BITSAT 2022

A capillary tube is attached horizontally to a constant heat arrangement. If the radius of the capillary tube is increased by 25%, then the rate of flow of liquid will change nearly by

0.20 g of an organic compound gave 0.12 g of AgBr. By using Carius method, the percentage of bromine in the compound will be

A machine gun fires 300 bullets per min if the mass of each bullet is 10 g and the velocity of the bullets is 600 ms^$$-$$1, the power (in kW) of the gun is

A projectile is projected with the velocity of $$(3\widehat i + 4\widehat j)$$ m/s. The horizontal range of the projectile will be

In a resonance coloum first and second resonance are obtained at depths 24 cm and 78 cm the third resonance will be obtained at depth.

A particle of mass m is projected with velocity v at an angle $$\theta$$ with the horizontal. At its highest point, it explodes into two pieces of equal mass, one of the piece continue to move on the original trajectory, then the velocity of second piece is

Four holes of radius 5 cm are cut from a thin square plate of 20 cm and mass 1 kg. The moment of inertia of the remaining portion about Z-axis is

What will be the acceleration due to gravity at a depth d, where g is acceleration due to gravity on the surface of earth?

A solid sphere of 80 kg and radius 15 m moving in a space becomes a circular disc of radius 20 m in 1 h. The rate of change of moment of Inertia in this process is .......

A submarine A travelling at 17 m/s is being chased along the line of its velocity by another submarine B travelling at 34 m/s. B sends a sonar signal of 600 Hz to detect A and receives a reflected sound of frequency $$\nu$$. The of $$\nu$$ is

[Speed of sound in water = 1500 ms^$$-$$1]

A mosquito O is sitting infront of a glass rod having spherical end of radius of curvature 40 cm. The image would be formed at

A monoatomic gas of molar mass m is kept in a insulated container. Container is moving with velocity v. If the container is suddenly stopped, then the change in the temperature of the gas is

In the diagram shown below, both the strings AB and CD are made of same material and have same cross-section. The pulleys are light and fictionless. If the speed of wave in string AB is v₁ and in CD is v₂, then $${{{v_1}} \over {{v_2}}}$$ is

Transverse waves of the same frequency are generated in two steel wires A and B. The diameter of A is twice that of B and the tension in A is half that in B. The ratio of the velocities of the waves in A and B is

In a young's double slit arrangement fringes are produced using light of wavelength 4000 $$\mathop A\limits^o $$. One slit is covered by a thin plate of glass of refractive index 1.4 and the other with another glass plate of same thickness but of refractive index 1.7. By doing so the central bright shifts to original sixth fringe from centre. Thickness of glass plate is ................. .

One mole of an ideal diatomic gas undergoes a process as shown in the figure. The molar specific heat of the gas in the process is

An achromatic convergent doublet of two lenses in contact has a power of +5 D. The power of converging lens is +6 D. The ratio of the dispersive power of the convergent and divergent lenses is

In the arrangement shown in figure, when the switch S₂ is open, the galvanometer, shows no deflection for $$l$$ = 50 cm when the switch S₂ is closed, the galvanometer shows no deflection for $$l$$ = 0.416 m. The internal resistance (r) of 6 V cell is

Which one of the following graphs represents the variation of electric potential with distance r from the centre of a non-conducting charged sphere of radius R?

A direct current of 6 A is superimposed on an alternating current I = 10 sin $$\omega$$t flowing through a wire. The effective value of the resulting current will be

An electric current I enters and leaves a uniform circular wire of radius r through diametrically opposite points. A charged particle q moves along the axis of circular wire passes through its centre at speed v. The magnetic force on the particle when it passes through the centre has a magnitude.

If the B - H curves of two samples of X and Y of iron are as shown below, then which one of the following statement is correct?

In a radioactive material the activity at time t₁, is A₁ and at a later time t₂, it is A₂. If the decay constant of the material is $$\lambda$$, then

An electromagnetic wave is propagating along X-axis. At x = 1 cm and t = 18s, its electric vector |E| = 8 V/m, then the magnitude of its magnetic vector is

In the circuit shown in the figure, the AC source gives a voltage V = 20 cos (2000t) neglecting source resistance, the voltmeter and ammeter reading will be

The stopping potential (V₀) versus frequency $$\nu $$ of a graph for photoelectric effect in a metal. From the graph, the Plank's constant (h) is

The de-Broglie wavelength of an electron moving with a velocity $$\frac{c}{3}$$ (c = 3 $$\times$$ 10⁸ m/s) is equal to the wavelength of photon. The ratio of the kinetic energies of electron and photon is

In the circuit shown assume the diode to be ideal. When V_i increases from $$-$$2V to 6V, the change in current is (in mA)

In the following circuit the equivalent resistance between X and Y is ......... $$\Omega$$

How will raise in temperature affects the viscosity of liquids and gases?

Which one of the following statements in relation to the hydrogen atom is correct?

A certain metal sulphide, MS₂, is used extensively as a high temperature lubricant. If MS₂ is 40.06% by mass sulphur, metal M has atomic mass.

A transistor is connected in common-emitter (CE) configuration. The collector supply is 8V and the voltage drop across a resistor is 500 $$\Omega$$ in the collector circuit is 0.6 V. IF the current gain factor $$\alpha$$ is 0.96, find the base current

For an insulator, the forbidden energy gap is

The given graph represents the variation of compressibility factor (Z) = $$\frac{pV}{nRT}$$, for three real gases A, B and C. Identify the only incorrect statement.

In an adiabatic process, no transfer of heat takes place between system and surrounding. Choose the correct option for free expansion of an ideal gas under adiabatic condition from the following.

100 mL of 2 M of formic acid (pK_a = 3.74) is neutralise by NaOH, at the equivalence point pH is

Standard entropy of X₂, Y₂ and XY₃ are 60, 40 and 50 JK^$$-$$1mol^$$-$$1, respectively. For the reaction, $$\frac{1}{2}$$X₂ + $$\frac{3}{2}$$Y₂ $$\to$$ XY₃, $$\Delta$$H = $$-$$30 kJ, to be at equilibrium, the temperature will be

What is [NH$$_{4}^+$$] in a solution that is 0.02 M NH₃ 0.01 M KOH ? [K_b(NH₃) = 1.8 $$\times$$ 10^$$-$$5]

For an isomerisation reaction A $$\rightleftharpoons$$ B, the temperature dependence of equilibrium constant is given by

log_e K = 4.0 $$-$$ $$\frac{2000}{T}$$

The value of $$\Delta$$S$$^\circ$$ at Hook is, therefore

In the molecules CH₄, NF₃, NH$$_4^ + $$ and H₂O

The structure of H₂O₂ is

In which pair or pairs is the stronger bond found in the first species?

I. O$$_2^{2 - }$$, O₂; II. N₂, N$$_2^{+ }$$; III. NO⁺, NO^$$-$$

Using the standard electrode potential, find out the pair between which redox reaction is not feasible.

E$$^\Theta $$ values Fe³⁺ / Fe²⁺ = + 0.77; I₂ / I^$$-$$ = + 0.54 Cu²⁺ / Cu = + 0.34; Ag⁺ / Ag = 0.80 V

OF and F₂ can be compared in terms of

Which compound has antifluorite structure?

Which of the following compounds is thermodynamically is the most stable?

ortho and para form of hydrogen have

Which one of the following is correct order of given isotopes?

I. T₂ > D₂ > P₂ (order of boiling point)

II. T₂ > D₂ > P₂ (order of bond energy)

III. T₂ = D₂ = P₂ (order of bond length)

IV. T₂ < D₂ < P₂ (order of reactivity with Cl₂)

The total number of P$$-$$OH bonds for pyrophosphoric acid

The number of 3C$$-$$2e^$$-$$ bonds present in diborane is

Ge (II) compounds are powerful reducing agents whereas Pb (IV) compounds are strong oxidants. It can be because

Select the correct statement about the complex [Co(NH₃)₅SO₄] Br.

The reaction of C₆H₅CH = CHCH₃ with HBr produces

What is the hybridisation of [CrF₆]^3$$-$$ ?

X and Y are

Match the species in Column I with their types in Column II.

Ninhydrin gives yellow colour in paper chromatography with which amino acid?

Glucose reacts with X number of molecules of phenyl hydrazine to yield osazone. The value of X is,

If $$\alpha$$ be a root of the equation $$4{x^2} + 2x - 1 = 0$$, then the other root of the equation is

Let a₁, a₂, ...... a₄₀ be in AP and h₁, h₂, ..... h₁₀ be in HP. If a₁ = h₁ = 2 and a₁₀ = h₁₀ = 3, then a₄h₇ is

Let a, b be the solutions of x² + px + 1 = 0 and c, d be the solution of x² + qx + 1 = 0. If (a $$-$$ c) (b $$-$$ c) and (a + d)(b + d) are the solution of x² + ax + $$\beta$$ = 0, then $$\beta$$ is equal to

Let a₁, a₂, a₃ .... be a harmonic progression with a₁ = 5 and a₂₀ = 25. The least positive integer n for which a_n < 0, is

Nylon-6, 6 is obtained from

A six faced die is a biased one. It is thrice more likely to show an odd numbers than show an even number. It is thrown twice. The probability that the sum of the numbers in two throws is even, is

The number of different seven-digit numbers that can be written using only the three digits 1, 2 and 3 with the condition that the digit 2 occurs twice in each number is

The number of ways of arranging letters of the word HAVANA so that V and N do not appear together is

The number of terms in the expansion of $${(1 + 5\sqrt {2x} )^9} + {(1 - 5\sqrt {2x} )^9}$$ is

If A = {x : x is a multiple of 4} and B = {x : x is a multiple of 6}, then A $$\cap$$ B consists of multiples of

In a sequence of 21 terms, the first 11 terms are in AP with common difference 2 and the last 11 terms are in GP with common ratio 2. If the middle term of AP be equal to the middle term of the GP, then the middle term of the entire sequence is

If the sum of the coefficients in the expansion of (x + y)ⁿ is 1024, then the value of the greatest coefficient in the expansion is

If the plane $$3x + y + 2z + 6 = 0$$ is parallel to the line $${{3x - 1} \over {2b}} = 3 - y = {{z - 1} \over a}$$, then the value of $$3a + 3b$$ is

If $$\left[ {\matrix{ 1 & { - \tan \theta } \cr {\tan \theta } & 1 \cr } } \right]{\left[ {\matrix{ 1 & {\tan \theta } \cr { - \tan \theta } & 1 \cr } } \right]^{ - 1}} = \left[ {\matrix{ a & { - b} \cr b & a \cr } } \right]$$, then

$$\widehat u$$ and $$\widehat v$$ are two non-collinear unit vectors such that $$\left| {{{\widehat u + \widehat v} \over 2} + \widehat u \times \widehat v} \right| = 1$$. Then the value of $$|\widehat u \times \widehat v|$$ is equal to

If p $$\ne$$ a, q $$\ne$$ b, r $$\ne$$ c and the system of equations

px + ay + az = 0

bx + qy + bz = 0

cx + cy + rz = 0

has a non-trivial solution, then the value of $$\frac{p}{p-a}+\frac{q}{q-b}+\frac{r}{r-c}$$ is

Given 2x $$-$$ y + 2z = 2, x $$-$$ 2y - z = $$-$$4, x + y + $$\lambda$$z = 4, then the value of $$\lambda$$ such that the given system of equation has no solution is

The smallest positive integral value of n such that $${\left[ {{{1 + \sin {\pi \over 8} + i\cos {\pi \over 8}} \over {1 + \sin {\pi \over 8} - i\cos {\pi \over 8}}}} \right]^n}$$ is purely imaginary, is equal to

The mean of five observations is 4 and their variance is 5.2. If three of these observations are 1, 2 and 6, then the other two are

Let $$A = \left[ {\matrix{ 1 & { - 1} & 1 \cr 2 & 1 & { - 3} \cr 1 & 1 & 1 \cr } } \right]$$ and $$10B = \left[ {\matrix{ 4 & 2 & 2 \cr { - 5} & 0 & \alpha \cr 1 & { - 2} & 3 \cr } } \right]$$

If B is the inverse of A, then the value of $$\alpha$$ is

If $$|w| = 2$$, then the set of points $$z = w - {1 \over w}$$ is contained in or equal to the set of points z satisfying

The sum of all the solution of the equation $$\cos \theta \cos \left( {{\pi \over 3} + \theta } \right)\cos \left( {{\pi \over 3} - \theta } \right) = {1 \over 4},\theta \in [0,6\pi ]$$

If $$\alpha,\beta,\gamma \in[0,\pi]$$ and if $$\alpha,\beta,\gamma$$ are in AP, then $${{\sin \alpha - \sin \gamma } \over {\cos \gamma - \cos \alpha }}$$ is equal to

If in a $$\Delta$$ABC, 2b² = a² + c², then $$\frac{\sin 3B}{\sin B}$$ is equal to

The value of $$\mathop {\lim }\limits_{x \to 0} {{1-\cos (1 - \cos x)} \over {{x^4}}}$$ is

If g(x) = x² + x $$-$$ 2 and $$\frac{1}{2}gof(x)=2x^2-5x+2$$, then f(x) is equal to

Given that a house forms a right angle view from a window of another house, and the angle of elevation from the base of the first house to the window is 60 degrees. If the separation between the two houses is 6 meters, calculate the height of the first house.

Let $$\alpha$$ be the solution of $${16^{{{\sin }^2}\theta }} + {16^{{{\cos }^2}\theta }} = 10$$ in $$\left( {0,{\pi \over 4}} \right)$$. If the shadow of a vertical pole is $${1 \over {\sqrt 3 }}$$ of its height, then the altitude of the sun is

If $$x \in \left( {0,{\pi \over 2}} \right)$$, then the value of $${\cos ^{ - 1}}\left( {{7 \over 2}(1 + \cos 2x) + \sqrt {({{\sin }^2}x - 48{{\cos }^2}x)\sin x} } \right)$$ is equal to

The value of $$\mathop {\lim }\limits_{x \to 0} {{{{(1 + x)}^{{1 \over x}}} - e + {1 \over 2}ex} \over {{x^2}}}$$ is

A running track of 440 ft is to be laid out enclosing a football field, the shape of which is a rectangle with a semi-circle at each end. If the area of the rectangular portion is to be maximum, then the lengths of its side are

$$\left( {{{dy} \over {dx}}} \right)\tan x = y{\sec ^2}x + \sin x$$, find general solution

Let $$f(x) = \int {{{{x^2}dx} \over {(1 + {x^2})(1 + \sqrt {1 + {x^2}} )}}} $$ and $$f(0) = 0$$, then the value of $$f(1)$$ be

A spherical balloon is filled with 4500$$\pi$$ cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of 72$$\pi$$ cubic meters per minute then the rate (in meters per minute) at which the radius of the balloon decreases 49 min after the leakage began is

The value of $$\int {{1 \over {{{[{{(x - 1)}^3}{{(x + 2)}^5}]}^{{1 \over 4}}}}}dx} $$, is

A normal is drawn at the point P to the parabola $${y^2} = 8x$$, which is inclined at 60$$^\circ$$ with the straight line $$y = 8$$. Then the point P lies on the straight line

What is the area enclosed by the parabola described by $${(y - 2)^2} = (x - 1)$$, its tangent line at the point (2, 3), and the X-axis?

The area enclosed by the curves $$y = \sin x + \cos x$$ and $$y = |\cos x - \sin x|$$ over the interval $$\left[ {0,{\pi \over 2}} \right]$$ is

If the straight line $$y = mx + c$$ touches the parabola $${y^2} - 4ax + 4{a^3} = 0$$, then c is

For each parabola y = x² + px + q, meeting coordinate axes at 3-distinct points, if circles are drawn through these points, then the family of circles must pass through

The locus of the mid-point of the chord if contact of tangents drawn from points lying on the straight line $$4x - 5y = 20$$ to the circle $${x^2} + {y^2} = 9$$ is

Then her face was bowed.

(A) Now under liberated economy they are learning to compete domestically and globally.

(B) In India corporations until recently achieved success by avoiding competition, using protected and regulated domestic markets.

(C) The trend is irreversible.

(D) Business leaders are preparing themselves to meet competitive challenges, and to avoid being swept away.

(A) Recovery was given inadequate attention and consequently some bank branches regularly incurred heavy losses and their parent bodies had to bale them out.

(B) As a result, banks indulged in extensive lending to borrowers who had little or no potential to make repayments.

(C) To fulfil the social objectives laid down by the masters of nationalisation, banks were asked to lend to identified priority sectors.

(D) 1992-93 results showed that the loss making branches of public sector banks increased from 10000 to 13000 and the quantum of losses showed at Rs.3369 crores.

$$\underline {Forthrightness} $$ in speech may not always be a desirable quality.

The attack on the freedom of the press is a $$retrograde$$ step.

The $$\underline {inexorable} $$ demands of the workers brought the company to a closure.

The complex form of the sentence given below would be

Spare the rod and spoil the child.

Regard for other as a principle of action or selflessly.

The leader might have had some $$covert$$ reason for the change of his political affiliations.

The average marks of 50 students in a class was found to be 64. If the marks of two students were incorrectly entered as 38 and 42 instead of 83 and 24, respectively, then what is the correct average?

Code of diplomatic etiquette and precedence is

Select the option in which the words share the same relationship as that shared by the given pair of words.

Barometer : Pressure

'A + B' means 'A is the mother of B'.

'A $$-$$ B' means 'A is the brother of B'.

'A $$\times$$ B' means 'A is the father of B'.

'A $$\div$$ B' means 'A is the daughter of B'.

If, P $$-$$ K $$\times$$ Y $$-$$ J $$\div$$ S + R, then which of the following statement is not correct?

Select the letter-cluster that can replace the question mark (?) in the following series.

TXB, QWE, NVH, KUK, ?

Select the option in which the words share the same relationship as that shared by the given set of words.

Cat : Lion : Jaguar

Select the option that is related to the fifth number in the same way as the second number is related to the first number and the fourth number is related to the third number.

14 : 289 : : 17 : 400 : : 21 : ?

Selecty the letter-cluster that can replace the question mark (?) in the following series.

TULG, WRPC, ZOTY, CLXU, ?

'Needle' is related to 'Sew' in the same way as 'Microscope' is related to '...........' .

Statements

Lawyers marry only fair girls.

Shobha is very fair.

Conclusions

I. Shobha is married to a lawyer.

II. Shobha is not married to a lawyer.

Five friends A, B, C, D and E bought cars which were priced differently. B's car was costlier than C's car but was less costly than E's car. A's car was costlier than D's car but less costly than C's car. Whose car was the 2nd costliest?

Six friends A, B, C, D, E and F are sitting around a round table facing the centre. A sits second to the right of B, E sits second to the left of C. B doesn't sit adjacent to E. D does not sit opposite to E or C. Who sits to the immediate left of E?

Statements

60% of government employees went on strike.

Mr. Gopal is a government employee.

Conclusions

I. Mr. Gopal went on strike.

II. Mr. Gopal did not participate in the strike.

In the following question, complete the missing segment by selecting the appropriate figure from the given alternatives, (a), (b), (c) and (d).

In the question given below, find out which of the figures can be formed from the pieces given in the problem figure.

Select the figure that can replace the question mark (?) in the following series.

Three different positions of the same dice are shown, the six faces of which are numbered from 1 to 6. Select the number that will be on the face opposite to the one showing '6'.

How many triangles are there in the given figure?

In each of the following question, find out which of the answer figures (a), (b), (c) and (d) completes the figure matrix?

Select the option in which the given figure X is embedded (rotation is not allowed).

Select the correct mirror image of the given figure when the mirror is placed on the right of the figure.