\hat{k}) \), then the value of \( (2\bar{a} - \bar{b}) \cdot ((\bar{a} \times \bar{b}) \times (\bar{a} + 2\bar{b})) = \)}
If \( ^{15}C_4 + ^{15}C_5 + ^{16}C_6 + ^{17}C_7 + ^{18}C_8 = ^{19}C_r \), then the value of \( r \) is equal to}
The difference between the maximum value and minimum value of objective function \( z = 3x + 5y \) subject to \( x + 3y \le 60, x + y \ge 10, x - y \ge 0, x, y \ge 0 \) is
If \( x = e^{\tan^{-1} \left( \frac{y-x^2}{x^2} \right)} \), then \( \frac{dy}{dx} \) at \( x = 1 \) is
The combined equation of the tangent and normal to the curve \( xy = 15 \) at the point (5, 3) is
If \( f(x) = 3x^3 + 2x^2 f'(1) + x f''(2) + f'''(3) \) then \( f(x) = ....... \)}
The rates of change of the perimeter and area of a rectangle respectively when length $x=5$ cm and breadth $y=2$ cm, if $dx/dt = -5$ cm/min and $dy/dt = 3$ cm/min, are
The angle between the line \( x = \frac{y-1}{2} = \frac{z-3}{\lambda} \) and the plane \( x + 2y + 3z = 6 \) is \( \cos^{-1} \sqrt{\frac{5}{14}} \), then the value of \( \lambda \) is
If \( x = \sin \theta, y = \sin^3 \theta \), then \( \frac{d^2y}{dx^2} \) at \( \theta = \frac{\pi}{6} \) is
The sum of two nonzero numbers is 4. The minimum value of the sum of their reciprocals is
\( \int \frac{x}{1+x^4} dx = \)}
Let the plane passing through point (2, 1, -1) containing line joining the points (1, 3, 2) and (1, 2, 1) makes intercepts \( p, q, r \) on co-ordinate axes, then \( p + q + r = \)}
If the line \( ax + by + c = 0 \) is normal to the curve \( xy = 1 \), then}
If \( 0 \le \cos^{-1} x \le \pi \) and \( -\frac{\pi}{2} \le \sin^{-1} x \le \frac{\pi}{2} \), then at \( x = \frac{1}{5} \) the value of \( \cos(2 \cos^{-1} x + \sin^{-1} x) \) is
In a triangle ABC with usual notations if \( b \sin C (b \cos C + c \cos B) = 42 \), then area of triangle ABC =}
\( \int \sqrt{x^2 + 3x} dx = \)}