Test: BITSAT Past Year Paper- 2016

The molecules of a given mass of a gas have r.m.s. velocity of 200 ms^–1 at 27°C and 1.0 × 10⁵ Nm^–2 pressure. When the temperature and pressure of the gas are respectively, 127°C and 0.05 × 10⁵ Nm^–2, the r.m.s. velocity of its molecules in ms^–1 is :

An inductor of inductance L = 400 mH and resistors of resistance R₁ = 2Ω and R₂ = 2Ω are connected to a battery of emf 12 V as shown in the figure. The internal resistance of the battery is negligible. The switch S is closed at t = 0. The potential drop across L as a function of time is

Two wires are made of the same material and have the same volume. However wire 1 has crosssectional area A and wire 2 has cross-sectional area 3A. If the length of wire 1 increases by Δx on applying force F, how much force is needed to stretch wire 2 by the same amount?

Two spheres of different materials one with double the radius and one-fourth wall thickness of the other are filled with ice. If the time taken for complete melting of ice in the larger sphere is 25 minute and for smaller one is 16 minute, the ratio of thermal conductivities of the materials of larger spheres to that of smaller sphere is

A biconvex lens h as a radius of curvature of magnitude 20 cm. Which one of the following options best describe the image formed of an object of height 2 cm placed 30 cm from the lens?

In the figure below, what is the potential difference between the point A and B and between B and C respectively in steady state

A radioactive element X converts into another stable element Y. Half life of X is 2 hrs. Initially only X is present. After time t, the ratio of atoms of X and Y is found to be 1 : 4, then t in hours is

The approximate depth of an ocean is 2700 m. The compressibility of water is 45.4 × 10^–11 Pa^–1 and density of water is 10³ kg/m³.What fractional compression of water will be obtained at the bottom of the ocean?

A frictionless wire AB is fixed  on a sphere of radius R. A very small spherical ball slips on this wire. The time taken by this ball to slip from A to B is

A string of length ℓ is fixed at both ends. It is vibrating in its 3^rd overtone with maximum amplitude 'a'.  The amplitude at a distance ℓ/3 from one end is

A deuteron of kinetic energy 50 keV is describing a circular orbit of radius 0.5 metre in a plane perpendicular to the magnetic field B. The kinetic energy of the proton that describes a circular orbit of radius 0.5 metre in the same plane with the same B is

In the circuit shown in the figure, find the current in 45 Ω.

Kepler's third law states that square of period of revolution (T) of a planet around the sun, is proportional to third power of average distance r between sun and planet i.e. T² = Kr³ here K is constant. If the masses of sun and planet are M and m respectively then as per Newton's law of gravitation force of attraction between them is here G is gravitational constant. The relation between G and K is described as

Find the number of photon emitted per second by a 25 watt source of monochromatic light of wavelength 6600 Å. What is the photoelectric current assuming 3% efficiency for photoelectric effect ?

A ray of light of intensity I is incident on a parallel glass slab at point A as shown in diagram. It undergoes partial reflection and refraction. At each reflection, 25% of incident energy is reflected. The rays AB and A'B' undergo interference. The ratio of I_max and I_min is :

A capillary tube of radius r is immersed vertically in a liquid such that liquid rises in it to height h (less than the length of the tube).  Mass of liquid in the capillary tube is m. If radius of the capillary tube is increased by 50%, then mass of liquid that will rise in the tube, is

The drift velocity of electrons in silver wire with cross-sectional area 3.14 × 10^–6 m² carrying a current of 20 A is. Given atomic weight of Ag = 108, density of silver = 10.5 × 10³ kg/m³.

A parallel plate capacitor of area ‘A’ plate separation ‘d’ is filled with two dielectrics as shown. What is the capacitance of the arrangement?

In the Young’s double-slit experiment, the intensity of light at a point on the screen where the path difference is λ is K, (λ being the wave length of light used). The intensity at a point where the path difference is λ/4, will be :

The mass of ₇N¹⁵ is 15.00011 amu, mass of ₈O¹⁶ is 15.99492 amu and m_p = 1.00783 amu. Determine binding energy of last proton of ₈O¹⁶.

A wire carrying current I has the shape as shown in adjoining figure. Linear parts of the wire are very long and parallel to X-axis while semicircular portion of radius R is lying in Y-Z plane. Magnetic field at point O is:

A stone projected with a velocity u at an angle θ with the horizontal reaches maximum height H₁. When it is projected with velocity u at an angle with the horizontal, it reaches maximum height H₂. The relation between the horizontal range R of the projectile, heights H₁ and H₂ is

If the series limit wavelength of Lyman series for the hydrogen atom is 912 Å then the series limit wavelength for Balmer series of hydrogen atoms is

In the shown arrangement of the experiment of the meter bridge if AC corresponding to null deflection of galvanometer is x, what would be its value if the radius of the wire AB is doubled?

A 1 kg mass is attached to a spring of force constant 600 N/m and rests on a smooth horizontal surface with other end of the spring tied to wall as shown in figure. A second mass of 0.5 kg slides along the surface towards the first at 3m/s. If the masses make a perfectly inelastic collision, then find amplitude and time period of oscillation of combined mass.

The frequency of vibration of string is given by 

Here p is number of segments in the string and / is the length. The dimensional formula for m will be

For the angle of minimum deviation of a prism to be equal to its refracting angle, the prism must be made of a material whose refractive index:

Consider elastic collision of a particle of mass m moving with a velocity u with another particle of the same mass at rest. After the collision, the projectile and the struck particle move in directions making angles θ₁ and θ₂ respectively with the initial direction of motion. The sum of the angles θ₁ + θ₂, is:

A conducting circular loop is placed in a uniform magnetic field of 0.04 T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at 2 mm/s. The induced emf in the loop when the radius is 2 cm is

Figure below shows two paths that may be taken by a gas to go from a state A to a state (c) In process AB, 400 J of heat is added to the system and in process BC, 100 J of heat is added to the system. The heat absorbed by the system in the process AC will be

Two resistances at 0°C with temperature coefficient of resistance α₁ and α₂ joined in series act as a single resistance in a circuit. The temperature coefficient of their single resistance will be

Two identical charged spheres suspended from a common point by two massless strings of lengths l, are initially at a distance d (d << l ) apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity v. Then v varies as a function of the distance x between the spheres, as :

A point particle of mass 0.1 kg is executing S.H.M. of amplitude of 0.1 m. When the particle passes through the mean position, its kinetic energy is 8 x 10^-3 Joule. Obtain the equation of motion of this particle if this initial phase of oscillation is 45°.

A source of sound S emitting waves of frequency 100 Hz and an observor O are located at some distance from each other. The source is moving with a speed of 19.4 ms^-1 at an angle of 60° with the source observer line as shown in the figure. The observor is at rest. The apparent frequency observed by the observer is (velocity of sound in air 330 ms^-1)

A resistor of resistance R, capacitor of capacitance C and inductor of inductance L are connected in parallel to AC power source of voltage ε₀ sin ωt. The maximum current through the resistance is half of the maximum current through the power source. Then value of R is

A lens having focal length f and aperture of diameter d forms an image of intensity I. Aperture of diameter d/2 in central region of lens is covered by a black paper. Focal length of lens and intensity of image now will be respectively:

A circular disc of radius R and thickness R/6 has moment inertia I about an axis passing through its centre perpendicular to its plane. It is melted and recasted into a solid sphere. The moment of inertia of the sphere about its diameter is

In PO^3-₄, the formal charge on each oxygen atom and the P - O bond order respectively are

The decreasing order of the ionization potential of the following elements is

Knowing that the chemistry of lanthanoids(Ln) is dominated by its + 3 oxidation state, which of the following statements is incorrect?

Which of the following arrangements does not represent the correct order of the property stated against it?

Which of the following is paramagnetic?

The hypothetical complex chloro-diaquatriamminecobalt (III) chloride can be represented as

The normality of 26% (wt/vol) solution of ammonia (density = 0.855 ) is approximately :

1.25 g of a sample of Na₂CO₃ and Na₂SO₄ is dissolved in 250 ml solution. 25 ml of this solution neutralises 20 ml of 0.1N H₂SO₄.The % of Na₂CO₃ in this sample is

Which of the following compound has all the four types (1°, 2°, 3° and 4°) of carbon atoms?

Which of the following has two stereoisomers?

The compounds A and B, respectively are

Give the possible structure of X in the following reaction :

An aromatic compound has molecular formula C₇H₇Br. Give the possible isomers and the appropriate method to distinguish them.

Which of the following method gives better yield of p-nitrophenol?

Formation of polyethylene from calcium carbide takes place as follows
CaC₂ + 2H₂O → Ca (OH)₂ + C₂H₂
C₂H₂ + H₂ → C₂H₄
nC₂H₄ → (-CH₂ - CH₂ -)n
The amount of polyethylene obtained from 64.1 kg of CaC₂ is

The most likely acid-catalysed aldol condensation products of each of the two aldehydes I and II will respectively be

Sometimes, the colour observed in Lassaigne’s test for nitrogen is green. It is because

Fructose on reduction gives a mixture of two alcohols which are related as

What will happen when D-(+)-glucose is treated with methanolic —HCl followed by Tollens’ reagent?

Which of the followings forms the base of talcum powder?

The important antioxidant used in food is

The first emission line in the atomic spectrum of hydrogen in the Balmer series appears at

An e^– has magnetic quantum number as –3, what is its principal quantum number?

At what temperature, the rate of effusion of N₂ would be 1.625 times than that of SO₂ at 50^oC?

The average kinetic energy of an ideal gas per molecule in SI unit at 25°C will be

The degree of dissociation of PCl₅ (α) obeying the equilibrium PCl5 ⇌ PCl₃ + Cl₂ is related to the equilibrium pressure by

In a closed system, A(s) ⇌ 2B(g) + 3C(g), if partial pressure of C is doubled, then partial pressure of B will be

For a particular reversible reaction at temperature T, ΔH and ΔS were found to be both +ve. If T_e is the temperature at equilibrium, the reaction would be spontaneous when

Given

Based on data provided, the value of electron gain enthalpy of fluorine would be:

The percentage hydrolysis of 0.15 M solution of ammonium acetate, K_a for CH₃COOH is 1.8 × 10^–5 and K_b for NH₃ is 1.8 × 10^–5

For a sparingly soluble salt A_pB_q, the relationship of its solubility product Ls → K_sp with its solubility (S) is

Consider the reaction :
Cl₂(aq) + H₂S(aq) → S(s) + 2H⁺ (aq) + 2Cl^– (aq)
The rate equation for this reaction is rate = k[Cl₂][H₂S]
Which of these mechanisms is/are consistent with this rate equation?
A. Cl₂ + H₂S → H⁺ + Cl^– + Cl⁺ + HS^– (slow)
Cl⁺ + HS^– → H⁺ + Cl^– + S (fast)
B. H₂S ⇌ H⁺ + HS^- (fast equilibrium)
Cl₂ + HS^- → 2Cl^- + H⁺ + S (Slow )

In the reaction, P + Q  → ? R + S
The time taken for 75% reaction of P is twice the time taken for 50% reaction of P. The concentration of Q varies with reaction time as shown in the figure. The overall order of the reaction is

The EMF of th e cell Tl/Tl⁺ (0.001M) || Cu²⁺ (0.01M) /Cu is 0.83. The cell EMF can be increased by

Electrolysis is carried out in three cells
(A) 1.0 M CuSO₄ Pt electrode
(B) 1.0 M CuSO₄ copper electrodes
(C) 1.0 M KCl Pt electrodes
If volume of electrolytic solution is maintained constant in each of the cell, which is correct set of pH changes in (A), (B) and (C) cell respectively?

The equilibrium constant for the disproportionation reaction 2Cu⁺ (aq) → Cu(s) + Cu²⁺ (ag) at 25°C
(E^o Cu⁺ / Cu = 0.52V, E^oCu²⁺ / Cu= 0.16V) is

The non stoichiometric compound Fe_0.94O is formed when x % of Fe²⁺ ions are replaced by as many 2/3 Fe³⁺ ions, x is

Al (at. wt 27) crystallizes in the cubic system with a cell edge of 4.05 Å. Its density is 2.7 g per cm³.
Determine the unit cell type calculate the radius of the Al atom

A compound of Xe and F is found to have 53.5% of Xe. What is oxidation number of Xe in this compound ?

Directions: Choose the word which best expresses the meaning of the given word.

CORPULENT

Directions: Choose the word which best expresses the meaning of the given word.

EMBEZZLE

Directions: Choose the word which is the exact OPPOSITE of the given words.

ARROGANT

Directions: Choose the word which is the exact OPPOSITE of the given words.

EXODUS

Directions: Read the following passage and answer the questions that follows.

At this stage of civilisation, when many nations are brought in to close and vital contact for good and evil, it is essential, as never before, that their gross ignorance of one another should be diminished, that they should begin to understand a little of one another's historical experience and resulting mentality. It is the fault of the English to expect the people of other countries to react as they do, to political and international situations. Our genuine goodwill and good intentions are often brought to nothing, because we expect other people to be like us. This would be corrected if we knew the history, not necessarily in detail but in broad outlines, of the social and political conditions which have given to each nation its present character.

Q. According to the author of 'Mentality' of a nation is mainly product of its

Directions: Read the following passage and answer the questions that follows.

At this stage of civilisation, when many nations are brought in to close and vital contact for good and evil, it is essential, as never before, that their gross ignorance of one another should be diminished, that they should begin to understand a little of one another's historical experience and resulting mentality. It is the fault of the English to expect the people of other countries to react as they do, to political and international situations. Our genuine goodwill and good intentions are often brought to nothing, because we expect other people to be like us. This would be corrected if we knew the history, not necessarily in detail but in broad outlines, of the social and political conditions which have given to each nation its present character.

Q. The need for a greater understanding between nations

Directions: Read the following passage and answer the questions that follows.

At this stage of civilisation, when many nations are brought in to close and vital contact for good and evil, it is essential, as never before, that their gross ignorance of one another should be diminished, that they should begin to understand a little of one another's historical experience and resulting mentality. It is the fault of the English to expect the people of other countries to react as they do, to political and international situations. Our genuine goodwill and good intentions are often brought to nothing, because we expect other people to be like us. This would be corrected if we knew the history, not necessarily in detail but in broad outlines, of the social and political conditions which have given to each nation its present character.

Q. The character of a nation is the result of its

Directions: Read the following passage and answer the questions that follows.

At this stage of civilisation, when many nations are brought in to close and vital contact for good and evil, it is essential, as never before, that their gross ignorance of one another should be diminished, that they should begin to understand a little of one another's historical experience and resulting mentality. It is the fault of the English to expect the people of other countries to react as they do, to political and international situations. Our genuine goodwill and good intentions are often brought to nothing, because we expect other people to be like us. This would be corrected if we knew the history, not necessarily in detail but in broad outlines, of the social and political conditions which have given to each nation its present character.

Q. According to the author his countrymen should

Directions: In questions below, each passage consist of six sentences. The first and sixth sentence are given in the beginning. The middle four sentences in each have been removed and jumbled up.
These are labelled as P, Q, R and S. Find out the proper order for the four sentences.

S1: A force of exists between everybody in the universe.
P: Normally it is very small but when the one of the bodies is a planet, like earth, the force is considerable.
Q: It has been investigated by many scientists including Galileo and Newton.
R: Everything on or near the surface of the earth is attracted by the mass of earth.
S: This gravitational force depends on the mass of the bodies involved.
S6: The greater the ma ss, the greater is the earth's force of attraction on it. We can call this force of attraction gravity.

Q. The Proper sequence should be:

Directions: In questions below, each passage consist of six sentences. The first and sixth sentence are given in the beginning. The middle four sentences in each have been removed and jumbled up.
These are labelled as P, Q, R and S. Find out the proper order for the four sentences.

S1: Calcutta unlike other cities kepts its trams.
P: As a result there horrendous congestion.
Q: It was going to be the first in South Asia.
R: They run down the centre of the road
S: To ease in the city decided to build an underground railway line.
S6: The foundation stone was laid in 1972.

Q. The Proper sequence should be:

Directions: Pick out the most effective word from the given words to fill in the blank to make the sentence meaningfully complete.

Q. The miser gazed ...... at the pile of gold coins in front of him.

Directions: Pick out the most effective word from the given words to fill in the blank to make the sentence meaningfully complete.

Q. I saw a ...... of cows in the field.

Directions: Read the each sentence to find out whether there is any grammatical error in it. The error, if any will be in one part of the sentence. The letter of that part is the answer. If there is no error, the answer is 'd'. (Ignore the errors of punctuation, if any).

Directions: Read the each sentence to find out whether there is any grammatical error in it. The error, if any will be in one part of the sentence. The letter of that part is the answer. If there is no error, the answer is 'd'. (Ignore the errors of punctuation, if any).

Directions: Read the each sentence to find out whether there is any grammatical error in it. The error, if any will be in one part of the sentence. The letter of that part is the answer. If there is no error, the answer is 'd'. (Ignore the errors of punctuation, if any).

Select a suitable figure from the four alternatives that would complete the figure matrix.

Select a suitable figure from the four alternatives that would complete the figure matrix.

Select a suitable figure from the four alternatives that would complete the figure matrix.

Direction: Choose the correct alternative that will continue the same pattern and replace the question mark in the given series.

3, 4, 7, 7, 13, 13, 21, 22, 31, 34, ?

Introducing a boy, a girl said, "He is the son of the daughter of the father of my uncle." How is the boy related to the girl?

Direction: In these series, you will be looking at both the letter pattern and the number pattern. Fill the blank in the middle of the series or end of the series.

QAR, RAS, SAT, TAU, _____

Direction: In these series, you will be looking at both the letter pattern and the number pattern. Fill the blank in the middle of the series or end of the series.

DEF, DEF₂, DE₂F₂, _____, D₂E₂F₃

Direction: In each question below are given two statements followed by two conclusions numbered I and II. You have to take the given two statements to be true even if they seem to be at variance from commonly known facts. Read the conclusion and then decide which of the given conclusions logically follows from the two given statements, disregarding commonly known facts.

Statements: Raman is always successful. No fool is always successful.
Conclusions:
I. Raman is a fool.
II. Raman is not a fool.

Direction: In each question below are given two statements followed by two conclusions numbered I and II. You have to take the given two statements to be true even if they seem to be at variance from commonly known facts. Read the conclusion and then decide which of the given conclusions logically follows from the two given statements, disregarding commonly known facts.

Statements: Some desks are caps. No cap is red.
Conclusions:
I. Some caps are desks.
II. No desk is red.

Choose the set of figures which follows the given rule.
Rule: Closed figures losing their sides and open figures gaining their sides.

Let f (x) = , then fof (x) = x, provided that:

Two finite sets have m and n elements. The number of subsets of the first set is 112 more than that of the second set. The values of m and n respectively are,

If A and B are positive acute angles satisfying 3 cos ² A + 2 cos ² B = 4 and , Then the value of A + 2B is equal to :

If sin θ₁ + sin θ₂ + sin θ₃ = 3, then cos θ₁ + cos θ₂ + cos θ₃ =

If tan (cot x) = cot (tan x), then sin 2x is equal to :

The general solution of the equation sin 2x + 2sin x +2 cos x+ 1 = 0 is

In a ΔABC, if  and the side a = 2, then area of the triangle is

If  , then what is the value of x?

The arithmetic mean of numbers a, b, c, d, e is M. What is the value of (a – M) + (b – M) + (c – M) + (d – M) + (e – M) ?

The fourth term of an A.P. is three times of the first term and the seventh term exceeds the twice of the third term by one, then the common difference of the progression is

The sum to n terms of the series is

If log a, log b, and log c are in A.P. and also log a – log 2b, log 2b – log 3c, log 3c – log a are in A.P., then

....upto n terms is

If z₁ = √3 + i√3 an d z₂ = √3 + i, then the complex number lies in the: 

If the matrix is singular, then λ  =

Let α₁, α₂ and β₁, β₂ be the roots of ax² + bx + c = 0 and px² + qx + r = 0 respectively. If the system of equations α₁y + α₂z = 0 and β₁y + β₂z = 0 has a non-trivial solution, then

If [ ] denotes the greatest integer less than or equal to the real number under consideration and –1 ≤ x < 0; 0 ≤ y < 1; 1 ≤ z < 2 , then the value of the determinant is

If α, β are the roots of the equations x² – 2x– 1 = 0, then what is the value of α² β^–2+ α ^–2 β²

If a, b and c are real numbers then the roots of the equation (x – a) (x – b) + (x – b) (x – c) + (x – c) (x – a) = 0 are always

, where a > b > 1, is equal to

The number of points at which the function is discontinuous is:

If then f(x) is

For any differentiable function y of x,

The set of all values of a for which the function f(x) = (a² – 3a + 2) (cos²x/4 –sin²x/4) + (a –1) x + sin 1 does not possess critical points is

Match List I with List II and select the correct answer using the code given below the lists:

Codes:

What is the x-coordinate of the point on the curve  f (x) = √x (7x –  6), where the tangent is parallel to x-axis?

A wire 34 cm long is to be bent in the form of a quadrilateral of which each angle is 90°. What is the maximum area which can be enclosed inside the quadrilateral?

Consider the following statements in respect of the function f (x) = x³ – 1, x ∈ [–1, 1]
I. f (x) is increasing in [– 1, 1]
II. f (x) has no root in (– 1, 1).
Which of the statements given above is/are correct?

At an extreme point of a function f (x), the tangent to the curve is

The curve y = xe^x has minimum value equal to

A ray of light coming from the point (1, 2) is reflected at a point A on the x-axis and then passes through the point (5, 3). The co-ordinates of the point A is

The equation x² - 2√3xy + 3y² - 3x + 3√3y - 4 = 0  represents

The line joining (5, 0) to ( (10 cos θ, 10 sin θ) is divided internally in the ratio 2 : 3 at P. If θ varies, then the locus of P is