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

Given \[ \frac{dy}{dx} \tan x = y \sec^2 x + \sin x, \quad {find the general solution:} \]

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:}

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:

If the sum of the coefficients in the expansion of \( (x + y)^n \) is 1024, then the value of the greatest coefficient in the expansion is:

Let \[ A = \begin{pmatrix} 1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1 \end{pmatrix}, \quad 10B = \begin{pmatrix} 4 & 2 & 2 \\ -5 & 0 & \alpha \\ 1 & -2 & 3 \end{pmatrix} \] If \( B \) is the inverse of \( A \), then the value of \( \alpha \) is:

A running track of 440 ft is to be laid out enclosing a football field, the shape of which is a rectangle with a semi-circle at each end. If the area of the rectangular portion is to be maximum, then the lengths of its sides are:

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 \( x \in \left( 0, \frac{\pi}{2} \right) \), then the value of \( \cos^{-1} \left( \frac{7}{2} (1 + \cos 2x) + \sqrt{(\sin^2 x - 48\cos^2 x)\sin x} \right) \) is equal to:

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:

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:

The value of \[ \int \frac{1}{x^1} \, dx, { is } \left[ \frac{(x - 1)^3}{(x + 2)^5} \right]_1^4 \]

If \(\hat{u}\) and \(\hat{v}\) are two non-collinear unit vectors such that \(\left| \frac{\hat{u} + \hat{v}}{2} + \hat{u} \times \hat{v} \right| = 1\), then the value of \(\left| \hat{u} \times \hat{v} \right|\) is equal to:

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:

The sum of all the solutions of the equation \( \cos \theta \cos \left( \frac{\pi}{3} + \theta \right) \cos \left( \frac{\pi}{3} - \theta \right) = \frac{1}{4} \), for \( \theta \in [0, 6\pi] \) 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 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:

Let \( \alpha \) be the solution of the equation \[ 16 \sin^2 \theta + 16 \cos^2 \theta = 10, \quad \theta \in \left( 0, \frac{\pi}{4} \right) \] {If the shadow of a vertical pole is \( \frac{1}{\sqrt{3}} \) of its height, then the altitude of the sun 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:}

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:

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:

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 number of ways of arranging the letters of the word HAVANA so that V and N do not appear together is: