BITSAT 2021

The relative lowering of vapour pressure of a dilute aqueous solution containing non-volatile solute is 0.0125. The molality of the solution is about

Which of the following is not an equivalence relation in z?

A cyclist speeding at 6 m/s in a circle of 18 m radius makes an angle $$\theta$$ with the vertical. The minimum possible value of coefficient of friction between the tyres and the ground is

The sum of 10 items is 12 and the sum of their squares is 18, then the standard deviation will be

The initial speed of a body of mass 2.0 kg is 5 m/s. A force acts for 4 s in the direction of motion of the body, as shown in force-time graph. The impulse of force is

A man walks in a straight line for 5 min with a velocity of 45 m/s. What is the speed with which he has to move in order to comeback to its original position in 1.5 min?

If nth division of main scale coincides with (n + 1)^th division of vernier scale. The least count of the vernier is (Given, one main scale division is equal to a units)

The value of $$\mathop {\lim }\limits_{x \to 0} {{\sqrt {1 - {{\cos x}^2}} } \over {1 - \cos x}}$$ is

A projectile is given an initial velocity of $$(\widehat i + \widehat j)$$ m/s, where, $$\widehat i$$ is along the ground and $$\widehat j$$ is along the vertical. If g = 10 m/s², then the equation of its trajectory is

A uniform rod AB of length L = 1 m is sliding along two mutually perpendicular surfaces OP and OQ as shown in the figure.

When the rod subtends an angle $$\theta$$ = 30$$^\circ$$ with OQ, the end B has a velocity $$\sqrt3$$ m/s. The velocity of end A at that time is

The angular momentum of a body placed at origin of mass 1 kg and having position vector $$r = 3t\widehat i + 4\widehat j$$ is

A force F = a + bx acts on a particle in the x-direction where a and b are constants. The work done by this force during a displacement from x = 0 to x = d is

Three particles each of mass m are kept at the vertices of an equilateral triangle of side b. Moment of inertia of the system about an axis passing through the centroid and perpendicular to its plane is

The bob of a pendulum of length 2 m lies at P, when it reaches Q, it losses 10% of its total energy due to air resistance.

The velocity of bob at Q is

A block of mass 10 kg rests on a rough inclined plane making an angle of 30$$^\circ$$ with the horizontal. The coefficient of static friction between the block and the plane is 0.1. The friction force on the block is

From a solid sphere of mass M and radius R, a spherical portion of radius $${R \over 2}$$ is removed as shown in the figure.

Taking gravitational potential V = 0 at r = $$\infty$$, the potential at the centre of the cavity thus formed is

A T-shaped object with dimensions shown in figure, is lying on a smooth floor. A force F is applied at the point P parallel to AB, such that the object has only the translational motion without rotation. Find the location of P with respect to C.

A tray of mass (M) 12 kg is supported by a spring as shown in the figure.

When the tray is pressed down and released, it executes SHM with a period of 1.5 s. When a block of mass m placed on the tray, the period of SHM changes to 3.0 s. The mass of block is

If the earth stops rotating about its axis, then what will be the change in the value of g at a place in the equatorial plane? (Radius of earth = 6400 km)

A particle executes SHM with a frequency f. The frequency with which its kinetic energy oscillates is

Two drops of equal radius (R) coalesce to form a bigger drop. What is the ratio of surface energy of bigger drop to smaller one?

Which of the following graphs show the correct relation between conductivity and temperature for a metallic conductor?

The ratio of the specific heats $${{{C_v}} \over {{C_p}}} = {1 \over \gamma }$$ in terms of degrees of freedom (n) is given by

The equation of progressive wave is given by $$Y = \sin \left[ {x\left( {{t \over 5} - {x \over 9}} \right) + {\pi \over 6}} \right]$$ cm. Which one of the following is correct?

Two cars approach a stationary observer from opposite sides as shown in the figure.

The observer hears no beats. If the frequency of the horn of the car B is 504 Hz, then the frequency of the horn of the car A will be

For a constant hydraulic stress on an object, the fractional change in the object's volume $$\left( {{{\Delta V} \over V}} \right)$$ and its bulk modulus B are related as

An ideal monoatomic gas is taken round the cycle ABCDA as shown in the p-diagram

The work done during the cycle is

The property of light used in optical fibre cables is

A shunt is connected in parallel with a galvanometer. Why?

Four charges equal to + Q are placed at the four corners of a square and a charge ($$-$$q) is at its centre. If the system is in equilibrium, then the value of $$-$$q is

In the following circuit, assuming point A to be at zero potential, then what is the potential at point B?

An electric dipole is placed at an angle of 30$$^\circ$$ in a non-uniform electric field. The dipole will experience

Two plane mirrors A and B are aligned parallel to each other as shown in the figure.

A ray of light is incident at an angle 30$$^\circ$$ at a point just inside one end of A. The plane of incidence coincides with the plane of the figure. The maximum number of times, the ray undergoes reflection (excluding the first one) before it emerges out is

The phasor diagram of a load represents which circuit?

Two particles A and B of masses m_A and m_B respectively, are having same charge and moving on same plane. A uniform magnetic field exists perpendicular to this plane. The speeds of the particles are v_A and v_B respectively and the trajectories are as shown in figure. Then,

Choose the correct statement.

The separation between two parallel plates of capacitor is 1 mm. What is the electric potential generates between the plates of capacitor, when electric field of 2000 N/C is applied on it?

A proton has kinetic energy E = 100 eV which is equal to that of a photon. The wavelength of photon is $$\lambda$$₂ and that of proton is $$\lambda$$₁. The ratio $${{{\lambda _2}} \over {{\lambda _1}}}$$ is proportional to

Two coils A and B have a mutual inductance 0.001 H. The current changes in the first coil according to the equation $$i = {i_0}\sin \omega t$$, where i₀ = 10A and $$\omega$$ = 10$$\pi$$ rads^$$-$$1. The maximum value of emf in the second coil is

The radius of a muonic hydrogen atom is 2.5 $$\times$$ 10^$$-$$13 m. The total atomic volume (in m³) of a mole of such hydrogen atoms is (Take, $$\pi$$ = 3.14)

The current in the circuit will be

The potential difference applied to an X-ray tube is decreased. As a result, in the emitted radiation,

A radioactive sample at any instant has its disintegration rate 5000 disintegrations per min. After 5 min, the rate is 1250 disintegrations per min. Then, the disintegration constant (per min) is

The density (in g mL^$$-$$1] of a 3.60 M sulphuric acid solution that is 29% H₂SO₄ (molar mass = 98 g mol^$$-$$1) by mass will be

The phase difference between V_out and V_in of CE amplifier circuit is

Rutherford model could not explain

What is the magnetic moment of Ti²⁺ ? (Given : Atomic number = 22)

Ionisation energy for H⁺ ion is proportional to rⁿ, then value of n is

In Victor Meyer's method 0.2 g of an organic substance displaced 56 mL of air at STP the molecular weight of the compound

Equal masses of methane and oxygen are mixed in an empty container at 25$$^\circ$$C. The fraction of the total pressure exerted by oxygen is

If Rydberg constant is same for all elements, the angular momentum and energy of Li²⁺ of which orbital is equal to angular momentum and energy of 1 s-orbital of hydrogen atom?

SI unit of Boltzmann's constant is

For the complete combustion of ethanol, $${C_2}{H_5}OH(I) + 3{O_2}(g) \to 2C{O_2}(g) + 3{H_2}O(I)$$, the amount of heat produced as measured in bomb calorimeter is 1364.47 kJ mol^$$-$$1 at 25$$^\circ$$C. Assuming ideality the enthalpy of combustion, $$\Delta$$H_C, for the reaction will be (R = 8.314 JK^$$-$$1 mol^$$-$$1)

The solubility of Pb(OH)₂ in water is 6.7 $$\times$$ 10^$$-$$6 M. Its solubility in a buffer solution of pH = 8 would be :

The incorrect expression among the following is

The process of removal of excess electrolyte from colloidal solution is

The approximate time duration in hours to electroplate 30 g of calcium from molten calcium chloride using a current of 5 A is (Atomic mass of Ca = 40)

Why only Xe can form compounds with fluorine among noble gases?

Which of the following is diamagnetic in nature?

The molar conductivities of KCl, NaCl and KNO₃ are 152, 128 and 111 S cm² mol^$$-$$1 respectively. What is the molar conductivity of NaNO₃?

For the following reaction

2A + 3B $$\to$$ 3C + 4D

expression for rate of reaction is

The most volatile compound among the given option is

Given, the reduction potential of Na⁺, Mg²⁺, Al³⁺ and Ag⁺ as $$E_{N{a^ + }/Na}^o$$ = $$-$$ 2.17 V; $$E_{M{g^{2 + }}/Mg}^o$$ = $$-$$ 2.37 V; $$E_{A{g^ + }/Ag}^o$$ = $$-$$ 0.08 V.

The least stable oxide is

The correct order of bond order in SO₂, SO₃, SO$$_4^{2 - }$$, SO$$_3^{2 - }$$ is

Which is not an anti-fluorite structure

Sodium iodide reacts with ammonia to gives

Some statements about heavy water are given below

3. Heavy water is more effective solvent than ordinary water.

Which of the above statements are correct?

The structure of CIF₃ is

Which of the following inert gas is used as cryogenic agnet?

Permanganate ion (MnO$$_4^ - $$) is dark purple coloured though Mn is in + 7 oxidation state with d⁰ configuration. This is due to

Methyl alcohol can be distinguished from ethyl alcohol using

CH₃$$-$$CHCl$$-$$CH₂$$-$$CH₃ has a chiral centre, which of the following represents its R configurations?

Magnetic moment of in [Co(F₆)]^2$$-$$ of unpaired electron .......... .

The major product obtained on reaction of 3-methylbutene with HCl is

Which is true in case of [Ni(CO)₄]?

Cyclohexanol on reacting with H₂SO₄ and then heating gives

Acetone does not undergo which type of reaction?

The compound formed on reaction of epoxy ethane with NH₃ and H₂O is

Starch is a polymer of

Maltase converts maltose into

In photography, which compound is used as a fixing agent

The solution of the inequality $${4^{ - x + 0.5}} - {7.2^{ - x}} < 4$$, x $$\in$$R is

Role of BHA in food industries

If log₇ 5 = a, log₅ 3 = b and log₃ 2 = c, then the logarithm of the number 70 to the base 225 is

Sodium stearate (C₁₇H₃₅COO^$$-$$Na⁺) is

If a$$\in$$R, b$$\in$$R, then the equation x² $$-$$ abx $$-$$ a² = 0 has

If a + 2b + 3c = 12, (a, b, c $$\in$$R⁺), then the maximum value of ab²c³ is

$${{{C_1}} \over {{C_0}}} + 2{{{C_2}} \over {{C_1}}} + 3{{{C_3}} \over {{C_2}}} + 4{{{C_4}} \over {{C_3}}} + ....20{{{C_{20}}} \over {{C_{19}}}} = $$

Two cards are drawn from a pack of 52 cards. What is the probability that either both are red or both are kings?

Sum of n terms of the infinite series

1.3² + 2.5² + 3.7² + ..... $$\infty$$ is

Box I contains 5 red and 2 blue balls, while box II contains 2 red and 6 blue balls. A fair coin is tossed. If it turns up head, a ball is drawn from box I, else a ball is drawn from box II. The probability ball drawn is from box I, if it is blue, is

The maximum number of points of intersection of 10 circles is :

If A and B are two independent events such that $$P(A) = {1 \over 2}$$ and $$P(B) = {1 \over 5}$$, then which of the following is correct?

Angle between the diagonals of a cube is

The points with position vectors $$10\widehat i + 3\widehat j$$, $$12\widehat i - 5\widehat j$$ and $$a\widehat i + 11\widehat j$$ are collinear, if a is

Let a, b, c be vectors of lengths 3, 4, 5 respectively and a be perpendicular to (b + c), b to (c + a) and c to (a + b), then the value of (a + b + c) is

The distance between the line $$r = 2\widehat i - 2\widehat j + 3\widehat k + \lambda (\widehat i - \widehat j + 4\widehat k)$$ and the plane $$a\,.\,(\widehat i + 5\widehat j + \widehat k) = 5$$ is

For non-zero vectors a, b, c; |(a $$\times$$ b) . c| = |a| |b| |c| holds if and only if

Consider the two lines

$${L_1}:{{x + 1} \over 3} = {{y + 2} \over 1} = {{z + 1} \over 2}$$ and $${L_2}:{{x - 2} \over 1} = {{y + 2} \over 2} = {{z - 3} \over 3}$$

The unit vector perpendicular to both the lines L₁ and L₂ is

The linear programming problem minimize z = 3x + 2y subject to constrains x + y $$\ge$$ 8, 3x + 5y $$\ge$$ 15, x $$\ge$$ 0 and y $$\ge$$ 0, has

Matrix $$A = \left| {\matrix{ x & 3 & 2 \cr 1 & y & 4 \cr 2 & 2 & z \cr } } \right|$$, if xyz = 60 and 8x + 4y + 3z = 20, then A(adj A) is equal to

For a random variable X, E(X) = 3 and E(X²) = 11. The variable of X is :

The runs of two players for 10 innings each are as follows

The more consistent player is

Which of the following is always true?

If Re(z + 2) = | z $$-$$ 2 |, then the locus of z is

Total number of solutions of $$\left| {\cot x} \right| = \cot x + {1 \over {\sin x}},x \in [0,3\pi ]$$ is equal to

If $${\cos ^3}x\,.\,\sin 2x = \sum\limits_{m = 1}^n {{a_m}\sin mx} $$ is identity in x, then

The height of the chimney when it is found that on walking towards it 50 m in the horizontal line through its base, the angle of elevation of its top changes from 30$$^\circ$$ to 60$$^\circ$$ is :

The minimum value of $${({\sin ^{ - 1}}x)^3} + {({\cos ^{ - 1}}x)^3}$$ is equal to

If f(x) = 4x $$-$$ x², x$$\in$$R, and f(a + 1) $$-$$ f(a $$-$$ 1) = 0, then a is equal to

Find the area enclosed by the loop in the curve 4y² = 4x² $$-$$ x³.

The maximum value of the function y = x(x $$-$$ 1)², is

Solution of $$\left( {{{x + y - 1} \over {x + y - 2}}} \right){{dy} \over {dx}} = \left( {{{x + y + 1} \over {x + y + 2}}} \right)$$, given that y = 1 when x = 1 is

If $$f(x) = \left\{ {\matrix{ {a{x^2} + 1,} & {x \le 1} \cr {{x^2} + ax + b,} & {x > 1} \cr } } \right.$$ is differentiable at x = 1, then

The slope of the tangent to the curve x = t² + 3t $$-$$ 8, y = 2t² $$-$$ 2t $$-$$ 5 at the point t = 2 is

The solution of $${x^3}{{dy} \over {dx}} + 4{x^2}\tan y = {e^x}\sec y$$ satisfying y (1) = 0, is

If $$y = \sin \left( {2{{\tan }^{ - 1}}\sqrt {{{1 - x} \over {1 + x}}} } \right)$$, then $${{dy} \over {dx}}$$ is :

$$\int\limits_0^1 {{{\log (1 + x)} \over {1 + {x^2}}}dx} $$ is equal to :

$$\int {{1 \over {1 - 2\sin x}}dx} $$ is equal to

If x = 9 is the chord of contact of the hyperbola x² $$-$$ y² = 9, then the equation of the corresponding pair of tangent is

The origin is shifted to (1, 2). The equation y² $$-$$ 8x $$-$$ 4y + 12 = 0 changes to y² = 4ax, then a is equal to

The area of one curvilinear triangle formed by curves y = sin x, y = cos x and X-axis, is

A. However, women hiring is catching up at a slow and steady rate in the recent times.

B. Gender ratio has been inclined more towards male employees.

C. As a result, recent reports have highlighted the rise in demand for women employees.

D. Women constitute a little over half of world's total population.

E. But, their contribution to measured economic activity is far below the potential.

The equations of the bisector of the angles between the straight lines 3x + 4y + 7 = 0 and 12x + 5y $$-$$ 8 = 0 are :

Decay is an $$\underline {immutable} $$ factor of human life.

Equation of circle which passes through the points (1, $$-$$2) and (3, $$-$$4) and touch the X-axis is

A. It is hoping that overseas friends will bring in big money and lift the morale of the people.

B. But a lot needs to be done to kick start industrial revival.

C. People had big hopes from the new government.

D. So far government has only given an incremental push to existing policies and programmes.

E. Government is to go for big time reforms, which it promised.

A. Tasty and healthy food can help you bring out their best.

B. One minute they are toddlers and next you see them in their next adventure.

C. Your young ones seem to be growing so fast.

D. Being their loving custodians, you always want to see them doing well.

E. Their eyes sparkle with curiosity and endless questions on their tongues.

A person who does not believe in any religion

His $$\underline {conjecture} $$ was the better than mine.

This is a barbarous act.

The Gupta rulers patronised all cultural activities and thus Gupta period was called the golden era in Indian History.

It was an $$\underline {ignominious} $$ defect for the team.

Neeraj starts walking towards South. After walking 15 m, he turns towards North. After walking 20 m, the turns towards East and walks 10 m. He then turns towards South and walks 5 m. How far is he from his original position and in which direction?

In a row of forty children, P is thirteenth from the left end and Q is ninth from the right end. How many children are there between P and R, if R is fourth to the left of Q?

A person who believes that pleasure is the chief good

One who loves mankind

Complete the series by replacing '?' mark.

G4T, J9R, M20P, P43N, S90L, ?

Shikha is mother-in-law of Ekta who is sister-in-law of Ankit. Pankaj is father of Sanjay, the only brother of Ankit. How is Shikha related to Ankit?

The average age of 8 men is increased by 2 yrs. when one of them whose age is 20 yr is replaced by a new man. What is the age of the new man?

Choose the answer figure which completes the problem figure matrix.

Problem Figure

In the following question, five figures are given. Out of them, find the three figures that can be joined to form a square.

Choose the correct answer figure which will make a complete square on joining with the problem figure.

From the given four positions of a single dice, find the color at the face opposite to the face having red color.

Pradeep's face spoke .................. of the happiness he was feeling.

In the following question, one or more dots are placed in the figure marked as (A). The figure is followed by four alternatives marked as (a), (b), (c) and (d). One out of these four options contains region(s) common to the circle, square, triangle, similar to that marked by the dot in figure (A).

Problem Figure

Freedom and quality are the ................ rights of every human.

His speech was disappointing : it ................ all the major issues.