List of top Mathematics Questions asked in BITSAT

The shortest distance between the lines \[ \frac{x - 3}{2} = \frac{y - 2}{3} = \frac{z - 1}{-1} \] and \[ \frac{x + 3}{2} = \frac{y - 6}{1} = \frac{z - 5}{3} \] is:

The ratio in which the YZ-plane divides the line segment formed by joining the points (-2, 4, 7) and (3, -5, 8) is 2 : m.
The value of m is:

Simplify $ i^{57} + \frac{1}{i^{25}} $ and find its value:

If $ \vec{a} = \hat{i} + \hat{j} + \hat{k} $, $ \vec{a} \cdot \vec{b} = 1 $ and $ \vec{a} \times \vec{b} = \hat{j} - \hat{k} $, then $ \vec{b} $ is:

Minimum value of 5^cos(2x) + 5^sin(2x)

Matrices when the solution of equations is not defined

circles (concyclic, 3 pts given and do they form equilateral, right angled triangle)

A pack of cards contains 4 aces, 4 kings,4 queens, 4 jacks. Two cards are drawn from the deck, find out the probability that at least one of them is ace.

Length of tangent from (3,4) to x²+y² = 9?

$∫1/(1 + sinx)?$

What is the probability of 53 Fridays in an ordinary year?

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

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

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