List of top Questions asked in BITSAT- 2013

Let $R$ be the relation on the set $R$ of all real numbers, defined by $aRb$ If $|a - b| \le 1$. Then, $R$ is
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-
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?
$S$ and $T$ are the foci of an ellipse and $B$ is an end of the minor axis. If $STB$ is an equilateral triangle, then the eccentricity of the ellipse is
A thermodynamical system is changed from state $(P_1, V_1)$ to $(P_2, V_2)$ by two different processes, the quantity which will remain same will be
For $k=1,2,3$ the box $Bk$ contains $k$ red balls and $(k+1)$ white balls. Let $P\left(B_{1}\right)=\frac{1}{2}, P\left(B_{2}\right)=\frac{1}{3}=\frac{1}{3}$ and $P\left(B_{3}\right)=\frac{1}{6} .$ A box is selected at random and a ball is drawn from it. If a red ball is drawn, then the probability that it has come from box $B_{2}$, 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
For the reaction $CO ( g )+\left(\frac{1}{2}\right) O _{2}( g ) \longrightarrow CO _{2}( g ), K _{ p } / K _{ c }$ is
If $1.0$ mole of $I_{2}$ is introduced into $1.0$ litre flask at $1000\, K$, at equilibrium $\left(K_{c}=10^{-6}\right)$, which one is correct?
A bob is hanging over a pulley inside a car through, a string. The second end of the string is in the hand of a person standing in the car. The car is moving with constant acceleration '$a$' directed horizontally as shown in figure. Other end of the string is pulled with constant acceleration '$a$' vertically. The tension in the string is equal to -
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 $k$.
Find the variance of the data given below
Occurance $(x_i)$ Frequency $(f_i)$ Freq $\ast (x_i)$ $(x_i-mean)$ $(x_i-mean)^2$ $f_i(x_i-mean)^2$
3.5 3 10.5 -3.59 12.887 38.661
4.5 7 31.5 -2.59 6.707 46.952
5.5 22 121 121 2.528 55.609
6.5 60 390 -0.59 0.348 20.876
7.5 85 637.5 0.41 0.168 14.298
8.5 32 272 1.41 1.988 63.632
9.5 8 76 2.41 5.809 46.47
Total 217 1538.5 - - 286.498
A light inextensible string that goes over a smooth fixed pulley as shown in the figure connects two blocks of masses $0.36\, kg$ and $0.72\, kg$. Taking $g =10\, m / s ^{2}$, find the work done (in joules) by the string on the block of mass $0.36\, kg$ during the first second after the system is released from rest.
For the dissociation reaction, $H _{2}( g ) \rightarrow 2 H ( g ) \quad \Delta H =162 Kcal$, heat of atomisation of $H$ is
A Carnot's heat engine works between the temperatures $427^{\circ} C$ and $27^{\circ} C$. What amount of heat should it consume per second to deliver mechanical work at the rate of $1.0\, kW$ ?
How many grams of concentrated nitric acid solution should be used to prepare $250\, mL$ of $2 \cdot 0\, M HNO _{3}$ ? The concentrated acid is $70 \% HNO _{3}$.
A particle of mass ' $m$ ' is projected with a velocity $v$ making an angle of $30^{\circ}$ with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height ' $h$ ' is
In the truth table for the statement $(p \wedge q) \rightarrow(q \vee \sim p)$, the last column has the truth value in the following order is
If x satisfies $| 3 x - 2 | + | 3x - 4 | + | 3x - 6 | \ge 12$, then
Among the following four structures $I$ to $IV$, it is true that
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
Let $f(x)=\left(x^{5}-1\right)\left(x^{3}+1\right), g(x)=\left(x^{2}-1\right)\left(x^{2}-x+1\right)$ and let $h(x)$ be such that $f(x)=g(x) h(x)$. Then $\displaystyle\lim _{x \rightarrow 1} h(x)$ is
A cube is subjected to a uniform volume compression. If the side of the cube decreases by $2\%$ the bulk strain is
A ball whose density is $0.4\times 10^3 kg/m^3$ falls into water from a height of $9\, cm$. To what depth does the ball sink ?