List of top Mathematics 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 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 $ \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:}

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:

Let $ f(x) = \int \frac{x^2 \, dx}{(1 + x^2)(1 + \sqrt{1 + x^2})} $ and $ f(0) = 0 $, then the value of $ f(A) $ is:

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

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 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:

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 $ \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 $ 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:

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 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 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 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:

If in a $ \triangle ABC $, $ 2b^2 = a^2 + c^2 $, then
\[ \frac{\sin 3B}{\sin B} { is equal to:} \]

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:

The number of terms in the expansion of $ (1 + 5\sqrt{2}x)^9 + (1 - 5\sqrt{2}x)^9 $ is:

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

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:

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: