List of top Questions asked in BITSAT

Number of solutions of equations \( \sin 9\theta = \sin \theta \) in the interval \( [0, 2\pi] \) is

The probability that a certain electronic component fails when first used is \(0.10\). If it does not fail immediately, the probability that it lasts for one year is \(0.99\). The probability that a new component will last for one year is:

If \( |z_1| = 2 \), \( |z_2| = 3 \), \( |z_3| = 4 \) and \( |2z_1 + 3z_2 + 4z_3| = 4 \), then absolute value of \( 8z_2 z_3 + 27z_3 z_1 + 64z_1 z_2 \) equals

If \( A = 1 + r^a + r^{2a} + r^{3a} + \cdots \infty \) and \( B = 1 + r^b + r^{2b} + r^{3b} + \cdots \infty \), then \( a/b \) is equal to

If the 17th and the 18th terms in the expansion of \( (2 + a)^{50} \) are equal, then the coefficient of \( x^{35} \) in the expansion of \( (a + x)^{-2} \) is:

The shortest distance between the lines \[ x = y + 2 = 6z - 6 \] and \[ x + 1 = 2y = -12z \] is:

If A and B are symmetric matrices of same order such that \(\text{AB} + \text{BA} = \text{X}\) and \(\text{AB} - \text{BA} = \text{Y}\), then \((\text{XY})^\text{T} =\)

The sum of the first \(20\) terms of an arithmetic progression is \(640\), and the difference between the \(15^\text{th}\) and \(5^\text{th}\) terms is \(30\). Find the first term of the A.P.

If a real matrix \(A\) satisfies \[ A^T=A \quad \text{and} \quad A^2=I, \] then the eigenvalues of \(A\) must be:

The domain of the function \(f(x) = \sqrt{x - \sqrt{1 - x^2}}\) is

Let \(\text{A} = \{1, 2, 3, 4, 5\}\) and \(\text{R}\) be a relation defined by \(\text{R} = \{(x, y) : x, y \in \text{A}, x + y = 5\}\). Then, \(\text{R}\) is

If \(\vec{a} = 2\hat{i} + \hat{j} + 2\hat{k}\), then the value of \(|\hat{i} \times (\vec{a} \times \hat{i})|^2 + |\hat{j \times (\vec{a} \times \hat{j})|^2 + |\hat{k} \times (\vec{a} \times \hat{k})|^2\) is equal to:}

Find the sum of the series \( \left(x + \frac{1}{x}\right)^2 + \left(x^2 + \frac{1}{x^2}\right)^2 + \left(x^3 + \frac{1}{x^3}\right)^2 + \cdots \) up to \( n \) terms.

Evaluate: \[ \int_0^1 x^3\ln(1+x)\,dx \]

Evaluate the definite integral: \( \int_{0}^{\pi/2} \sin^2(x) \, dx \).

The sum of the series $\left(x + \frac{1}{x}\right)^2 + \left(x^2 + \frac{1}{x^2}\right)^2 + \left(x^3 + \frac{1}{x^3}\right)^2 \dots\dots\dots$ up to $n$ terms is:

The domain of the function \(f(x) = \sqrt{x - \sqrt{1 - x^2\) is:}

The line \(y = mx\) bisects the area enclosed by the lines \(x = 0\), \(y = 0\), \(x = \frac{3}{2}\) and the curve \(y = 1 + 4x - x^2\). Then, the value of \(m\) is:

If $p$ and $q$ be the longest and the shortest distance respectively of the point $(-7, 2)$ from any point $(\alpha, \beta)$ on the curve whose equation is $x^2 + y^2 - 10x - 14y - 51 = 0$, then find the Geometric Mean (G.M.) of $p$ and $q$.

If \( z_1, z_2, \ldots, z_n \) are complex numbers such that \( |z_1| = |z_2| = \ldots = |z_n| = 1 \), then \( |z_1 + z_2 + \ldots + z_n| \) is equal to:

Decreasing order of reactivity towards electrophilic substitution for the following compounds is:

The number of valence electrons present in the metal among Cr, Co, Fe and Ni which has the lowest enthalpy of atomisation is

Ionisation energy of H-atom is \(13.6 \text{ eV}\). The wavelength of the spectral line emitted when an electron in \(\text{Be}^{3+}\) comes from \(5^{\text{th}}\) energy level to \(2^{\text{nd}}\) energy level is:

The degeneracy of a hydrogen atom whose energy equals \(-R_H/16\) is:

An evacuated glass vessel weighs 40.0 g when empty, 135.0 g when filled with a liquid of density 0.95 g mL\(^{-1}\) and 40.5 g when filled with an ideal gas at 0.82 atm at 250 K. The molar mass of the gas in g mol\(^{-1}\) is: (Given: R = 0.082 L atm K\(^{-1}\) mol\(^{-1}\))