BITSAT 2013 Question Paper PDF is available for download. BITSAT 2013 was conducted in online CBT mode by BITS Pilani. BITSAT 2013 Question Paper had 150 questions to be attempted in 3 hours.
BITSAT 2013 Question Paper with Answer Key PDF
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The velocity and acceleration vectors of a particle undergoing circular motion are \( \vec{v} = 2i + 4j \, m/s \) and \( \vec{a} = 2i + 4j \, m/s^2 \) respectively at an instant of time. The radius of the circle is –
A man runs at a speed of 4 m/s to overtake a standing bus. When he is 6 m behind the door at \( t = 0 \), the bus moves forward and continuous with a constant acceleration of 1.2 m/s². The man reaches the door in time t. Then,
Wave pulse can travel along a tense string like a violin spring. A series of experiments showed that the wave velocity \( V \) of a pulse depends on the following quantities, the tension \( T \) of the string, the cross-section area \( A \) of the string and density \( \rho \) of the string. Obtain an expression for \( V \) in terms of \( T \), \( A \), and \( \rho \) using dimensional analysis.
A body is projected, making an acute angle \( \theta \) with the horizontal. If angle between velocity \( \vec{v} \) and acceleration \( \vec{g} \) is \( \theta \), then
The minimum velocity (in m/s) with which a car driver must traverse a flat curve of radius 150 m and coefficient of friction 0.6 to avoid skidding is
A bob is hanging over a pulley inside a car moving with constant acceleration \( a \) directed horizontally as shown. The second end of the string is in the hand of a person standing in the car. The car is moving with constant acceleration \( a \) 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 block of mass \( m \) is placed on a smooth inclined wedge ABC of inclination \( \theta \) as shown in the figure. The wedge is given an acceleration \( a \) towards the right. The relation between \( a \) and \( g \) for the block to remain stationary on the wedge is
A 3.628 kg freight car moving along a horizontal rail road spur track at 7.2 km/hour strikes a bumper whose coil springs experiences a maximum compression of 30 cm in stopping the car. The elastic potential energy of the springs at the instant when they are compressed 15 cm is –
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.
Two rings of radius \( R \) and \( nR \) made of same material have the ratio of moment of inertia about an axis passing through the centre is 1 : 8. The value of \( n \) is –
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 –
A disc is performing pure rolling on a smooth stationary surface with constant angular velocity as shown in the figure. At any instant, for the lower most point of the disc –
There is a shell of mass \( M \) and density of the shell is uniform. The work done to take a point mass from point A to B is \( [AB = r] \)
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?
Figure shows a copper rod joined to a steel rod. The rods have equal length and equal cross-sectional area. The free end of the copper rod is kept at 0°C and that of steel rod is kept at 100°C. Find the temperature of the junction of the rod.
Conductivity of copper = \( 390 \, W/m°C \)
Conductivity of steel = \( 46 \, W/m°C \)
If the radius of a star is \( R \) and it acts as a black body, what would be the temperature of the star, in which the rate of energy production is \( Q \)?
A thermodynamic 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 –
A Carnot's heat engine works between the temperatures 427°C and 27°C. What amount of heat should it consume per second to deliver mechanical work at the rate of 1.0 kW?
A vessel containing 1 more of \( O_2 \) gas (molar mass 32) at temperature \( T \). The pressure of the gas is \( p \). An identical vessel containing one mole of He gas (molar mass 4) at temperature 2T has a pressure of –
The temperature of an ideal gas is increased from 27°C to 127°C, then the percentage increase in \( v_{rms} \) is
Two gases occupy two containers A and B. The gas in A, of volume 0.10 m³, exerts a pressure of 1.40 MPa and that in B of volume 0.15 m³ exerts a pressure of 0.7 MPa. The two containers are united by a tube of negligible volume and the gases are allowed to intermingle. Then if the temperature remains constant, the final pressure in the container will be (in MPa)
An instantaneous displacement of a simple harmonic oscillator is \( x = A \cos(\omega t + \pi/4) \). Its speed will be maximum at time
Two waves of wavelengths 99 cm and 100 cm both travelling with velocity 396 m/s are made to interfere. The number of beats produced by them is
If the equation of transverse wave is \( y = x_0 \cos \left( 2\pi \left( nt - \frac{x}{\lambda} \right) \right) \), the maximum velocity of the particle is twice of wave velocity, if \( k \) is –
Three equal charges (\( q \)) are placed at corners of an equilateral triangle of side \( a \). The force on any charge is –
Two identical capacitors, have the same capacitance \( C \). One of them is charged to potential \( V_1 \) and the other to \( V_2 \). The negative ends of the capacitors are connected together. When the positive ends are also connected, the decrease in energy of the combined system is –
What should be the characteristic of fuse wire?
In the circuit shown in figure, the potential difference between points A and B is 16 V. The current passing through \( 2 \Omega \) resistance will be
Two parallel conductors carry current in opposite directions as shown in figure. One conductor carries a current of 10.0 A. Point C is a distance \( \frac{d}{2} \) to the right of the 10.0 A current. If \( d = 18 \, cm \) and \( I \) is adjusted so that the magnetic field at C is zero, the value of the current \( I \) is
A uniform electric field and uniform magnetic field are acting along the same direction in a certain region. If an electron is projected in the region such that its velocity is pointed along the direction of fields, then the electron
Eddy currents are produced when
Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross-sectional area \( A = 10 \, cm^2 \) and length 20 cm. If one of the solenoids has 300 turns and the other 400 turns, their mutual inductance is
The ratio of secondary and primary turns of step-up transformer is 4 : 1. If a current of 4 A is applied to the primary, the induced current in secondary will be
Which of the following electromagnetic radiations has the smallest wavelength?
When light is refracted, which of the following does not change?
The given lens is broken into four parts and rearranged as shown. If the initial focal length is \( f \), then after rearrangement the equivalent focal length is –
In Young's double slit experiment 10th order maximum is obtained at the point of observation in the interference pattern for \( \lambda = 7000 \, Å \). If the source is replaced by another one of wavelength 5000 Å then the order of maximum at the same point will be –
Transfer characteristics (output voltage \( V_o \) vs input voltage \( V_i \)) for a base biased transistor in CE configuration is as shown in the figure. For using transistor as a switch, it is used
The circuit is equivalent to
How many grams of concentrated nitric acid solution should be used to prepare 250 mL of 2.0 M \( HNO_3 \)? The concentrated acid is 70% \( HNO_3 \).
The Bohr orbit radius for the hydrogen atom (\( n = 1 \)) is approximately 0.530 Å. The radius for the first excited state (\( n = 2 \)) orbit is (in Å)
The screening effect of \( d \)-electrons is
When the first ionisation energies are plotted against atomic number, the peaks are occupied by
The ions \( O^{2-} \), \( F^- \), \( Na^+ \), \( Mg^{2+} \) and \( Al^{3+} \) are isoelectronic. Their ionic radii show:
Using MOT, which of the following pairs denote paramagnetic species?
Increasing order of rms velocities of \( H_2 \), \( O_2 \), \( N_2 \) and \( HBr \) is
For the dissociation reaction, \( H_2 \rightarrow H + H \), \( \Delta H = 162 \, Kcal \), heat of atomisation of H is
The enthalpy of combustion of 2 moles of benzene at 27°C differs from the value determined in bomb calorimeter by
If 1.0 mole of \( I_2 \) is introduced into a 1.0 litre flask at 1000 K, at equilibrium (\( K_c = 10^{-6} \)), which one is correct?
For the reaction \( CO(g) + \frac{1}{2} O_2 (g) \rightarrow CO_2 (g) \), \( K_c \) is
The oxidation state of sulphur in \( Na_2 S_4 O_6 \) is
When same amount of zinc is treated separately with excess of sulphuric acid and excess of sodium hydroxide solution, the ratio of volumes of hydrogen evolved is:
The alkali metals form salt-like hydrides by the direct synthesis at elevated temperature. The thermal stability of these hydrides decreases in which of the following orders?
The most stable carbocation among the following is
Among the following four structures I to IV, it is true that
The number of enantiomers of the compound \( CH_3 CHBr CHBrCOOH \) is
Which one of the following reactions is expected to readily give a hydrocarbon product in good yields?
What will be the main product when acetylene reacts with hypochlorous acid?
The greenhouse effect is because of the
Due to Frenkel defect, the density of ionic solids
Equal weights of NaCl and KCl are dissolved separately in equal volumes of solutions. Molarity of the two solutions will be:
A current of 2.0 A passed for 5 hours through a molten metal salt deposits 22.2 g of metal (At wt. = 177). The oxidation state of the metal in the salt is
The electrolytic cells, one containing acidified ferrous chloride and another acidified ferric chloride are connected in series. The ratio of iron deposited at cathodes in the two cells when electricity is passed through the cells will be:
Velocity constant of a reaction at 290 K was found to be \( 3.2 \times 10^{-3} \). At 300 K it will be:
At high pressure, the entire surface gets covered by a monomolecular layer of the gas follows
Which of the following is incorrect with respect to property indicated?
Strong reducing behaviour of \( H_3 PO_4 \) is due to
The pair in which both species have same magnetic moment (spin only value) is:
Which of the following is less acidic among the given halogen compounds?
In an \( S_N2 \) substitution reaction of the type \( R - Br + Cl^- \xrightarrow{DMF} R - Cl + Br^- \), which one of the following has the highest relative rate?
Which of the following is not the product of dehydration of \( OH \)?
What will be the correct structural formula of the product for the following reaction?
Nucleophilic addition reaction will be most favoured in
Identify the product C in the series
Insulin production and its action in the human body are responsible for the level of diabetes. This compound belongs to which of the following categories?
Which statement is incorrect about peptide bond?
A mixture of chlorides of copper, cadmium, chromium, iron, and aluminium was dissolved in water acidified with HCl and hydrogen sulphide gas was passed for sufficient time. It was filtered, boiled and a few drops of nitric acid were added while boiling. To this solution ammonium chloride and sodium hydroxide were added and filtered. The filtrate shall give test for.
Volume of 3%solution of sodium carbonate necessary to neutralise a litre of 0.1 N sulphuric acid is
Volume of 3%solution of sodium carbonate necessary to neutralise a litre of 0.1 N sulphuric acid 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 18. How many students have offered Mathematics alone?
If \( \cos \theta + \sin \theta = x \cos \theta \) and \( \sin \theta = y \cos \theta \), then \( x^2 + y^2 = \)
If \( \cos 76^\circ = \cos \left( 90^\circ - \theta \right) \), then the general value of \( \theta \) 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
If \( \alpha \) and \( \beta \) are the roots of \( x^2 - x + 1 = 0 \), then the equation whose roots are \( \alpha^{100} \) and \( \beta^{100} \) is
The set of all real \( x \) satisfying the inequality
\[ \frac{3 - |x|}{4 - |x|} \geq 0 \]
is
If \( x \) satisfies \( |3x-2| + |3x-4| \geq |3x-6| \), then
In how many ways can 5 boys and 5 girls be seated at a round table so that no two girls may be together?
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?
The coefficient of the middle term in the expansion of \( (2 + 3x)^4 \) 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
The sum of the series
\[ 1 + 2^2 + 3^2 + 4^2 + \dots + 100^2 \]
is
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 \( 4a^2 + b^2 + 2c^2 + 4ab - 6ac - 3bc = 0 \), the family of lines \( ax + by + c = 0 \) is concurrent at one or the other of the two points-
A 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
An ellipse has OB as semi-minor axis, \( F \) and \( F' \) its foci and the angle \( \angle FBF' \) is a right angle. Then the eccentricity of the ellipse is
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 \( \triangle STB \) is an equilateral triangle, then the eccentricity of the ellipse is
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
In the truth table for the statement \( (p \land q) \rightarrow (q \lor \neg p) \), the last column has the truth value in the following order is
If the value of mode and mean is 60 and 66 respectively, then the value of median is
Find the variance of the data given below
\[ Size of item: \quad 3.5, 4.5, 5.5, 6.5, 7.5, 8.5, 9.5
Frequency: \quad 3, 7, 22, 60, 85, 32, 8 \]
Let \( R \) be the relation on the set \( \mathbb{R} \) of all real numbers, defined by \( aRb \) if \( |a - b| \leq 1 \). Then, \( R \) is
The greatest and least values of \( \left( \sin(x) \right)^2 + \left( \cos(x) \right)^2 \) are respectively
The value of
\[ \frac{1}{2} \cos^{-1} \left( \cos \left( \frac{\pi}{3} - \frac{\sqrt{63}}{8} \right) \right) \]
is
The determinant
\[ \left| \begin{matrix} 1 & x & x^2
1 & x^3 & x^4
1 & x^5 & x^6 \end{matrix} \right| \]
vanishes for
If the lines \( \ell_1 : \ell m + mn + n = 0 \), \( \ell_2 : mn + m + n = 0 \) are concurrent then
If \( y = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \dots + \infty \), then
If \( f(x) = \begin{cases} \frac{x^2 + 3x - 10}{x^2 + 2x - 15}, & x \neq -5
a, & x = -5 \end{cases} \) is continuous at \( x = -5 \), then the value of \( a \) will be
The equation of all lines having slope 2 which are tangent to the curve \( y = \frac{1}{x - 3} \), is
The function \( f(x) = (x(x - 2))^2 \) is increasing in the set
If \( a^2 x^4 + b^2 y^4 = c^4 \), then the maximum value of \( xy \) is
\[ \int \frac{1}{(x^2 + 1)^{\frac{3}{4}}} \, dx \]
is equal to
Evaluate
\[ \int_0^{\frac{\pi}{2}} \frac{\sin x}{1 + \cos^2 x} \, dx \]
is
The area intercepted by the curves \( y = \cos x \), \( x \in [0, \pi] \) and \( y = \cos 2x \), \( x \in [0, \pi] \), is
The general solution of the differential equation
\[ \frac{dy}{dx} + \sin(x + y) = \sin(x - y) \]
is
The solution to the differential equation
\[ \frac{dy}{dx} = \frac{yf'(x) - y^2}{f(x)} \]
where \( f(x) \) is a given function is
If \( \mathbf{a}, \mathbf{b}, \mathbf{c} \) are three unit vectors such that
\[ \mathbf{a} + \mathbf{b} + \mathbf{c} = \mathbf{0}, \quad \mathbf{a} \cdot \mathbf{b} = \mathbf{b} \cdot \mathbf{c} = \mathbf{c} \cdot \mathbf{a} \]
then the value of \( \mathbf{a} \cdot \mathbf{a} \) is
If vectors \( 2i + j + k \), \( 2j - 3k \), and \( 3i + j + 5k \) are coplanar, then the value of \( a \) is
The coordinates of the point where the line through the points \( A(3, 4, 1) \) and \( B(5, 1, 6) \) crosses the \( XY \)-plane are
Find the angle between the two planes \( 2x + y - 2z = 5 \) and \( 3x - 6y - 2z = 7 \).
For \( k = 1, 2, 3 \), the box \( B_k \) contains red balls and \( (k+1) \) white balls. Let \( P(B_1) = \frac{1}{2}, P(B_2) = \frac{1}{3}, P(B_3) = \frac{1}{6} \). A box is selected at random and a ball is drawn from it. If a red ball is drawn, then the probability that it came from box \( B_2 \) is
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
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
A shopkeeper wants to purchase two articles A and B of cost price \( 4 \) and \( 3 \) respectively. He thought that he may earn 30 paise by selling article A and 10 paise by selling article B. He has not to purchase total articles worth more than \( 24 \). If he purchases the number of articles of A and B, \( x \) and \( y \) respectively, then linear constraints are
Out of the four alternatives, choose the one which expresses the correct meaning of the word "SAGACIOUS".
Out of the four alternatives, choose the one which expresses the correct meaning of the word "REMEDIAL".
Out of the four alternatives, choose the one which expresses the correct meaning of the word "RETICENT".
Choose the word opposite in meaning to the given word "FIDELITY".
Choose the word opposite in meaning to the given word "INFRINGABLE".
Choose the word opposite in meaning to the given word "PROGENY".
It was not possible to drag any conclusion so he left the case.
I am looking after my pen which is missing.
“Mind your language!” he shouted.
I ..... to go there when I was a student.
She was angry ..... me.
You should not laugh ..... the poor.
1. He is a famous doctor.
2. Once I had to consult with him.
3. I never believed him.
4. He suggested me a proper remedy.
5. I become completely fine.
6. Now I also admit this fact.
We don’t know the plan of Ram.
He cares for his friends.
He is a complete person.
We want some help and advice.
As we are in trouble.
We hope he will do his best for us.
It is not my problem.
All residents of this society are careless.
I am unable to convince anyone.
They don’t want to do some good.
Every one seems to be unwise here.
We all have to suffer one day.
In a certain code language "DOME" is written as "8943" and "MEAL" is written as "4321". What group of letters can be formed for the code "38249"?
Find the missing number from the given response.
Which of the following correctly represents the relationship among illiterates, poor people, and unemployed?
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?
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
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.
\[ 3 \, - \, 5 \, + \, 8 \, + \, 2 \, - \, 10 = 13 \]
Assertion: [A] India is a democratic country.
Reason: [R] India has a constitution of its own.
Choose the correct alternative from the given options.
Which one of the following figures completes the original figure?
How many squares are there in the following figure?
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