IPU CET 2018 Physics, Chemistry, Biology Question Paper with Answer Key PDFs (April 21)

Choose the most appropriate option.
Velocity of sound in a gaseous medium is 330 ms\(^{-1}\). If the pressure is increased by 4 times without change in temperature, the velocity of sound in the gas is

(a) 330 ms−1
(b) 660 ms−1
(c) 156 ms−1
(d) 990 ms−1

A gas is enclosed in a metal container with a movable piston on top. Heat is added to the gas by placing a candle flame in contact with the container's bottom. Which of the following is true about the temperature of the gas?

(a) The temperature must go up, if the piston remains stationary
(b) The temperature must go up, if the piston is pulled out dramatically
(c) The temperature must go up no matter what happens to the piston
(d) The temperature must go down no matter what happens to the piston

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio of \( \frac{C_p}{C_v} \) for the gas is

(a) 3/2
(b) 5/3
(c) 4/3
(d) 2

A parallel plate capacitor is connected to a battery. A metal sheet of negligible thickness is placed between the plates. The sheet remains parallel to the plates of the capacitor. Which of the following is correct?

(a) The battery will supply more charge
(b) The capacitance will increase
(c) The potential difference between the plates will increase
(d) Equal and opposite charges will appear on the two faces of the metal plate

The diagrams show three circuits with identical batteries, identical inductors, and identical resistors.
Rank them according to the current through the battery just after the switch is closed from least to greatest.

(a) 3, 2, 1
(b) 1, 3, 2
(c) 1, 2, 3
(d) 3, 1, 2

A parallel plate capacitor C has a charge Q. The actual charges on its plates are

A constant voltage is applied between two ends of a uniform metallic wire. Some heat is developed in it. The heat developed is doubled, if

Use the diagram below to answer the following questions. 40 spheres of equal mass make two rings of 20 spheres each. The ring on the right has a radius twice as large as the ring on the left.



At what position could a mass be placed so that the net gravitational force that it would experience would be zero?

In a closed organ pipe, the fundamental frequency is \( v \). What will be the ratio of the frequencies of the next three overtones?

The Reynolds number for fluid flow in a pipe is independent of

A metallic ball has a spherical cavity at its centre. If the ball is heated, what happens to the cavity?

Velocity of sound in an open organ pipe is 330 m/s. The frequency of the wave is 1.1 kHz and the length of the tube is 30 cm. To which harmonic does this frequency correspond?

An electric charge \( q \) is placed at the centre of a cube of side \( l \). The electric flux through one of its faces will be

A cyclotron is operating at a frequency of 12 MHz. Mass and charge of deuteron are \( 3.3 \times 10^{-27} \, kg \) and \( 1.9 \times 10^{-19} \, C \). To accelerate deuteron, the necessary magnetic field is

A cylinder rolls up an inclined plane at an angle of 30°. At the bottom of the inclined plane, the centre of mass of the cylinder has speed of 5 m/s. How long will it take to return to the bottom?

Wave represented by the equation \( y_1 = A \cos(kx - \omega t) \) is superimposed on another wave to form a stationary wave such that the point \( x = 0 \) is a node. The equation representing the wave is given by

Two liquid drops of equal radii are falling through air with the terminal velocity \( v \). If these two drops coalesce to form a single drop, its terminal velocity will be

Five organ pipes are described below. Which one has the highest frequency fundamental?

A coil in the shape of an equilateral triangle of side \( l \) is suspended between two pole pieces of a permanent magnet, such that the magnetic field, \( B \), is in the plane of the coil. If due to a current \( I \) in the triangle, a torque \( \tau \) acts on it, the side \( l \) of the triangle is

The engineer of a train blows the train whistle as he approaches a crossing. A few moments later, he hears an echo from the whistle. The engineer hears the echo of the whistle because of

A Carnot engine takes \( 3 \times 10^8 \) cal of heat from a reservoir at 627°C and gives it to a sink at 27°C. The work done by the engine is

Photoelectron emission rate is a direct function of radiation

Two identical non-conducting spheres having charges of -12 nC and +8 nC are touched together and then separated. The final charge on each is

The potential energy of gravitational interaction of a point mass \( m \) and a thin uniform rod of mass \( M \) and length \( L \), if they are located along a straight line at a distance \( a \) from each other, is

A positive charge enters a magnetic field and travels parallel to but opposite the field. The charge feels or experiences

A simple harmonic wave of amplitude 8 units travels along the positive x-axis. At any given instant of time, for a particle at a distance of 10 cm from the origin, the displacement is +6 units and for a particle at a distance of 25 cm from the origin, the displacement is +4 units. Calculate the wavelength.

The diagrammatic representation of a heat engine above shows which of the following?

A force is applied to an object that is free to move. Which of the following statements is correct?

A rigid bar of mass 15 kg is supported symmetrically by three wires each 2 m long. Those at each end are of copper and the middle one is of iron. Determine the ratio of their diameters if each is to have the tension.

An astronaut is standing on an asteroid when he accidentally drops a wrench. He observes that the gravitational acceleration on the asteroid is 2.4 m/s². If he had thrown the wrench at an upward angle instead, he would have found the gravitational acceleration on the asteroid to be

The two-dimensional cube in the diagram below has charged objects placed at the corners as shown. An electron that is free to move is placed at the exact centre of the cube. In which direction will the electron move?

A body takes 5 min for cooling from 50°C to 40°C. Its temperature comes down to 33.33°C in the next 5 min. Temperature of the surroundings is

A TV tower has a height of 100 m. How much population is covered by TV broadcast, if the average population density around the tower is \( 1000 \, km^{-2} \) (radius of Earth = \( 6.4 \times 10^6 \, m \))?

The number of neutrons released during the fission reaction \[ n + ^{235} U \longrightarrow ^{133} Sb + ^{99} Nb + neutrons is \]

For a monoatomic gas, work done at constant pressure is W. The heat supplied at constant volume for the same rise in temperature of the gas is

For constructive interference to take place between two monochromatic light waves of wavelength \( \lambda \), the path difference should be

If the work done in stretching a wire by 1 mm is 2 J, the work necessary for stretching another wire of the same material but with double radius of cross-section and half the length by 1 mm is

A particle of mass \( m \) executes SHM with amplitude \( a \) and frequency \( v \). The average kinetic energy during its motion from the position of equilibrium to the end is

Two identical thin plano-convex glass lenses (refractive index 1.5) each having radius of curvature of 20 cm are placed with their convex surfaces in contact at the center. The intervening space is filled with oil of refractive index 1.7. The focal length of the combination is

A force \( F = (2 + x) \, N \) acts on a particle in the x-direction. The work done by this force during a displacement from \( x = 1.0 \, m \) to \( x = 2.0 \, m \) is

When a hydrogen atom is raised from the ground state to the fifth state

A particle moves in one dimension. Its velocity is given by \( v(t) = c_2 t^2 + c_1 t + c_0 \) where \( c_1 \) and \( c_2 \) are constants. What is the acceleration of the particle at time \( t = 1 \)?

A light ray falls on a square glass slab as shown in the figure. The index of refraction of the glass, if total internal reflection is occur at vertical face, is equal to

A positive point charge is placed at the origin. There is an electric field \( E'(x) = 2, 2 + 3 \) that accelerates the Udder point charge along the x-axis. Determine the energy of the charge when it reaches the position \( x = 21 \).

A 4 cm thick layer of water covers a 6 cm thick glass slab. A coin is placed at the bottom of the slab and is being observed from the air side along the normal to the surface. Find the apparent position of the coin from

A substance's specific heat is a function of its

There is a plane of uniform positive charge density \( \sigma \) parallel to the yz-plane and located at \( x = 2d \). A point charge \( q^+ \) is placed at the origin. Solve for the position \( x \) along the x-axis, where a positive test charge will have a net force of zero.

A displacement vector is a

The difference between two audible frequencies is about 4 Hz. If one frequency and the speed of sound is 340 m/s, the other frequency might be about

At high altitude, a body at rest explodes into two equal fragments with one fragment receiving horizontal velocity of 10 m/s. Time taken by the two radius vectors connecting point of explosion of fragments to make 90° is

Which of the following best explains, why a hot air balloon rises?

Which of the following molecules can be described as having sp hybridisation?

How many milliliters of water must be added to 50.0 mL of 10.0 M HNO3 to prepare 4.00 M HNO3?

The energy required to excite the electron in the atom from n=1 to n=2, when the ionisation enthalpy of hydrogen atom is \(1.312 \times 10^6\) J/mol will be (in the unit of \(10^5\))

Beyond the critical point of H2O

For the isoelectronic series \(S^{2-}, Cl^{-}, Ar, K^{+}\) and \(v\), which species requires the least energy to remove an outer electron?

Stomach acid has a pH of approximately 2. Sour milk has a pH of 6. Stomach acid is

Which of the following choices represents \(^{239}_{94}Pu\) producing a positron?

What is the conjugate base of \(H_2CO_3\) according to the Bronsted-Lowry theory?

What happens when the temperature of a reaction increases?

What is the minimum power required for heat engine to lift a 80 kg mass 5 m in 20 s if it releases 1000 J of heat energy from its exhaust each second?

Calculate the mass percent of 60 g H2SO4 dissolved in the solution of 180 mL of water.

Which of the following stereoisomers is a major image of itself?

Among all the given compounds, which will have D-configuration?

All of the following may be true concerning catalysts and the reaction which catalyse except,

NH3 has a Kb of \(1.8 \times 10^{-3}\). Which of the following has a \(5.6 \times 10^{-10}\)?

When 2.00 g of a certain volatile liquid is heated, the volume of the resulting vapour is 821 mL at a temperature of 127°C at standard pressure. The molecular mass of this substance is:

• (a) 20.0 g/mol
• (b) 40.0 g/mol
• (c) 80.0 g/mol
• (d) 120.0 g/mol

Among [Ni(CN)4]^{2-}, [NiCl4]^{2-} and [Ni(CO)4], which one has the following:

• (a) [NiCl4]^{2-} is square planar and [Ni(CN)4]^{2-}, Ni(CO)4 are tetrahedral
• (b) Ni(CO)4 is square planar and [Ni(CN)4]^{2-} [NiCl4]^{2-} are tetrahedral
• (c) Ni(CN)4^{2-} is square planar [NiCl4]^{2-} Ni(CO)4
• (d) None of these

Given a molecule with the general formula AB, which one of the following would be the most useful in determining whether the molecule was bent or linear?

Which of the following expressions represents the solubility product for Cu(OH)\(_2\)?

Which of the following represents an ester?

Ammonia burns in air to form nitrogen dioxide and water. \[ 4NH_3(g) + 7O_2(g) \longrightarrow 4NO_2(g) + 6H_2O(l) \]
If 8 moles of NH3 are reacted with 14 moles of O2 in a rigid container with an initial pressure of 11 atm, what is the partial pressure of NO2 in the container when the reaction runs to completion? (Assume constant temperature)

Beryllium gives a compound X with the following percentage composition: Be = 6.1%, N = 37.8%, Cl = 48%, H = 8.1%. Molecular weight of X is 148 g/mol and that of Be is 9 g/mol. The molecular formula of the compound is

An object experiences a greater buoyant force in seawater than in fresh water. The most likely reason for this is

The reaction below represents the Haber process for the industrial production of ammonia, \[ N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g); \Delta H^\circ = -92 \, kJ \]
The optimum conditions of temperature and pressure are chosen as a compromise between those that favour a high yield of ammonia and those that favour a fast rate of production. Economic considerations are also important. Which statement is correct?

On combustion of x-g of ethanol in a bomb calorimeter, y-joules of heat energy is produced. The heat of combustion of ethanol (\(\Delta H_{comb}\)) is

A balloon contains 2.0 g of hydrogen gas. A second balloon contains 4.0 g of helium gas. Both balloons are at the same temperature and pressure. Pick the false statement from the following list.

Ammonia reacts with water to form the ammonium ion and hydroxide ion. \[ NH_3 + H_2O \longrightarrow NH_4^+ + OH^- \]
According to the Bronsted-Lowry definition of acids and bases, what is the conjugate acid of ammonia?

The vapour pressure of pure water is 23.5 mm Hg. Then, the vapour pressure of an aqueous solution which contains 5 mass percent of urea is (Molar mass of urea is 60).

Choose the one false statement.

Choose the most appropriate option.
The first step in producing pure lead from galena (PbS) is as follows: \[ 2PbS(s) + 3O_2(g) \longrightarrow 2PbO(s) + 2SO_2(g) \]
All of the following are true concerning this reaction except:

When the following 1.0 mol dm\(^{-3}\) aqueous solutions are arranged in order of increasing pH, which is the correct order?

I. Ammonium chloride
II. Ammonium ethanoate
III. Sodium ethanoate

When the solids Ba(OH)2 and NH4SCN are mixed, a solution is produced and the temperature drops. \[ Ba(OH)_2(s) + 2NH_4SCN(s) \rightarrow Ba(SCN)_2(aq) + 2NH_3(g) + 2H_2O(l) \]
Which statement about the energetics of this reaction is correct?

Argon crystallises in fcc arrangement and the density of solid and liquid Ar is 1.59 g/cm\(^3\) and 1.42 g/cm\(^3\), respectively. The percentage of empty space in liquid Ar is

A student wished to produce only carbon from the dioxide and water vapour combustion of methane, CH\(_4\). To accomplish this the student should

Which of the following elements is the most chemically similar to Na?

The rate of the chemical reaction between substance A and B is found to follow the rate law.
rate = \( k[A]^2[B] \), where k is the rate constant. The concentration of A is reduced to half of its original value. To make the reaction occur at 50% of its original rate, the concentration of B should be

When 4A of current is passed through a 1.0L, 0.10 M Fe\(^3+\)(aq) solution for 1 hour, it is partly reduced to Fe(s) and partly to Fe\(^2+\)(aq). Identify the incorrect statement.

Calculate the rate constant for the radioactive disintegration of an isotope that has a half-life of 6930 yr.

Choose the most appropriate options. Identify the product B of the following reactions.

The following data was obtained for the reaction,

Which of the following are true statements?

I. The heat capacity of a substance is the amount of heat that substance can hold per unit of temperature.
II. The specific heat for a single substance is the same for all phases of that substance.
III. When heat is added to a fluid, its temperature will change less if it is allowed to expand.

Compared to an electron with a principal quantum number of 1, an electron with a principal quantum number of 2 will have a

What is the minimum number of moles of Pb(NO3) must be added to 0.10L of a solution that is 1.0M in MgCl2 and 1.0 M in KCl? The compound PbCl2 precipitates.

Which one of the following electrolytes is most effective for the coagulation of \(Fe(OH)_3\) sol?

Which species have delocalised electrons?

Choose the most appropriate options.
Arrange the following compounds in the increasing order of their reactivity towards HCN:
I. Acetaldehyde
II. Acetone
III. Di-tert-butyl ketone

The Ksp for Mn(OH)\(_2\) is \(1.6 \times 10^{-13}\). What is the molar solubility of this compound in water?

Choose the most appropriate options.
The magnetic moment of M^{x+ (atomic number = 25) is \(\sqrt{5}\) BM. Then, the oxidation number x of M is:

Choose the most appropriate options.
Arrange the following in the decreasing order of basic character:
I. p-toluidine
II. N,N-dimethyl-p-toluidine
III. p-nitroaniline
IV. Aniline

In how many ways can 10 identical objects be put in 8 distinct boxes in such that no box is empty?

Choose the most appropriate option.
\(\lim_{x \to 1} x^{(1-x)}\) is equal to:

In how many ways can 3 blue, 4 white and 2 red balls be distributed into 4 distinct boxes?

Choose the most appropriate options.
If \(\alpha\) and \(\beta\) are non-real numbers satisfying \(x^3 - 1 = 0\), then the value of \[ \left| \begin{matrix} \lambda+1 & \alpha & \beta
\beta & \lambda + \beta & 1
1 & \lambda + \alpha & \lambda + \alpha \end{matrix} \right| \]
is:

In how many ways can 5 men and 3 women be seated in a row such that no two women sit adjacent?

Choose the most appropriate option. \[ \int_{-2}^{2} \frac{3x^7 - 2x^5 + x^3 - 3}{x^4 + 3x^2 + 1} \, dx \]

Choose the most appropriate option. \[ \left| \begin{matrix} x+1 & x+2 & x+4
x+3 & x+5 & x+8
x+7 & x+10 & x+14 \end{matrix} \right| \]

In a class, there are 10 boys and 8 girls. When 3 students are selected at random, the probability that 2 girls and 1 boy are selected, is

Is equal to \[ \left| \begin{matrix} b^2 + c^2 & c^2 + b^2
c^2 & c^2 + a^2
b^2 & a^2 + b^2 \end{matrix} \right| \]

Choose the most appropriate option.
If \(y = a^b x\), then

Let \( S \) be the set of all points with coordinates \( (x, y, z) \), where \( x, y, z \) are each chosen from the set \([0, 1, 2]\). How many equilateral triangles have all their vertices in \( S \)?

The value of the integral \( \int_{-3}^{5} |x - 3| \, dx \) is

Six ants simultaneously stand on the six vertices of a regular octahedron with each ant at a different vertex. Simultaneously and independently, each ant moves from its vertex to one of the four adjacent vertices, each with equal probability. What is the probability that no two ants arrive at the same vertex?

If A and B are independent events such that \( P(B) = \frac{2}{7} \), \( P(A \cup B) = 0.8 \), then \( P(A) = \)?

The series \( 1 + 1 + \frac{3}{2^2} + \frac{4}{2^3} + \frac{5}{2^4} + \cdots \) is equal to

The line \( y = mx + C \) will be tangent to the ellipse \( \frac{x^2}{9} + \frac{y^2}{4} = 1 \) if \( C \) is equal to

Determine the form of the conic section described by the equation \( x^2 + y^2 + 2xy - 8x + 8y = 0 \)

• (a) Circle
• (b) Parabola
• (c) Hyperbola
• (d) A pair of straight lines

Choose the most appropriate options.
Let \( P = \{ \theta : \sin \theta - \cos \theta = \sqrt{2} \cos \theta \} \) and \( Q = \{ \theta : \sin \theta + \cos \theta = \sqrt{2} \sin \theta \} \). Then,

• (a) \( P \subset Q \) and \( Q - P \neq \emptyset \)
• (b) \( Q \not\subset P \)
• (c) \( P \not\subset Q \)
• (d) \( P = Q \)

\( 8 \cos^4 x - 8 \cos^2 x + 1 \) is equal to

• (a) \( \cos 4x \)
• (b) \( \sin 4x \)
• (c) \( \cos 2x - \sin 4x \)
• (d) \( \cos 2x + \sin 4x \)

Choose the most appropriate options.
If \(a, b, c\) are positive real numbers, then
\[ \frac{1}{\log_{abc}} + \frac{1}{\log_{abc}} + \frac{1}{\log_{abc}} = \]

• (a) 0
• (b) 1
• (c) 2
• (d) 3

Find the distance from the point \( A(2, 3, -1) \) to the given straight lines \( 2x - 2y + z + 3 = 0 \) and \( 3x - 2y + 2z + 17 = 0 \).

• (a) \( \frac{1}{\sqrt{5}} \)
• (b) 19.13
• (c) \( \frac{3}{\sqrt{5}} \)
• (d) \( \frac{6}{\sqrt{5}} \)

If \( \sin \theta + \csc \theta = 2 \), then the value of \( \sin^{10} \theta + \csc^{10} \theta \) is

The determinant of the matrix \[ \begin{pmatrix} 1 & 2 & 3
4 & 5 & 6
7 & 8 & 9 \end{pmatrix} \]
is equal to

The standard deviation of a data is 6, when each observation is increased by 1, then the standard deviation of the new data is

Compute the determinant of the \(n \times n\) matrix whose elements are identified by the condition \(a_{ij} = \min(i,j)\), where \(i\) is the row number and \(j\) is the column number.

Let \( T_n \) denote the number of triangles which can be formed using the vertices of a regular polygon of \( n \) sides. If \( T_{n+1} - T_n = 21 \), then \( n \) equals

Find \( \frac{dy}{dx} \) where \( a^y = \left( \frac{x}{y} \right)^a \)

If the arithmetic mean of the following data is 7, then \( a + b = \) \[ \begin{array}{|c|c|c|c|c|} \hline x_i & 4 & 6 & 7 & 9
f_i & a & 4 & b & 5
\hline \end{array} \]

The integral \( \int 34x^4 dx \) is equal to

The integral \( \int e^{\sec x} \tan x \sec x \, dx \) is equal to

Solve for \( x \left(a \neq 0\right) } \sqrt{(a + x)^2 + 4\sqrt{(a - x)^2} = 5\sqrt{a^2 - x^2}}

The value of \( \int_0^{\frac{\pi}{2}} e^x \cos x \, dx \) is equal to:

Find the area of the figure bounded by the parabola \( y^2 = 4x \) and \( x^2 = 4y \).

The eccentricity of the hyperbola \( \frac{\sqrt{1999}}{3} \left( x^2 - y^2 \right) = 1 \) is

Consider sequences of positive real numbers of the form \( x, 2000, y, \dots \), in which every term after the first is 1 less than the product of its two immediate neighbors. For how many different values of \( x \) does the term 2001 appear somewhere in the sequence?

The exradii of a triangle \( r_1, r_2, r_3 \) are in harmonic progression, then the sides \( a, b \) and \( c \) are in

Let \( f(x) = x^2 + 6x + 1 \) and let \( R \) denote the set of points \( (x, y) \) in the coordinate plane such that \( f(x) + f(y) \) so and \( f(x) - f(y) \leq 0 \). Which of the following is closest to the area of \( R \)?

Let \( n \) be a 5-digit number and let \( q \) and \( r \) be the quotient and remainder respectively, when \( n \) is divided by 100. For how many values of \( n \) is \( q + r \) divisible by 11?

If \( \tan \frac{\pi}{18}, x \) and \( \tan \frac{\pi}{18} \) are in AP and \( \tan \frac{5\pi}{18} \) are in AP, then the value of \( \frac{x}{y} \) will be

A line segment with the end points \( A(3,-2) \) and \( B(6,4) \) is divided into three equal parts. Find the coordinates of the division points.

Three mutually tangent spheres of radius 1 rest on a horizontal plane. A sphere of radius 2 rests on them. What is the distance from the plane to the top of the larger sphere?

If the line \( x - 1 = 0 \) is the directrix of the parabola \( y^2 - kx + 8 = 0 \), then one of the values of \( k \) is

Find the limit \[ \lim_{x \to 0} \left( 1 + \tan^2 \sqrt{x} \right)^{3/x} \]

Evaluate the limit: \[ \lim_{x \to a} \frac{\log{(x^{a-1})}}{x-a} \]

For real \( x \), let \( f(x) = x^3 + 5x + 1 \), then:

Evaluate the limit: \[ \lim_{x \to 0} \frac{1 - \cos 4x}{2 \sin^2 x + x \tan 7x} \]

Negation of the statement \( (\rho \land r) \rightarrow (r \lor q) \) is

Given the vertices of a triangle are \( A(1, -1, -3) \), \( B(2, 1, -2) \), and \( C(-5, 2, -6) \). Compute the length of the bisector of the interior angle at vertex A.

It is known that \( AB = 2a - 6b \) and \( AC = 3a + b \), where \( a \) and \( b \) are mutually perpendicular unit vectors. Determine the angles of the AABC.

The value of \( \int \frac{\sin^2 x \cos^2 x}{(\sin^3 x + \cos^3 x)^2} \, dx \) is