List of top Mathematics Questions

The maximum value of k for which the sum $\sum_{i=0}^k \binom{10}{i} \binom{15}{k-i} + \sum_{i=0}^{k+1} \binom{12}{i} \binom{13}{k+1-i}$ exists, is equal to __________.

If a + α = 1, b + β = 2 and a f(x) + α f(1/x) = b x + β / x, then [f(x) + f(1/x)] / [x + 1/x] is ________

If the shortest distance between x - λ = 2y - 1 = -2z and x = y + 2λ = z - λ is √7 / 2√2, then |λ| is _______

If $n \geq 2$ is a positive integer, then the sum of the series ${ }^{n+1} C_{2}+2\left({ }^{2} C_{2}+{ }^{3} C_{2}+{ }^{4} C_{2}+\ldots .+{ }^{n} C_{2}\right)$ is:

An electric instrument consists of two units. Each unit must function independently for the instrument to operate. The probability that the first unit functions is \(0.9\) and that of the second unit is \(0.8\). The instrument is switched on and it fails to operate. If the probability that only the first unit failed and second unit is functioning is \(p\), then \(98p\) is equal to \dots\dots.

The sum of first 4 terms of a G.P. is 65/12 and sum of their reciprocals is 65/18. If product of first 3 terms is 1 and the 3rd term is α, then 2α is _________

If \( |x + 3| + x>1 \), then \( x \in \):

The value of \( \tan^{-1} (1) + \tan^{-1} (0) + \tan^{-1} (2) + \tan^{-1} (3) \) is equal to:

The distance of the point \( (-5, -5, -10) \) from the point of intersection of the line \[ r = -2i - j + 2k + \lambda(3i + 4j + 2k) \] and the plane \( r \cdot (i - j + k) = 5 \) is:

\[ \int_{\log \sqrt{n}}^{\log \sqrt{r}} 2x \sec^2\left( \frac{1}{3} \cdot 2x \right) \, dx \] is equal to:

In a culture, the bacteria count is 1,00,000. The number is increased by 10% in 2 hours. In how many hours will the count reach 2,00,000 if the rate of growth of bacteria is proportional to the number present?

What is the angle between the two straight lines \[ y = (2 - \sqrt{3})x + 5 \quad \text{and} \quad y = (2 + \sqrt{3})x - 7? \]

If the angle \( \theta \) between the line \[ \frac{x + 1}{2} = \frac{z - 2}{2} = \frac{y + 4}{\sqrt{n}} \] and the plane \( 2x - y + z + 4 = 0 \) is such that \( \sin \theta = \frac{1}{3} \), then the value of \( n \) is:

Area bounded by the curve \( y = \log x \) and the coordinate axes is:

The angle of intersection of the curve \( y = x^2 \), \( dy = 7 - x^2 \) at \( (1, 1) \) is:

The angle formed by the positive Y-axis and the tangent to \( y = x^2 + 4x - 17 \) at \( (2, -3) \) is:

The value of \( (1 + i)^4 \) is:

The relation \( R \) defined on the set \( A = \{1, 2, 3, 4, 5\} \) by \( R = \{(x, y) : |x^2 - y^2|<16 \} \) is given by:

\[ \int \frac{2dx}{(e^x + e^{-x})^2} = ? \]

Which of the following is an infinite set?

The domain of the function \[ \sqrt{2x - 5x^2 + 6} + \sqrt{2x + 8 - x^2} \] is:

If \( \mathbf{a} = 2i - 2j + k \) and \( \mathbf{c} = -i + 2k \), then \( \mathbf{a} \times \mathbf{c} \) is equal to:

Let \[ \int \frac{x^{1/2}}{\sqrt{1 - x^3}} \, dx = \frac{3}{3} \, g(x) + C \] then

If \( (-4, 5) \) is one vertex and \( 7x - y + 8 = 0 \) is one diagonal of a square, then the equation of second diagonal is: