Que: The density of cube is measured by measuring its mass and the length of its sides. If the maximum errors
in the measurement of mass and length are 3% and 2% respectively, then the maximum error in the
measurement of density is

1. 9%
2. 7%
3. 5%
4. 1%

Que: The incorrect statement among the following is

1. The first ionization potential of Al is less than the first ionization potential of Mg
2. The second ionization potential of Mg is greater than the second ionization potential of Na
3. The first ionization potential of Na is less than the first ionization potential of Mg
4. The third ionization potential of Mg is greater than the third ionization potential of Al

Que: An infinite number of masses, each of 1 kg, are placed on the positive x-axis at 1 m, 2 m, 4 m, 8 m, …. from the origin. The value of the gravitational field at the origin due to this distribution is

1. 2G
2. 
3. 
4. ∞

Que: Base strength of

(A)

1. (B) > (A) > (C)
2. (C) > (B) > (A)
3. (A) > (C) > (B)
4. (A) > (B) > (C)

Que: The work done by the frictional force on a surface in drawing a circle of radius r on the surface by a pencil of negligible mass with a normal pressing force N (coefficient of friction μ_k) is :

1. 4πr²μ_k N
2. -2πr²μ_k N
3. -3πr²μ_k N
4. -2πrμ_k N

Que: Three masses of 1 kg, 6 kg and 3 kg are connected to each other with threads and are placed on table as shown in figure, What is the acceleration with which the system is moving ? Take g = 10m s^-2

1. Zero
2. 1 m s^-2
3. 2 m s^-2
4. 3 m s^-2

Que: Identify the correct order of the size of the following:

1. Ca²⁺< K⁺< Ar < Cl^- < S^2-
2. Ar < Ca²⁺< K⁺< Cl^- < S^2-
3. Ca²⁺< Ar < K⁺< Cl^- < S^2-
4. Ca²⁺ < K⁺ < Ar < S^2- < Cl^-

Que: The accepted IUPAC name of camphor is:

1. 1, 7, 7 - trimethylbicyclo [2, 2, 1] heptan - 2 - one
2. 1, 7, 7 - trimethylbicyclo [2, 1, 2] heptan - 2 - one
3. 1, 2, 2 - trimethylbicyclo [2, 2, 1] heptan - 6 - one
4. none of these

Que:

1. 
2. 
3. 
4. None of these

Que: A thin circular ring of mass M and radius R is rotating about its axis with a constant angular velocity ω. Two objects, each of mass m are attached gently to the opposite ends of the diameter of the ring. The wheel now rotates with an angular velocity.

Que: There are 60 terms in an A.P. of which the first term is 8 and the last term is 185. The 31^st term is

1. 56
2. 94
3. 85
4. 98

Que: The number of moles of H₂ in 0.224 litres of hydrogen gas at STP(273 K, 1 atm) is:

1. 0.1
2. 0.01
3. 0.001
4. 1

Que:

1. 
2. 
3. 
4. zero

Que: Equation of a line which is passing through (3, - 4) and making an angle of with x-axis is:

1. x - y - 7 = 0
2. x + y + 7 = 0
3. x - y + 7 = 0
4. x + y - 7 = 0

Que:

1. ab + bc + cd
2. (ab + bc + cd)²
3. (ab + bc + cd)⁴
4. None of these

Que: In the following balanced reaction, values of X, Y, and Z respectively are

1. 2, 5, 16
2. 8, 2, 5
3. 5, 2, 16
4. 5, 8, 4

Que: If the nitrogen atom had electronic configuration 1s⁷ it would have energy lower than that of the normal ground state configuration 1s² 2s² 2p³ because the electrons would be closer to the nucleus. Yet 1s⁷  is not observed because it violates:

1. Heisenberg's uncertainty principle
2. Hund's rule
3. Pauli's exclusion principle
4. Bohr postulate of stationary orbits

Que: A thin uniform wire is bent to form the two equal sides AB and AC of triangle ABC, where AB = AC = 5 cm. The third side BC, of length 6cm, is made from uniform wire of twice the density of the first. The distance of centre of mass from A is :

Que: When 97.52 is divided by 2.54, the correct result is

1. 38.3937
2. 38.394
3. 38.39
4. 38.4

Que: Two cylinders having radii 2R and R and moments of inertia 4I and I about their central axes are supported by axles perpendicular to their
planes. The large cylinder is initially rotating clockwise with angular velocity  . The small cylinder is moved to the right until it touches the large cylinder and is caused to rotate by the frictional force between the two. Eventually slipping ceases and the two cylinders rotate at rates in opposite directions. During this

1. angular momentum of system is conserved
2. kinetic energy is conserved
3. neigher the angular momentum nor the kinetic energy is conserved
4. both the angular momentum and kinetic energy are conserved.

Que: Let R be the relation on the set N of natural numbers defined by R:{(x, y): x + 3y = 12, x ϵ N, y ϵ N}. Find R

1. {(8, 1), (6, 2), (3, 3)}
2. {(9, 1), (4, 2), (3, 3)}
3. {(9, 1), (6, 2), (3, 3)}
4. {(7, 1), (6, 2), (2, 2)}

Que: A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement x is proportional to

1. x²
2. e^x
3. x
4. log_e^x

Que: A straight line L perpendicular to the line 5x – y = 1. The area of the triangle formed by the line L and co-ordinates axes is 5, then the equation of line is-

1. 
2. 
3. 
4. None of these

Que: The frequency of light emitted for the transition n = 4 to n = 2 of the  is equal to the transition in H atom corresponding to which of the following?

1. n = 2 to n = 1
2. n = 3 to n = 2
3. n = 4 to n = 3
4. n = 3 to n = 1

Que: An organic compound contains 49.3% carbon, 6.84% hydrogen and its vapour density is 73. The molecular formula of the compound is

1. C₃H₅O₂
2. C₄H₁₀O₂
3. C₆H₁₀O₄
4. C₃H₁₀O₂

Que: A uniform rod of length 2l is placed with one end in contact with the horizontal table and is then inclined at an angle  to the horizontal and allowed to fall. When it becomes horizontal, its angular velocity will be

Que: If a, b, c are real and a ≠ b, then the roots of the equation 2 (a - b)x² - 11 (a + b + c) x - 3 (a - b) = 0 are

1. Real and equal
2. Real and unequal
3. Purely imaginary
4. None of these

Que: A man can swim at a speed of 5 km/h w.r.t. water. He wants to cross a 1.5 km wide river flowing at 3 km/h. He keeps himself always at an angle of 60º with the flow direction while swimming. The time taken by him to cross the river will be

1. 0.25 hr
2. 0.35 hr
3. 0.45 hr
4. 0.55 hr

Que: If A and B are any two sets, then

1. 
2. 
3. 
4. Both 1 and 2

Que: The Low density of ice compared to water is due to:

1. Hydrogen bonding interactions
2. dipole-dipole interactions
3. Dipole-induced dipole interactions
4. Induced dipole-induced dipole interactions

Que: Which molecule/ion out of the following does not contain unpaired electrons?

1. 
2. O₂
3. 
4. B₂

Que:

1. 1/a
2. -1/a
3. 1/a²
4. -1/a²

Que: Which of the following has the highest dipole moment?

Que: A space ship is launched into a circular orbit close to the earth’s surface. What additional velocity should now be imparted to the space ship in the orbit to over come the gravitational pull (radius of earth = 6400 km and g = 9.8 m/sec²).

1. 4.2 km/sec
2. 4.8 km/sec
3. 3.2 km/sec
4. 3.3 km/sec

Que: Which of the following sequence of T and F is correct for given statements. Here T stands for True statement and F stands for False statement

a. The more the number of contributing structures, the more is the resonance energy.

b. The resonance structures have different positions of nuclei but the same number of unpaired electrons

c. The energy of the actual structure of the molecule (the resonance hybrid) is lower than that of any of the canonical structures.

1. TTT
2. TFT
3. FFF
4. TFF

Que: Fractional distillation is used when:

1. there is a large difference in the boiling points of liquids
2. there is a small difference in the boiling points liquids
3. boiling points of liquid are same
4. liquids form a constant boiling mixture

Que: If we consider that 1/6, in place of 1/12, the mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of the substance will

1. Be a function of the molecular mass of the substance
2. Remain unchanged
3. increase two-fold
4. decrease twice

Que:

1. 1
2. 2
3. 3
4. None of these

Que:

1. 
2. 1 and 0
3. 
4. 

Que: A semicircular portion of radius ‘r’ is cut from a uniform rectangular plate as shown in figure. The distance of centre of mass 'C' of remaining plate, from point ‘O’ is :

Que:

1. -2
2. -1
3. -3
4. -4

Que: If sample A contains 100 observations 101, 102, …..200 and sample B contains 100 observations 151, 152, …….250, then the ratio of variance v_A /v_B =

1. 1
2. 9/4
3. 4/9
4. 2/3

Que: The coordinates of a moving particle at any time t are given by x = ct²  and y = bt². The speed of the particle is given by:

1. 2t(c + b)
2. 
3. 
4. 

Que: All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given?

1. Mean
2. Median
3. Mode
4. Variance

Que: What does the shaded region represent in the figure given below?