List of top Questions asked in BITSAT

What is [NH₄⁺] in a solution that is 0.02 M NH₃ and 0.01 M KOH? $$ K_b (\text{NH}_3) = 1.8 \times 10^{-5} $$

The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line $$ 4x - 5y = 20 $$ to the circle $$ x^2 + y^2 = 9 \text{ is:} $$

If $ \alpha $ be a root of the equation $ 4x^2 + 2x - 1 = 0 $, then the other root of the equation 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 $ |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 value of \[ \lim_{x \to 0} \frac{1 - \cos(1 - \cos x)}{x^4} \] 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:

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:

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:

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:

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 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:

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

If the straight line $ y = mx + c $ touches the parabola $ y^2 - 4ax + 4a^3 = 0 $, then $ c $ is:

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

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:

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:

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:

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:}

For each parabola $ y = x^2 + px + q $, meeting the coordinate axes at three distinct points, if circles are drawn through these points, then the family of circles must pass through:

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

Let $a, b$ be the solutions of $x^2 + px + 1 = 0$ and $c, d$ be the solution of $x^2 + qx + 1 = 0$. If $(a - c)(b - c)$ and $(a + d)(b + d)$ are the solution of $x^2 + ax + \beta = 0$, then $\beta$ is equal to: