Chemistry
1. The most volatile compound among the given option is 2. What is the magnetic moment of Ti2+ ? (Given : Atomic number = 22) 3. Why only Xe can form compounds with fluorine among noble gases? 4. Which of the following inert gas is used as cryogenic agnet? 5. For the following reaction
2A + 3B $$\to$$ 3C + 4D
expression for rate of reaction is 6. Cyclohexanol on reacting with H2SO4 and then heating gives 7. The major product obtained on reaction of 3-methylbutene with HCl is 8. If Rydberg constant is same for all elements, the angular momentum and energy of Li2+ of which orbital is equal to angul 9. Sodium iodide reacts with ammonia to gives 10. In photography, which compound is used as a fixing agent 11. The compound formed on reaction of epoxy ethane with NH3 and H2O is 12. The process of removal of excess electrolyte from colloidal solution is 13. Maltase converts maltose into 14. Starch is a polymer of 15. Methyl alcohol can be distinguished from ethyl alcohol using 16. Sodium stearate (C17H35COO$$-$$Na+) is 17. Which is not an anti-fluorite structure 18. The structure of CIF3 is 19. Which of the following is diamagnetic in nature? 20. The correct order of bond order in SO2, SO3, SO$$_4^{2 - }$$, SO$$_3^{2 - }$$ is 21. Ionisation energy for H+ ion is proportional to rn, then value of n is 22. Role of BHA in food industries 23. Permanganate ion (MnO$$_4^ - $$) is dark purple coloured though Mn is in + 7 oxidation state with d0 configuration. This 24. Rutherford model could not explain 25. Which is true in case of [Ni(CO)4]? 26. SI unit of Boltzmann's constant is 27. Acetone does not undergo which type of reaction? 28. Magnetic moment of in [Co(F6)]2$$-$$ of unpaired electron .......... . 29. Some statements about heavy water are given below
1. Heavy water is used as a moderator in nuclear reactors.
2. Heavy wa 30. CH3$$-$$CHCl$$-$$CH2$$-$$CH3 has a chiral centre, which of the following represents its R configurations? 31. In Victor Meyer's method 0.2 g of an organic substance displaced 56 mL of air at STP the molecular weight of the compoun 32. 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 33. The incorrect expression among the following is 34. 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 35. 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 36. The relative lowering of vapour pressure of a dilute aqueous solution containing non-volatile solute is 0.0125. The mola 37. Equal masses of methane and oxygen are mixed in an empty container at 25$$^\circ$$C. The fraction of the total pressure 38. The molar conductivities of KCl, NaCl and KNO3 are 152, 128 and 111 S cm2 mol$$-$$1 respectively. What is the molar cond 39. The approximate time duration in hours to electroplate 30 g of calcium from molten calcium chloride using a current of 5 40. Given, the reduction potential of Na+, Mg2+, Al3+ and Ag+ as $$E_{N{a^ + }/Na}^o$$ = $$-$$ 2.17 V; $$E_{M{g^{2 + }}/Mg}^
English Proficiency
1. Decay is an $$\underline {immutable} $$ factor of human life. 2. It was an $$\underline {ignominious} $$ defect for the team. 3. His $$\underline {conjecture} $$ was the better than mine. 4. Freedom and quality are the ................ rights of every human. 5. Pradeep's face spoke .................. of the happiness he was feeling. 6. His speech was disappointing : it ................ all the major issues. 7. Hydra is biologically believed to be immortal. 8. The Gupta rulers patronised all cultural activities and thus Gupta period was called the golden era in Indian History. 9. This is a barbarous act. 10. A person who does not believe in any religion 11. A person who believes that pleasure is the chief good 12. One who loves mankind 13. A. Tasty and healthy food can help you bring out their best.
B. One minute they are toddlers and next you see them in th 14. 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 b 15. A. However, women hiring is catching up at a slow and steady rate in the recent times.
B. Gender ratio has been inclined
Logical Reasoning
1. Choose the correct answer figure which will make a complete square on joining with the problem figure.
2. In the following question, five figures are given. Out of them, find the three figures that can be joined to form a squa 3. Choose the answer figure which completes the problem figure matrix.
Problem Figure
4. From the given four positions of a single dice, find the color at the face opposite to the face having red color.
5. In the following question, one or more dots are placed in the figure marked as (A). The figure is followed by four alter 6. Complete the series by replacing '?' mark.
G4T, J9R, M20P, P43N, S90L, ? 7. Neeraj starts walking towards South. After walking 15 m, he turns towards North. After walking 20 m, the turns towards E 8. 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 th 9. Shikha is mother-in-law of Ekta who is sister-in-law of Ankit. Pankaj is father of Sanjay, the only brother of Ankit. Ho 10. 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 t
Mathematics
1. If Re(z + 2) = | z $$-$$ 2 |, then the locus of z is 2. If a$$\in$$R, b$$\in$$R, then the equation x2 $$-$$ abx $$-$$ a2 = 0 has 3. If a + 2b + 3c = 12, (a, b, c $$\in$$R+), then the maximum value of ab2c3 is 4. Sum of n terms of the infinite series
1.32 + 2.52 + 3.72 + ..... $$\infty$$ is 5. If log7 5 = a, log5 3 = b and log3 2 = c, then the logarithm of the number 70 to the base 225 is 6. The maximum number of points of intersection of 10 circles is : 7. $${{{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_ 8. If p$$\ne$$ q $$\ne$$ r and $$\left| {\matrix{
0 & {x - p} & {x - q} \cr
{x + p} & 0 & {x - r} \cr
{x + q} 9. Matrix $$A = \left| {\matrix{
x & 3 & 2 \cr
1 & y & 4 \cr
2 & 2 & z \cr
} } \right|$$, if xyz = 60 and 10. If f(x) = 4x $$-$$ x2, x$$\in$$R, and f(a + 1) $$-$$ f(a $$-$$ 1) = 0, then a is equal to 11. Which of the following is not an equivalence relation in z? 12. Which of the following is always true? 13. The solution of the inequality $${4^{ - x + 0.5}} - {7.2^{ - x}} 14. If $${\cos ^3}x\,.\,\sin 2x = \sum\limits_{m = 1}^n {{a_m}\sin mx} $$ is identity in x, then 15. Total number of solutions of $$\left| {\cot x} \right| = \cot x + {1 \over {\sin x}},x \in [0,3\pi ]$$ is equal to 16. The minimum value of $${({\sin ^{ - 1}}x)^3} + {({\cos ^{ - 1}}x)^3}$$ is equal to 17. The origin is shifted to (1, 2). The equation y2 $$-$$ 8x $$-$$ 4y + 12 = 0 changes to y2 = 4ax, then a is equal to 18. The equations of the bisector of the angles between the straight lines 3x + 4y + 7 = 0 and 12x + 5y $$-$$ 8 = 0 are : 19. Equation of circle which passes through the points (1, $$-$$2) and (3, $$-$$4) and touch the X-axis is 20. If x = 9 is the chord of contact of the hyperbola x2 $$-$$ y2 = 9, then the equation of the corresponding pair of tangen 21. The points with position vectors $$10\widehat i + 3\widehat j$$, $$12\widehat i - 5\widehat j$$ and $$a\widehat i + 11\w 22. Let a, b, c be vectors of lengths 3, 4, 5 respectively and a be perpendicular to (b + c), b to (c + a) and c to (a + b), 23. For non-zero vectors a, b, c; |(a $$\times$$ b) . c| = |a| |b| |c| holds if and only if 24. Angle between the diagonals of a cube is 25. Consider the two lines
$${L_1}:{{x + 1} \over 3} = {{y + 2} \over 1} = {{z + 1} \over 2}$$ and $${L_2}:{{x - 2} \over 1} 26. The distance between the line $$r = 2\widehat i - 2\widehat j + 3\widehat k + \lambda (\widehat i - \widehat j + 4\wideh 27. Two cards are drawn from a pack of 52 cards. What is the probability that either both are red or both are kings? 28. If A and B are two independent events such that $$P(A) = {1 \over 2}$$ and $$P(B) = {1 \over 5}$$, then which of the fol 29. Box I contains 5 red and 2 blue balls, while box II contains 2 red and 6 blue balls. A fair coin is tossed. If it turns 30. For a random variable X, E(X) = 3 and E(X2) = 11. The variable of X is : 31. The sum of 10 items is 12 and the sum of their squares is 18, then the standard deviation will be 32. The height of the chimney when it is found that on walking towards it 50 m in the horizontal line through its base, the 33. The value of $$\mathop {\lim }\limits_{x \to 0} {{\sqrt {1 - {{\cos x}^2}} } \over {1 - \cos x}}$$ is 34. If $$f(x) = \left\{ {\matrix{
{a{x^2} + 1,} & {x \le 1} \cr
{{x^2} + ax + b,} & {x > 1} \cr
} } \right.$$ is 35. The slope of the tangent to the curve x = t2 + 3t $$-$$ 8, y = 2t2 $$-$$ 2t $$-$$ 5 at the point t = 2 is 36. $$\int {{1 \over {1 - 2\sin x}}dx} $$ is equal to 37. $$\int\limits_0^1 {{{\log (1 + x)} \over {1 + {x^2}}}dx} $$ is equal to : 38. The area of one curvilinear triangle formed by curves y = sin x, y = cos x and X-axis, is 39. Solution of $$\left( {{{x + y - 1} \over {x + y - 2}}} \right){{dy} \over {dx}} = \left( {{{x + y + 1} \over {x + y + 2} 40. If $$y = \sin \left( {2{{\tan }^{ - 1}}\sqrt {{{1 - x} \over {1 + x}}} } \right)$$, then $${{dy} \over {dx}}$$ is : 41. The maximum value of the function y = x(x $$-$$ 1)2, is 42. The solution of $${x^3}{{dy} \over {dx}} + 4{x^2}\tan y = {e^x}\sec y$$ satisfying y (1) = 0, is 43. The runs of two players for 10 innings each are as follows
The more consistent player is 44. The linear programming problem minimize z = 3x + 2y subject to constrains x + y $$\ge$$ 8, 3x + 5y $$\ge$$ 15, x $$\ge$$ 45. Find the area enclosed by the loop in the curve 4y2 = 4x2 $$-$$ x3.
Physics
1. An ideal monoatomic gas is taken round the cycle ABCDA as shown in the p-diagram
The work done during the cycle is 2. 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 sho 3. For a constant hydraulic stress on an object, the fractional change in the object's volume $$\left( {{{\Delta V} \over V 4. A shunt is connected in parallel with a galvanometer. Why? 5. The phase difference between Vout and Vin of CE amplifier circuit is 6. If nth division of main scale coincides with (n + 1)th division of vernier scale. The least count of the vernier is (Giv 7. A uniform rod AB of length L = 1 m is sliding along two mutually perpendicular surfaces OP and OQ as shown in the figure 8. A tray of mass (M) 12 kg is supported by a spring as shown in the figure.
When the tray is pressed down and released, i 9. The phasor diagram of a load represents which circuit?
10. The equation of progressive wave is given by $$Y = \sin \left[ {x\left( {{t \over 5} - {x \over 9}} \right) + {\pi \ove 11. The property of light used in optical fibre cables is 12. 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 13. From a solid sphere of mass M and radius R, a spherical portion of radius $${R \over 2}$$ is removed as shown in the fig 14. Four charges equal to + Q are placed at the four corners of a square and a charge ($$-$$q) is at its centre. If the syst 15. 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 16. A proton has kinetic energy E = 100 eV which is equal to that of a photon. The wavelength of photon is $$\lambda$$2 and 17. A block of mass 10 kg rests on a rough inclined plane making an angle of 30$$^\circ$$ with the horizontal. The coefficie 18. Which of the following graphs show the correct relation between conductivity and temperature for a metallic conductor? 19. 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 hy 20. The angular momentum of a body placed at origin of mass 1 kg and having position vector $$r = 3t\widehat i + 4\widehat j 21. If the earth stops rotating about its axis, then what will be the change in the value of g at a place in the equatorial 22. Two cars approach a stationary observer from opposite sides as shown in the figure.
The observer hears no beats. If the 23.
In the following circuit, assuming point A to be at zero potential, then what is the potential at point B? 24. Two plane mirrors A and B are aligned parallel to each other as shown in the figure.
A ray of light is incident at an a 25. A projectile is given an initial velocity of $$(\widehat i + \widehat j)$$ m/s, where, $$\widehat i$$ is along the groun 26. Two drops of equal radius (R) coalesce to form a bigger drop. What is the ratio of surface energy of bigger drop to smal 27. Two particles A and B of masses mA and mB respectively, are having same charge and moving on same plane. A uniform magne 28. The potential difference applied to an X-ray tube is decreased. As a result, in the emitted radiation, 29. The ratio of the specific heats $${{{C_v}} \over {{C_p}}} = {1 \over \gamma }$$ in terms of degrees of freedom (n) is gi 30. A cyclist speeding at 6 m/s in a circle of 18 m radius makes an angle $$\theta$$ with the vertical. The minimum possible 31. Three particles each of mass m are kept at the vertices of an equilateral triangle of side b. Moment of inertia of the s 32. An electric dipole is placed at an angle of 30$$^\circ$$ in a non-uniform electric field. The dipole will experience 33. Two coils A and B have a mutual inductance 0.001 H. The current changes in the first coil according to the equation $$i 34. The current in the circuit will be
35. 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 resistanc 36. A particle executes SHM with a frequency f. The frequency with which its kinetic energy oscillates is 37. A radioactive sample at any instant has its disintegration rate 5000 disintegrations per min. After 5 min, the rate is 1 38. The separation between two parallel plates of capacitor is 1 mm. What is the electric potential generates between the pl 39. Choose the correct statement. 40. A T-shaped object with dimensions shown in figure, is lying on a smooth floor. A force F is applied at the point P paral
1
BITSAT 2021
MCQ (Single Correct Answer)
+3
-1
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
A
$${{ - \widehat i + 7\widehat j + 7\widehat k} \over {\sqrt {99} }}$$
B
$${{ - \widehat i - 7\widehat j + 5\widehat k} \over {5\sqrt 3 }}$$
C
$${{ - \widehat i + 7\widehat j + 5\widehat k} \over {5\sqrt 3 }}$$
D
$${{7\widehat i - 7\widehat j + \widehat k} \over {\sqrt {99} }}$$
2
BITSAT 2021
MCQ (Single Correct Answer)
+3
-1
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
A
$${10 \over {9}}$$
B
$${{10} \over {3\sqrt 3 }}$$
C
$${10 \over {3}}$$
D
None of these
3
BITSAT 2021
MCQ (Single Correct Answer)
+3
-1
Two cards are drawn from a pack of 52 cards. What is the probability that either both are red or both are kings?
A
$${{7} \over {13 }}$$
B
$${{63} \over {221 }}$$
C
$${{55} \over {221 }}$$
D
$${{3} \over {26 }}$$
4
BITSAT 2021
MCQ (Single Correct Answer)
+3
-1
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?
A
$$P\left( {{A \over B}} \right) = {1 \over 2}$$
B
$$P\left( {{A \over {A \cup B}}} \right) = {5 \over 6}$$
C
$$P\left( {{{A \cap B} \over {A' \cup B'}}} \right) = 0$$
D
All of these
Paper analysis
Total Questions
Chemistry
40
English Proficiency
15
Logical Reasoning
10
Mathematics
45
Physics
40
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