List of top Questions asked in BITSAT

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 $$ x^2 + y^2 = 9 \text{ is:} $$

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

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:

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:

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:

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:

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:

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:

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 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:

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:

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

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

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 $ 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:

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:

A normal is drawn at the point $ P $ to the parabola $ y^2 = 8x $, which is inclined at $ 60^\circ $ with the straight line $ y = 8 $. Then the point $ P $ lies on the straight line:

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

If $ \alpha, \beta, \gamma \in [0, \pi] $ and if $ \alpha, \beta, \gamma $ are in AP, then \[ \frac{\sin \alpha - \sin \gamma}{\cos \gamma - \cos \alpha} \] {is equal to:}