BITSAT 2020

When a body is dropped from a height h, then it hits the ground with a momentum p. If the same body is dropped from a height which is three times more than previous height, the percentage change in momentum when it hits the ground is

The enthalpies of combustion of carbon and carbon monoxide in excess of oxygen at 298 K and constant pressure are $$-$$393.5 kJ/mol and $$-$$280.0 kj/mol respectively. The heat of formation of carbon monoxide at constant volume is

If $$a = - \widehat i + \widehat j + \widehat k$$ and $$b = 2\widehat i + \widehat k$$, then find z component of a vector r, which is coplanar with a and b, r . b = 0 and r . a = 7.

Two small conducting spheres of equal radius have charges +20 $$\mu$$ C and $$-$$40 $$\mu$$C respectively and placed at a distance R from each other experience for F₁. If they are brought in contact and separated to the same distance, they experience force F₂. The ratio of F₁ to F₂ is

A satellite is moving around the earth with speed v in a circular orbit of radius r. If the orbit radius is decreased by 2%, its speed will increase by

How many rectangles are there in the following figure?

The length of the rectangle is l = 15.2 cm and breadth is b = 2.9 cm and the minimum possible measurement by scale = 0.1 cm. Then, the area of the rectangle is (Taking significant figures into consideration)

A plane requires for take off a speed of 72 kmh^$$-$$1, the run on the ground being 50 m. The mass of the plane is 10000 kg and the coefficient of friction between the plane and the ground is 0.2. Assume that the plane accelerates uniformly during take off. The minimum force required by the engine of the plane for take off is

A ball of mass 0.5 kg is thrown up with initial speed 16 ms^$$-$$1 and reaches maximum height of 9 m. How much energy is dissipated by air drag acting on the ball during the ascent?

If L, R, C and V represent inductance, resistance, capacitance and potential difference respectively, then dimensions of $${L \over {RCV}}$$ are the same as those of

Based on the provided velocity-time graph for an object’s straight-line movement, determine the total distance covered and the average speed between t = 0 and t = 20 seconds.

The acceleration of a particle in m/s² is given by a = (3t² $$-$$ 2t + 1), where t is in second. If the particle starts with a velocity v = 1 m/s at t = 1s, then velocity of the particle at the end of 4s is

A time dependent force F = (8t) acts on a particle of mass 2 kg. If the particle starts from rest, the work done by the force during the first 1s will be

A simple pendulum is placed inside a lift, the lift is moving with a uniform acceleration. If the time periods of the pendulum while the lift is moving upwards and downwards are in the ratio of 1 : 3, then the acceleration of the lift is

[Take acceleration due to gravity, g = 10 m/s²]

Two spheres of the same material and same radii r are touching each other. The gravitational force between the spheres is proportional to

The work done by a force acting on a body is as shown in the following graph. The total work done in covering an initial distance of 40 m is

The wheel of a car, accelerated uniformly from rest, rotates through 5 radians during the first second. The angle (in radians) rotated during the next second is

If a man becomes a giant, expanding his linear dimensions by a factor of eight, and assuming his density remains unchanged, the factor by which the stress in his legs will increase is

The vibrations of a string of length 60 cm fixed at both ends are represented by the equation

$$y = 4\sin \left( {{{\pi x} \over {15}}} \right)\cos (96\pi t)$$

where x and y are in cm and t is in second. Calculate the velocity of the particle at x = 7.5 cm at t = 0.25 s.

The figure shows graphs of pressure (p) versus density (d) for an ideal gas at two temperatures T₁ and T₂, then

A black body radiates energy at the rate E Wm^$$-$$2 at high temperature TK. When the temperature is reduced to $$\left( {{T \over 4}} \right)$$ K, the new radiant energy is

A Carnot engine has the same efficiency between 600 K to 300 K and 1600 K to x K, then the value of x is

A vessel contains one mole of O₂ gas (molar mass 32) at a temperature T. The pressure of the gas is p. An identical vessel containing one mole of He gas (molar mass 4) at a temperature 2T has a pressure of

When 2 moles of a monoatomic gas are mixed with 3 moles of a diatomic gas, the value of adiabatic exponent for the mixture is

In an adiabatic process, where pressure is decreased by $${3 \over 4}$$%, if $${{{C_p}} \over {{C_v}}} = {4 \over 3}$$, then the volume increases by

A moving coil galvanometer has a resistance of 60 $$\Omega$$ and it indicates full deflection on passing a current of 4.5 mA. A voltmeter is made using this galvanometer and a 4.5 k$$\Omega$$ resistance. The maximum voltage, that can be measured using this voltmeter, will be close to

A charge +q is placed at the origin O of XY-axes as shown in the figure. The work done in taking a charge Q from A to B along the straight line AB is

A thin equi-convex lens is made of glass of refractive index 1.5 and its focal length is 0.2 m. If it acts as a concave lens of focal length 0.5 cm when dipped in a liquid, the refractive index of the liquid is

A potentiometer wire, 10 m long, has a resistance of 40$$\Omega$$. It is connected in series with a resistance box and a 4 V storage cell. If the potential gradient along the wire is 0.4 mV cm^$$-$$1, the resistance unplugged in the box is

In the circuit shown, if the 10 $$\Omega$$ resistor is replaced by a resistor of 15 $$\Omega$$, then what is the amount of current drawn from the battery?

A spherical lens of power $$-$$4D is placed at a distance of 15 cm from another spherical lens of power 5 D. A beam of parallel light falls on the first spherical lens. The final image formed is

Three solenoid coils of same dimensions, same number of turns and same number of layers of windings are taken. Coil 1 has inductance L₁ wounded by Mn wire of resistance 6 $$\Omega$$m^$$-$$1, coil 2 with inductance L₂ wounded by similar wire but in reverse direction in each layer. Coil 3 with inductance L₃ wounded by a superconducting wire. The relation between their self inductances will be

Given that in a fluorescent lamp's choke, a reverse voltage of 120 V is generated as the choke's current changes steadily from 0.50 A to 0.20 A in a time frame of 0.030 ms. Calculate the self inductance of the choke in millihenrys (mH).

In the circuit shown in figure, the AC source has angular frequency $$\omega$$ = 2000 rad s^$$-$$1. The amplitude of the current will be nearest to

A long cylindrical iron core of cross-sectional area 5 cm² is inserted into a long solenoid having 4000 turns/meter and carrying a current 5 A. The magnetic field inside the core is $$\pi$$ T. Find the pole strength developed.

What is the magnitude of the force experienced per unit length by a thin wire that carries a current of I = 10 A and is formed into a semi-circle with a radius of R = 20$$\pi$$ cm at a point O?

The magnetic field of a beam emerging from a fitter facing a flood light is given by

B = 10 $$\times$$ 10^$$-$$8 sin(1 $$\times$$ 10⁷z $$-$$ 3.6 $$\times$$ 10¹⁵t)T. The average intensity of the beam is

The decay constants of two radioactive substances X and Y are 4$$\lambda$$ and $$\lambda$$ respectively. At t = 0, a sample has the same number of two nuclei. The time taken for the ratio of number of nuclei to become $${1 \over {{e^3}}}$$ will be

The reading of the ammeter for a germanium diode in the given circuit is

Identify the hydrogen-like element whose spectral lines are four times shorter in wavelength compared to those of atomic hydrogen.

The combination of the gates shown in following figure yields

At the top of a mountain the thermometer reads 0$$^\circ$$C and the barometer reads 710 mm Hg. At the bottom of the mountain the temperature is 30$$^\circ$$C and the pressure is 760 mm Hg. The ratio of the density of air at the top to that of the bottom is

Sulphuric acid is a dibasic acid. It ionises in two stages and hence has two dissociation constants K_a1 and K_a2. Which of the following is the correct observation regarding K_a1 and K_a2 ?

Which of the following statement is correct?

If the quantum number I could have the value 'n' also then, Sc(21) would have electronic configuration as (other rules strictly followed)

Ionisation energy of H-atom is 13.6 eV. The wavelengths of the spectral line emitted when an electron in Be³⁺ comes them 5th energy level to 2nd energy level is

Which of the following statements on critical constants of gases are correct?

I. Larger the T_c/p_c value of a gas, larger would be the included volume.

II. Critical temperature (T_c) of a gas is greater than its Boyle temperature (T_B).

III. At the critical point in the van der Waals' gas isotherm, $${\left( {{{\partial p} \over {\partial {V_m}}}} \right)_{{T_c}}} = 0$$

Select the correct answer using the codes given below.

1.1 mole of A mixed with 2.2 moles of B and the mixture is kept in a 1 L flask and the equilibrium, A + 2B $$\rightleftharpoons$$ 2C + D is reached. If at equilibrium 0.2 mole of C is formed then the value of K_c will be

How many mL of perhydrol is required to produce sufficient oxygen which can be used to completely convert 2 L of SO₂ gas?

The molar heat of vaporisation of water at 100$$^\circ$$C is 40.585 kJ/mol. The temperature at which a solution containing 5.60 g of Al₂(SO₄)₃ per 1000 g of water boil is __________. (Assuming the degree of ionisation of salt to be 1).

Titration of 0.1467 g of primary standard Na₂C₂O₄ required 28.85 mL of KMnO4

Choose the correct chemical reaction among the following:

Which of the following reactions represents disproportionation?

A(g) $$\to$$ P(g) + Q(g) + R(g),

Follow first order kinetics with a half-life of 69.3 s at 500$$^\circ$$C. Starting from the gas 'A' an container at 500$$^\circ$$C and at a pressure of 0.4 atm, the total pressure of the system after 230 s will be

A volume of 50.00 mL of a weak acid of unknown concentration is titrated with 0.10 M solution of NaOH. The equivalence point is reached after 39.30 mL of NaOH solution has been added. At the half equivalence point (19.65 mL) the pH is 4.85. Thus, initial concentration of the acid and its pK_a values are

Following statements regarding the periodic trends of chemical reactivity to the alkali metals and the halogens are given. Which of these statements gives the correct picture?

Out of the options listed below, which one cannot be explained by adsorption?

A solution of copper sulphate is electrolyzed between copper electrodes by a current of 10.0A passing for one hour. Which of the following statements is correct regarding the changes occur at the electrodes and in the solution?

An element occurs in two crystalline forms $$\alpha$$ and $$\beta$$. The $$\alpha$$-form has an fcc with $$a = 3.68\,\mathop A\limits^o $$ and $$\beta$$ form has a bcc with $$a = 2.92\,\mathop A\limits^o $$. Calculate the ratio of their densities.

Which of the following is not a mixed pair of oxides?

The correct order of pseudohalide, polyhalide and interhalogen is

An inorganic halide (A) reacts with water to form two acids (B) and (C). (A) also reacts with NaOH to form two salts (D) and (E) which remain in solution. The solution gives white precipitate with both AgNO₃ and BaCl₂ solutions respectively. (A) is a useful organic reagent. The compound (A) is

On the basis of Ellingham diagram, which of the following is not correct?

(B) is identified by the characteristic colour of the flame. (A) and (B) are respectively :

Match the following columns:

The process of 'eutrophication' is due to the

Identify the incorrect statement regarding the complex [Cr(NH₃)₆]Cl₃.

In qualitative analysis when H₂S is passed through an aqueous solution of salt acidified with dilute HCl, a black ppt. is obtained. On boiling the precipitate with dil. HNO₃, it forms a solution of blue colour. Addition of excess of aqueous solution of NH₃ to this solution gives

Identify structure of compound (D).

Most acidic hydrogen is present in

According to IUPAC nomenclature sodium nitroprusside is named as

In the given reaction,

Product (D) is

Compound C is

In a set of reactions, m-bromobenzoic acid gives a product D. Identify the product D:

The final product of the following reaction is/are

Identify 'A' and 'B' in the following reaction

1-phenyl-1, 3-dibromopropane on treatment with alc. KOH givens diastereomeric mixture in which compound (A) is major product. (A) gives the following reaction

(A) $$\buildrel {AlC{l_3}/\Delta } \over \longrightarrow $$ (B) $$\buildrel {:CuBr} \over \longrightarrow $$ (C) + (D)

When x¹⁰⁰ is divided by x² $$-$$ 3x + 2, the remainder is (2^{k + 1} $$-$$ 1)x $$-$$(2^k $$-$$ 1), then k is

Let x₁ and x₂ be the real roots of the equation $${x^2} - (k - 2)x + ({k^2} + 3k + 5) = 0$$, then maximum value of $$x_1^2 + x_2^2$$ is

Which of the following statement is incorrect?

Which of the following gives paracetamol on acetylation?

An organic base C₈H₁₁N(X) reacts with nitrous acid at 0$$^\circ$$C to give a clear solution. Heating the solution with KCN and cuprous cyanide followed by continued heating with conc. HCl gives a crystalline solid. Heating this solid with alkaline potassium permanganate gives a compound which dehydrates on heating to an anhydride (C₈H₄O₃). Compound X is

If $${\log _5}{{(a + b)} \over 3} = {{{{\log }_5}a + {{\log }_5}b} \over 2}$$, then $${{{a^4} + {b^4}} \over {{a^2}{b^2}}}$$ is equal to

The value of the sum $$\sum\limits_{k = 1}^\infty {\sum\limits_{n = 1}^\infty {{k \over {{2^{n + k}}}}} } $$ is

If a₁, a₂, a₃, ......., a₂₀ are AM's between 13 and 67, then the maximum value of a₁, a₂, a₃, ......, a₂₀ is equal to

Given that x, y, and z are three consecutive positive integers and x $$-$$ z + 2 = 0, what is the value of $${1 \over 2}{\log _e}x + {1 \over 2}{\log _e}z + {1 \over {2xz + 1}} + {1 \over 3}{\left( {{1 \over {2xz + 1}}} \right)^3} + ...$$?

The number of numbers divisible by 3 that can be formed by four different even digits is

If p, q, r are in AP and are positive, the roots of the quadratic equation px² + qx + r = 0 are all real for

If one GM, g and two AM's p and q are inserted between two numbers a and b, then (2p $$-$$ q) (p $$-$$ 2q) is equal to

If $$A = \{ x:{x^2} = 1\} $$ and $$B = \{ x:{x^4} = 1\} $$, then A $$\Delta$$ B is equal to

How many three digit number satisfy the property that the middle digit is arithmetic mean of the first and the last digit.

If n(A) = 1000, n(B) = 500, n(A $$\cap$$ B) $$\ge$$ 1 and n(A $$\cup$$ B) = P, then

The coefficient of x⁸ in the polynomial (x $$-$$ 1) (x $$-$$ 2) ..... (x $$-$$ 10)

If 4 dice are rolled, then the number of ways of getting the sum 10 is

The value of $${}^{47}{C_4} + \sum\limits_{r = 1}^5 {{}^{52 - r}{C_3}} $$ is equal to

If $$z = r{e^{i\theta }}$$, then arg(e^iz) is

If a and b are two vectors such that | a | = 1, | b | = 4 a . b = 2. If c = (2a $$\times$$ b) $$-$$ 3b, then angle between b and c

An ordered pair ($$\alpha$$, $$\beta$$) for which the system of linear $$(1 + \alpha )x + \beta y + z = 2$$, $$\alpha x + (1 + \beta )y + z = 3$$, $$\alpha x + \beta y + 2z = 2$$ has a unique solution.

Consider matrix $$A = \left[ {\matrix{ 2 & 1 \cr 1 & 2 \cr } } \right]$$, if $${A^{ - 1}} = \alpha I + \beta A$$, where $$\alpha$$, $$\beta$$ $$ \notin $$ R, then ($$\alpha$$ + $$\beta$$) is equal to (where A^$$-$$1 denotes the inverse of matrix A)

The mean of five observation is 5 and their variance is 9.20. If three of the given five observation are 1, 3 and 8, then a ratio of other two observations is

A line passing through P(3, 7, 1) and R(2, 5, 7) meet the plane 3x + 2y + 11z $$-$$ 9 = 0 at Q. Then PQ is equal to

A bird is sitting on the top of a vertical pole 20 m high and its elevation from a point O on the ground is 45$$^\circ$$. If flies off horizontally straight way from the point O. After one second, the elevation of the bird from O is reduced to 30$$^\circ$$, then the speed (in m/s) of the bird is

The number of distinct solutions of the equation $${5 \over 4}{\cos ^2}2x + {\cos ^4}x + {\sin ^4}x + {\cos ^6}x = 2$$ in the interval [0, 2$$\pi$$] is

If $$z = {{7 + i} \over {3 + 4i}}$$, then z¹⁴ is

The root of the equation $$2(1 + i){x^2} - 4(2 - i)x - 5 - 3i = 0$$, where $$i = \sqrt { - 1} $$, which has greater modulus, is

The equation $$(\cos \beta - 1){x^2} + (\cos \beta )x + \sin \beta = 0$$ in the variable x has real roots, then $$\beta$$ lies in the interval

Let f(x) = x $$-$$ 3, g(x) = 4 $$-$$ x. Then the set of values of x for which $$|f(x) + g(x)|\, < \,|f(x)| + |g(x)|$$ is true, is given by :

Let $$f(x) = {x \over {\sqrt {1 + {x^2}} }}$$, $$\underbrace {fofofo.....of(x)}_{x\,times}$$ is

The solution set of $${{|x - 2|\, - 1} \over {|x - 2|\, - 2}} \le 0$$ is

The solution of differential equation $$(x{y^5} + 2y)dx - xdy = 0$$, is

The value of $$\mathop {\lim }\limits_{x \to \infty } {1 \over n}\left\{ {{1 \over {n + 1}} + {2 \over {n + 2}} + .... + {{3n} \over {4n}}} \right\}$$ is

$$\left\{ {x \in R:{{2x - 1} \over {{x^3} + 4{x^2} + 3x}} \in R} \right\}$$ is equal to

If $$2f(xy) = {(f(x))^x} + {(f(y))^x}$$ for all $$x,y \in R$$ and $$f(1) = a( \ne 1)$$. Then $$\sum\limits_{k = 1}^n {f(k) = } $$

Let $$f(x) = {a_0} + {a_1}{x^2} + {a_2}{x^4} + {a_3}{x^6} + ... + {a_n}{x^{2n}}$$ be a polynomial in a real variable x with $$0 < {a_1} < {a_2} < {a_3} < .... < {a_n}$$, the function f(x) has

The solution of the equation $${{dy} \over {dx}} + {1 \over x}\tan y = {1 \over {{x^2}}}\tan y\sin y$$ is

Let f(x) be a polynomial function of second degree. If f(1) = f($$-$$1) and a, b, c are in AP, then f'(a), f'(b) and f'(c) are in.

The value of the definite integral $$\int\limits_0^{\pi /2} {{{dx} \over {\tan x + \cot x + \cos ec\,x + \sec x}}} $$

Given that $$f(x) = 2{x^3} + {x^4} + \log x$$ and assuming g to be the inverse function of f, compute the value of g'(3).

Which one of the following statements is correct?

The distance of point of intersection of the tangents to the parabola x = 4y $$-$$ y² drawn at the points where it is meet by Y-axis, from its focus is

If the tangent at a point $$\left( {4\cos \phi ,{{16} \over {\sqrt {11} }}\sin \phi } \right)$$ to the ellipse $$16{x^2} + 11{y^2} = 256$$ is also a tangent to $${x^2} + {y^2} - 2x = 15$$, then $$\phi$$ equsls

Which one of the following statements is not correct?

The measurement of the distance from point A(1, 2) parallel to the line 3x $$-$$ y = 10 to the line x + y + 5 = 0 is

Circle centered at origin and having radius $$\pi$$ units is divided by the curve y = sin x in two parts. Then area of upper parts equals to

What would force the planning process to undergo a change?

What should be given priority attention?

Which one of the following is implied by the expression 'momentous trends'?

Find out which part of a sentence has an error. If there is no error mark part (d) as your answer.

The road a. / to famous monument b. / passes through a forest. c./ No error d

Find out which part of a sentence has an error. If there is no error mark part (d) as your answer.

Find out which part of a sentence has an error. If there is no error mark part (d) as your answer.

Select the related word from the given alternatives.

Mechanic : Spanner : : Carpenter : ?

Yuvraj Singh is suffering from a BENIGN cancer.

SAGACIOUS decisions taken at right time in one's career has long effects.

He is a NOTED figure of film industry.

The engineer 'ROUGHED OUT' his ideas on a piece of paper while he talked.

The actor got 'PEEVISH' on asking personal questions.

Find out the wrong number.

2, 6, 12, 72, 865, 62208

In the following question find the odd letters/group from the given alternatives.

Each of P, Q, T, A and B has different heights. T is taller than P and B but shorter than A and Q. P is not the shortest, who is the tallest?

Identify the missing part of the question figure and select it from given answer figures.

In the following question three 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).

Among the four answer figures, which one can be formed from the cut out pieces given below in the question figures?

A piece of paper is folded and cut as shown below in the question figures. From the given answer figures, indicates how it will appear when opened.

Find out which of the answer figures (a), (b), (c) and (d) completes the figure matrix?

A curve passes through (2, 0) and the slope of the tangent at P(x, y) is equal to $${{{{(x + 1)}^2} + y - 3} \over {x + 1}}$$ then the equation of the curve is

She has not got .................... the shock of losing her father.