List of top Mathematics Questions asked in BITSAT

If \[ \left[ \begin{array}{cc} 1 & -\tan(\theta) \\ \tan(\theta) & 1 \end{array} \right] \left[ \begin{array}{cc} 1 & \tan(\theta) \\ -\tan(\theta) & 1 \end{array} \right]^{-1} = \left[ \begin{array}{cc} a & -b \\ b & a \end{array} \right], \] then:

The area of the region bounded by the parabola \( (y - 2)^2 = (x - 1) \), the tangent to the parabola at the point \( (2, 3) \), and the X-axis is:
A spherical balloon is filled with \( 4500\pi \) cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of \( 72\pi \) cubic meters per minute, then the rate (in meters per minute) at which the radius of the balloon decreases 49 minutes after the leakage began is:

If the plane \( 3x + y + 2z + 6 = 0 \) { is parallel to the line} \[ \frac{3x - 1}{2b} = \frac{3 - y}{1} = \frac{z - 1}{a}, \] {then the value of \( 3a + 3b \) is:}

Given \[ \frac{dy}{dx} \tan x = y \sec^2 x + \sin x, \quad {find the general solution:} \]
The value of \( \lim_{x \to 0} \frac{(1 + x)^{\frac{1}{x}} - e + \frac{1}{2}e^x}{x^2} \) is:
If \( |w| = 2 \), then the set of points \( z = w - \frac{1}{w} \) is contained in or equal to the set of points \( z \) satisfying:
If the straight line \( y = mx + c \) touches the parabola \( y^2 - 4ax + 4a^3 = 0 \), then \( c \) is:
A house subtends a right angle at the window of the opposite house and the angle of elevation of the window from the bottom of the first house is 60°. If the distance between the two houses is 6m, then the height of the first house is:
Let \( a_1, a_2, a_3, \dots \) be a harmonic progression with \( a_1 = 5 \) and \( a_{20} = 25 \). The least positive integer \( n \) for which \( a_n<0 \) is:
If \[ g(x) = x^2 + x - 2 \] and \[ \frac{1}{2} g \circ f(x) = 2x^2 - 5x + 2, \] then \( f(x) \) is equal to:
If in a \( \triangle ABC \), \( 2b^2 = a^2 + c^2 \), then
\[ \frac{\sin 3B}{\sin B} { is equal to:} \]
The area enclosed by the curves \( y = \sin x + \cos x \) { and } \( y = | \cos x - \sin x | \) { over the interval} \( \left[ 0, \frac{\pi}{2} \right] \) { is:}

The smallest positive integral value of \( n \) such that \[ \left( \frac{1 + \sin \frac{\pi}{8} + i \cos \frac{\pi}{8}}{1 + \sin \frac{\pi}{8} - i \cos \frac{\pi}{8}} \right)^n \] is purely imaginary, is equal to:

If \( p \neq a \), \( q \neq b \), \( r \neq c \), and the system of equations \[ px + ay + az = 0 \] \[ bx + qy + bz = 0 \] \[ cx + cy + rz = 0 \] has a non-trivial solution, then the value of \[ \frac{p}{p - a} + \frac{q}{q - b} + \frac{r}{r - c} \] is:

A six-faced die is a biased one. It is three times more likely to show an odd number than an even number. It is thrown twice. The probability that the sum of the numbers in two throws is even is:
The mean of five observations is 4 and their variance is 5.2. If three of these observations are 1, 2, and 6, then the other two are:
In a sequence of 21 terms, the first 11 terms are in AP with common difference 2 and the last 11 terms are in GP with common ratio 2. If the middle term of the AP is equal to the middle term of the GP, then the middle term of the entire sequence is:
The number of different seven-digit numbers that can be written using only the digits 1, 2, and 3 with the condition that the digit 2 occurs twice in each number is:
Let \( a_1, a_2, \dots, a_{40} \) be in AP and \( h_1, h_2, \dots, h_{10} \) be in HP. If \( a_1 = h_1 = 2 \) and \( a_{10} = h_{10} = 3 \), then \( a_4 h_7 \) is:
The number of terms in the expansion of \( (1 + 5\sqrt{2}x)^9 + (1 - 5\sqrt{2}x)^9 \) is:
If \( A = \{ x : x { is a multiple of 4} \} \) and \( B = \{ x : x { is a multiple of 6} \} \), then \( A \cap B \) consists of multiples of:
If \( \alpha \) be a root of the equation \( 4x^2 + 2x - 1 = 0 \), then the other root of the equation is

The value of \[ \lim_{x \to 0} \frac{1 - \cos(1 - \cos x)}{x^4} \] is:

Given \[ 2x - y + 2z = 2, \quad x - 2y + z = -4, \quad x + y + \lambda z = 4, \] then the value of  \( \lambda \) such that the given system of equations has no solution is: