List of top Questions asked in BITSAT- 2013

An ellipse has $OB$ as semi-minor axis, $F$ and $F$ are its foci and the $\angle FBF$, is a right angle. Then, the eccentricity of the ellipse is

A class has $175$ students. The following data shows the number of students obtaining one or more subjects. Mathematics $100$, Physics $70$, Chemistry $40$; Mathematics and Physics $30$, Mathematics and Chemistry $28$, Physics and Chemistry $23$; Mathematics, Physics and Chemistry $18$. How many students have offered Mathematics alone?

If the line \( 2x - 3y = k \) touches the parabola \( y^2 = 6x \), then find the value of \( k \).

S and T are the foci of an ellipse and B is an end of the minor axis. If \( \triangle \text{STB} \) is an equilateral triangle, then the eccentricity of the ellipse is

An ellipse has OB as semi-minor axis, \( F \) and \( F' \) its foci and the angle \( \angle \text{FBF'} \) is a right angle. Then the eccentricity of the ellipse is

If the real part of \( \frac{z + 1}{z - 1} = 4 \), then the locus of the point representing \( z \) in the complex plane is

A pair of tangents are drawn from the origin to the circle \( x^2 + y^2 + 20(x + y) + 20 = 0 \), then the equation of the pair of tangent are

If the lines \( \ell_1 : \ell m + mn + n = 0 \), \( \ell_2 : mn + m + n = 0 \) are concurrent then

If \( 4a^2 + b^2 + 2c^2 + 4ab - 6ac - 3bc = 0 \), the family of lines \( ax + by + c = 0 \) is concurrent at one or the other of the two points-

The quadratic equation whose roots are the \( x \) and \( y \) intercepts of the line passing through \( (1, 1) \) and making a triangle of area \( A \) with the co-ordinate axes is

If \( C_0, C_1, C_2, \dots \) denote the binomial coefficients in the expansion of \( (1 + x)^n \), then the value of \[ C_0 + (C_0 + C_1) + (C_0 + C_1 + C_2) + \dots + (C_0 + C_1 + C_2 + \dots + C_n) \] is

A box contains two white balls, three black balls and four red balls. In how many ways can three balls be drawn from the box if at least one black ball is to be included in the draw?

In how many ways can 5 boys and 5 girls be seated at a round table so that no two girls may be together?

Let \( f(x) = (x^5 - 1)(x^3 + 1) \), \( g(x) = (x^2 - 1)(x^2 - x + 1) \) and let \( h(x) \) be such that \( f(x) = g(x)h(x) \). Then

The probability of India winning a test match against West Indies is \( \frac{1}{2} \). Assuming independence from match to match, the probability that in a 5 match series India’s second win occurs at the third test is

If \( \cos 76^\circ = \cos \left( 90^\circ - \theta \right) \), then the general value of \( \theta \) is

The greatest and least values of \( \left( \sin(x) \right)^2 + \left( \cos(x) \right)^2 \) are respectively

An object is observed from the points A, B and C lying in a horizontal straight line which passes directly underneath the object. The angular elevation at A is \( \theta \), at B is \( 2\theta \), and at C is \( 3\theta \). If AB = a, BC = b, and the height of the object is h, then the height of the object is

The value of \[ \frac{1}{2} \cos^{-1} \left( \cos \left( \frac{\pi}{3} - \frac{\sqrt{63}}{8} \right) \right) \] is

Which of the following will fill the series? \[ 2, 9, 28, 2, 126 \]

Two signs in the equations have been interchanged, find out the two signs to make the equation correct. \[ 3 \, - \, 5 \, + \, 8 \, + \, 2 \, - \, 10 = 13 \]

In a classroom, there are 5 rows and 5 children A, B, C, D and E are seated one behind the other in 5 separate rows as follows. - A is sitting behind C but in front of B. - C is sitting behind E and D is sitting in front of E. The order in which they are sitting from the first row to the last is

Sushma walks 20m towards north. Then she turns right and walks 30m. Now, she turns right and walks 35m. Now turning left, she walks 15m. Again, she turns left and moves 15m. Finally, she turns left and walks 15m. In which direction and how far is she from her original position?