BITSAT 2012 Question Paper PDF is available for download. BITSAT 2012 was conducted in online CBT mode by BITS Pilani. BITSAT 2012 Question Paper had 150 questions to be attempted in 3 hours.
BITSAT 2012 Question Paper with Answer Key PDF
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What is the moment of inertia of a solid sphere of density \( \rho \) and radius \( R \) about its diameter?
A body moves with uniform acceleration, then which of the following graph is correct?
A projectile can have the same range \( R \) for two angles of projection. If \( t_1 \) and \( t_2 \) are the times of flight in two cases, then what is the product of two times of flight?
A horizontal overhead powerline is at a height of 4m from the ground and carries a current of 100A from east to west. The magnetic field directly below it on the ground is \( \mu_0 I / 2 \pi r \). What is the magnetic field at this point?
A man of mass 100 kg is standing on a platform of mass 200 kg, which is kept on a smooth ice surface. If the man starts moving on the platform with a speed 30 m/sec relative to the platform, calculate with what velocity relative to the ice the platform will recoil?
If the unit of force and length be each increased by four times, then the unit of energy is increased by:
Which of the following must be known in order to determine the power output of an automobile?
If the force is given by \( F = at + bt^2 \) with \( t \) as time, then the dimensions of \( a \) and \( b \) are:
A wheel of radius \( R \) rolls on the ground with a uniform velocity \( v \). The relative acceleration of topmost point of the wheel with respect to the bottom most point is:
If the radius of the earth were to shrink by one percent, its mass remaining the same, the value of \( g \) on the earth’s surface would:
The Young's modulus of a perfectly rigid body is:
An ice block floats in a liquid whose density is less than water. A part of block is outside the liquid. When whole of ice has melted, the liquid level will:
A large drop of oil (density 0.8 g/cm³ and viscosity \( \eta_0 \)) floats up through a column of another liquid (density 1.2 g/cm³ and viscosity \( \eta_L \)). Assuming that the two liquids do not mix, the velocity with which the oil drop rises will depend on:
A solid body of constant heat capacity 1 J/°C is being heated by keeping it in contact with reservoirs in two ways:
Which of the following process is possible according to the first law of thermodynamics?
For an isothermal expansion of a perfect gas, the value of \( \frac{\Delta P}{P} \) is equal to:
A sample of ideal monoatomic gas is taken round the cycle ABCA as shown in the figure. The work done during the cycle is:
The average translational kinetic energy of \( O_2 \) (molar mass 32) molecules at a particular temperature is 0.048 eV. The translational kinetic energy of \( N_2 \) (molar mass 28) molecules in eV at the same temperature is:
For a gas if ratio of specific heats at constant pressure and volume is \( \gamma \), then value of degrees of freedom is:
One end of a long metallic wire of length \( L \) tied to the ceiling. The other end is tied with a massless spring of spring constant \( K \). A mass hangs freely from the free end of the spring. The area of cross section and the Young’s modulus of the wire are \( A \) and \( Y \) respectively. If the mass slightly pulled down and released, it will oscillate with a time period \( T \) equal to:
The transverse displacement \( y(x, t) \) of a wave on a string is given by \( y(x,t) = e^{-(x^2 + t^2)} \sin(kx - \omega t) \). This represents a:
A sound source is moving towards a stationary listener with \( \frac{1}{10} \)th of the speed of sound. The ratio of apparent to read frequency is:
In a region of space having a uniform electric field \( E \), a hemispherical bowl of radius \( r \) is placed. The electric flux \( \Phi \) through the bowl is:
The electric field intensity just sufficient to balance the earth’s gravitational attraction on an electron will be:
Two capacitors \( C_1 \) and \( C_2 \) are charged to 120 V and 200 V respectively. It is found that by connecting them together the potential on each one can be made zero. Then:
Three voltmeters \( A \), \( B \), and \( C \) having resistances \( R \), \( 1.5R \), and \( 3R \), respectively, are connected as shown. When some potential difference is applied between X and Y, the voltmeter readings are \( V_A \), \( V_B \), and \( V_C \) respectively. Then:
The range of the particle when launched at an angle of 15° with the horizontal is 1.5 km. What is the range of the projectile when launched at an angle of 45° to the horizontal?
If \( m \) is magnetic moment and \( B \) is the magnetic field, then the torque is given by:
Magnetic moment of bar magnet is \( M \). The work done to turn the magnet by 90° of magnet in direction of magnetic field \( B \) will be:
The laws of electromagnetic induction have been used in the construction of a:
The impedance of a circuit consists of 3 \( \Omega \) resistance and 4 \( \Omega \) reactance. The power factor of the circuit is:
The r.m.s. value of potential difference \( V \) shown in the figure is:
A ray of light is incident at the glass-water interface at an angle \( i \), it emerges finally parallel to the surface of water, then the value of \( \mu_g \) would be:
A mica slit of thickness t and refractive index \( \mu \) is introduced in the ray from the first source \( S_1 \). By how much distance of fringes pattern will be displaced?
In a Young's double slit experiment the angular width of a fringe formed on a distant screen is \( 1^\circ \). The wavelength of the light used is \( 6280 \, Å \). What is the distance between the two coherent sources?
A light having wavelength 300 nm falls on a metal surface. The work function of metal is 2.54 eV, what is stopping potential?
If the total binding energies of \( ^{235}U \) and \( ^{233}U \) nuclei are 2.22, 28.3, 392 and 1786 MeV respectively, identify the most stable nucleus of the following.
An oscillator is nothing but an amplifier with:
In an experiment on photoelectric effect photons of wavelength 300 nm eject electrons from a metal of work function 2.25 eV. A photon of energy equal to that of the most energetic electron corresponds to the following transition in the hydrogen atom:
A letter 'A' is constructed of a uniform wire with resistance 1.0 \( \Omega \) per cm. The sides of the letter are 20 cm and the cross piece in the middle is 10 cm long. The apex angle is 60°. The resistance between the ends of the legs is close to:
Number of atoms of He in 100 amu of He (atomic wt. of He is 4) are:
If the radius of \( H \) is 0.53 Å, then what will be the radius of \( Li^{2+} \)?
Which of the following does not have valence electron in 3d-subshell?
The vapor pressure of
An ideal gas can’t be liquefied because
In which of the following reactions, standard entropy change (\( \Delta S^\circ \)) is positive and standard Gibbs’s energy change (\( \Delta G^\circ \)) decreases sharply with increasing temperature?
Bond enthalpies of \( H_2 \), \( X_2 \), and \( HX \) are in the ratio 2:1:2. If enthalpy of formation of \( HX \) is -50 kJ/mol\(^{-1}\), the bond enthalpy of \( X_2 \) is:
The pOH value of a solution whose hydroxide ion concentration is \( 6.2 \times 10^{-9} \, mol/litre \) is:
Which of the following combinations would not result in the formation of a buffer solution?
The reaction, \( SO_2 + Cl_2 \to SO_2 Cl_2 \), is exothermic and reversible. A mixture of \( SO_2 \), \( Cl_2 \), and \( SO_2 Cl_2 \) is at equilibrium in a closed container. Now a certain quantity of extra \( SO_2 \) is introduced into the container, the volume remaining the same. Which of the following is/are true?
In the reaction \[ Br_2 + 6 CO \to 3 H_2 + Br^+ + 3 CO_3 \]
The boiling point of water is exceptionally high because
Which of the following has correct increasing basic strength?
The following two compounds are:
In paper chromatography:
In which case the \( NO_2 \) will attack at the meta position?
Which alkene on ozonolysis gives \( CH_2 CHO \) and \( CH_3 CO \)?
Formation of ozone in the upper atmosphere from oxygen takes place by the action of:
\( CO_2 \) goes to air, causes greenhouse effect and gets dissolved in water. What will be the effect on soil fertility and pH of the water?
The van’t Hoff factor i for an electrolyte which undergoes dissociation and association in solvents are respectively:
If the elevation in boiling point of a solution of 10 g of solute (mol. wt. = 100) in 100 g of water is \( \Delta T_b \), the ebullioscopic constant of water is:
The ionic conductance of \( Ba^{2+} \) and \( Cl^- \) respectively are 127 and 76 \( S \, cm^{-1} \) at infinite dilution. The equivalent conductance of \( BaCl_2 \) at infinite dilution will be:
\( 2N_2O_5 \to 4NO_2 + O_2 \)
If rate and rate constant for above reaction are \( 2.40 \times 10^{-5} \, mol L^{-1} s^{-1} \) and \( 3 \times 10^{-5} \, s^{-1} \), respectively, then calculate the concentration of \( N_2O_5 \):
Which of the following gives maximum value of enthalpy of physiolysis?
Which of the following will be most effective in the coagulation of \( Fe(OH)_3 \) (soil)?
When chlorine water is exposed to sunlight, \( O_2 \) is liberated. Hence,
An extremely hot copper wire reacts with steam to give:
Among the following, the lowest degree of paramagnetism per mole of the compound at 298 K will be shown by:
The following reaction is known as:
\[ C_6 H_5 COOH + CO_2 \xrightarrow{120-140^\circ C, 1.5 \, atm} C_6 H_4 COONa \xrightarrow{NaOH} C_6 H_5 COOH \]
Which of the following processes is used for the preparation of acetone?
The preparation of ethyl acetoacetate involves:
Which one of the following pairs is not correctly matched?
Identify ‘C’ in the following reaction:
The helical structure of protein is stabilized by:
Complete hydrolysis of cellulose gives:
Alizarin is an example of:
2,4-Dichlorophenoxyacetic acid is used as:
0.45 g of acid molecular weight 90 is neutralized by 20 mL of 0.5N caustic potash. The basicity of the acid is:
In the reaction of KMnO\(_4\) with an oxalate in acidic medium, MnO\(_4^-\) is reduced to Mn\(^{2+}\) and C\(_2\)O\(_4^{2-}\) is oxidized to CO\(_2\). Hence, 50 mL of 0.02 M KMnO\(_4\) is equivalent to:
Which of the following is soluble in yellow ammonium sulphide?
Let A and B be two sets then \( (A \cup B) \cup (A \cap B) \) is equal to:
Let \( x \) and \( y \) be two natural numbers such that \( x \cdot y = 12(x + y) \) and \( x \leq y \). Then the total number of pairs \( (x, y) \) is:
In \( \sin \theta + \sin^2 \theta = 1/2 \), cos\( 2\theta + \) cos\( \theta = 3/2 \), then cos\( \theta - \phi \) is equal to:
Let \( T(k) \) be the statement \( 1 + 3 + 5 + \dots + (2k - 1) = k^2 + 10 \). Which of the following is correct?
The amplitude of \( \sin \frac{\pi}{5} + i \left( 1 - \cos \frac{\pi}{5} \right) \) is:
If \( x \to \infty \), then the value of \( x^4 + 3x^3 + 2x^2 - 11x - 6 \) is:
In how many ways can 5 prizes be distributed among 4 boys when every boy can take one or more prizes?
The number of positive integral solutions of \( abc = 30 \) is:
The coefficient of \( x^{20} \) in the expansion of \( (1 + x^2)^{40} \left( x^2 + 2 + \frac{1}{x^2} \right)^{-5} \) is:
If \( x \) is positive then the sum to infinity of the series
\[ \frac{1}{1+3x} - \frac{1}{1+3x^2} + \frac{1}{1+3x^3} - \dots \, \infty \]
is:
The nearest point on the line \( 3x + 4y = 12 \) from the origin is:
The length of the tangent drawn from any point on the circle \( x^2 + y^2 + 2\lambda x + \mu = 0 \) to the circle \( x^2 + y^2 + 2\gamma x + \lambda = 0 \), where \( \mu \geq \lambda \), is:
Find the eccentricity of the conic represented by \( x^2 - y^2 - 4x + 4y + 16 = 0 \):
\( \lim_{x \to \infty} \frac{1 - \tan \left( \frac{x}{2} \right)}{1 + \tan \left( \frac{x}{2} \right)}\) = ?
Let \( f(x + y) = f(x) \cdot f(y) \) for all \( x, y \), where \( f(0) = 0 \). If \( f(5) = 2 \) and \( f'(0) = 3 \), then \( f'(5) \) is equal to:
If sample A contains 100 observations 101, 102, .... 200 and sample B contains 100 observations 151, 152, .... 250, then the ratio of variance \( \frac{V_A}{V_B} \) is:
The probability of simultaneous occurrence of at least one of two events A and B is \( p \). If the probability that exactly one of A, B occurs is \( q \), then \( P(A' \cup B') \) is equal to:
If \( f(x) \) is an even function and \( g(x) \) is an odd function, then the function \( f \circ g \) is:
\( \tan^{-1} \left( \frac{1}{4} \right) + \tan^{-1} \left( \frac{1}{9} \right) \) equals to:
If \( k \leq \sin^{-1} x + \cos^{-1} x + \tan^{-1} x \leq 5 \), then:
The equations \( 2x + 3y + 4 = 0, 3x + 4y + 6 = 0 \) and \( 4x + 5y + 8 = 0 \) are:
The value of the determinant
\[ \begin{vmatrix} 265 & 240 & 219
240 & 225 & 198
191 & 198 & 181 \end{vmatrix} \]
is:
If \( x = a \sin \theta \) and \( y = b \cos \theta \), then \( \frac{d^2y}{dx^2} \) is:
If \( f(x) = x^\alpha \log x \) and \( f(0) = 0 \), then the value of \( \alpha \) for which Rolle's theorem can be applied in \( [0, 1] \) is:
If the function \( f(x) = ax + b \), \( 2 < x < 4 \), is continuous at \( x = 2 \) and 4, then the values of \( a \) and \( b \) are:
If \( f(x) = a^2 - 1 \), \( x^3 - 3x + 5 \) is a decreasing function of \( x \in R \), then the set of possible values of \( a \) (independent of \( x \)) is:
The diagonal of a square is changing at the rate of \( 0.5 \, cm/sec \). Then the rate of change of area, when the area is 400 \( cm^2 \), is equal to:
If the normal to the curve \( y = f(x) \) at the point \( (3, 4) \) makes an angle \( 3\pi/4 \) with the positive x-axis, then \( f'(3) \) is:
Evaluate:
\[ \int_0^{\pi/2} \frac{x}{\sqrt{4 - x^2}} \, dx \]
\( \lim_{x \to \infty} \frac{1 - \tan \left( \frac{x}{2} \right)}{1 + \tan \left( \frac{x}{2} \right)}\) = ?
The area bounded by the curve \( y = \sin x \), x-axis and the ordinates \( x = 0 \) and \( x = \pi/2 \) is:
The differential equation whose solution is \( Ax^2 + Bx + C = 1 \) where A and B are arbitrary constants is of:
The unit vector perpendicular to the vectors \( 6i + 2j + 3k \) and \( 3i - 6j - 2k \) is:
If \( \mathbf{a} = \mathbf{c} \) and \( \mathbf{b} = \mathbf{a} \times \mathbf{c} \), then the correct statement is:
What is the value of \( n \) so that the angle between the lines having direction ratios \( (1, 1, 1) \) and \( (1, 1, n) \) is \( 60^\circ \)?
The foot of the perpendicular from the point \( (7, 14, 5) \) to the plane \( 2x + 4y - z = 7 \) is:
Find the coordinates of the point where the line joining the points \( (2, -3, 1) \) and \( (3, -4, -5) \) cuts the plane \( 2x + y + z = 7 \):
A boy is throwing stones at a target. The probability of hitting the target at any trial is \( \frac{1}{2} \). The probability of hitting the target 5th time at the 10th throw is:
Two dice are thrown together 4 times. The probability that both dice will show same numbers twice is:
In a triangle ABC, if \( A = a \), \( B = 60^\circ \), and \( C = 75^\circ \), then \( b \) equals:
Prabhat wants to invest the total amount of ₹15,000 in saving certificates and national saving bonds. According to rules, he has to invest at least ₹2,000 in saving certificates and ₹2,500 in national saving bonds. The interest rate is 8% on saving certificates and 10% on national saving bonds per annum. He invests \( x \) in saving certificate and \( y \) in national saving bonds. Then the objective function for this problem is:
For the function \[ f(x) = \frac{x^{100}}{100} + \frac{x^{99}}{99} - x^2 + x + 1, \] \( f'(1) = mf'(0) \), where \( m \) is equal to:
Let \( A = \begin{bmatrix} 0 & \alpha
0 & 0 \end{bmatrix} \) and \( (A + I)^5 - 50A = \begin{bmatrix} a & b
c & d \end{bmatrix} \). Find \( abc + abd + bcd + acd \):
If the line \( x \cos \alpha + y \sin \alpha = p \) represents the common chord of the circles \( x^2 + y^2 = a^2 \) and \( x^2 + y^2 + b^2 = 2b \), where \( a > b \), where A and B lie on the first circle and P and Q lie on the second circle, then \( AP \) is equal to:
Let \( a_1, a_2, a_3, \dots \) be terms on A.P. If
\[ a_1 + a_2 + \dots + a_p = p^2, \, p \neq q, \, then \, a_q = \frac{p^2}{q^2} \]
Then \( a_q \) equals:
Florid means:
Verity means:
Perspicuity means:
Disgrace means:
Striking means:
Fiasco means:
Power got with money is the most craved for today:
You are asked to copy this letter word by word:
Let us quickly:
Rajesh's car wasn’t __________ Ramesh's, so we were too exhausted by the time we reached home:
1. The most vulnerable section of the society are the students.
P. Revolutionary and new fledged ideas have a great appeal to them.
Q. Agitations may be non-violent methods of protest.
R. They cannot resist the charm of persuasion.
S. They are to be taught that without discipline they cannot get proper education.
6. However if these become violent, the antisocial elements get encouraged and they pull all proper working out of gear.
Which of the following is correct?
Venice is a strange city.
P. There are about 400 odd bridges connecting the islands of Venice.
Q. There are no motor cars, no horses and no buses there.
R. These small islands are close to one another.
S. It is not one island but a hundred islands.
6. This is because Venice has no streets.
Which of the following is correct?
Passage:
The World Health Organisation is briefly called W.H.O. It is a specialised agency of the United Nations and was established in 1948.
International health workers can be seen working in all kinds of surroundings in deserts, jungles, mountains, coconut groves, and rice fields. They help the sick to attain health and the healthy to maintain their health.
This global health team assists the local health workers in stopping the spread of what are called communicable diseases, like cholera. These diseases can spread from one country to another and so can be a threat to world health.
138.
W.H.O. assists different national health authorities not only in controlling diseases but also in preventing them altogether. Total prevention of diseases is possible in a number of ways. Everyone knows how people, particularly children, are vaccinated against one disease or another. Similarly, most people are familiar with the spraying of houses with poisonous substances which kill disease-carrying insects.
W.H.O. means:
"International health workers can be seen working in all kinds of surroundings: in deserts, jungles, mountains, coconut groves, and rice fields." Here International means:
They help the sick to attain health and the healthy to maintain their health. Here they stands for:
In a code language, if SUMMER is coded as SDUMV, then how WINTER will be coded as:
View Solution
The given puzzle involves multiplying the numbers in a pattern. The first column is multiplied by the second column, and the third column is the sum of those values. The correct result is 888.
Thus, the correct answer is (1).
Quick Tip: Look for patterns in the arrangement of numbers when solving puzzles of this type.
Today is Monday. After 61 days, it will be:
Rahul and Nitesh are standing in a row of persons. Rahul is 12th from left side and Nitesh is 18th from the right side of the row. If they interchanged their positions, Rahul becomes 25th from left. Find the new position of Nitesh from the right side.
One of the numbers does not fit into the series. Find the wrong number.
52, 152, 414, 1312, 5348, 26840
In the following question, A stands for any of Mathematical signs at different places, which are given as choices under each question. Select the choice with the correct sequence of signs which when substituted makes the question as correct equation:
\[ 24 A 4 A 5 A 4 = ? \]
Which represents carrot, food, vegetable?
"All the members of the Tennis club are members of the badminton club too". Who plays badminton?
View Solution
By visualizing the mirror image, the correct answer is (d), which is the exact mirror image of the given figure.
Thus, the correct answer is (4).
Quick Tip: To solve mirror image problems, visualize how the figure would appear in a mirror.
Which answer figure is the exact mirror image of the given figure when the mirror is held from the right at PQ?
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