Chemistry
1. Which one of the following is correct order of given isotopes?
I. T2 > D2 > P2 (order of boiling point)
II. T2 > D2 > P2 2. Ninhydrin gives yellow colour in paper chromatography with which amino acid? 3. How will raise in temperature affects the viscosity of liquids and gases? 4. Which of the following compounds is thermodynamically is the most stable? 5. Glucose reacts with X number of molecules of phenyl hydrazine to yield osazone. The value of X is, 6. Nylon-6, 6 is obtained from 7. What is the hybridisation of [CrF6]3$$-$$ ? 8. OF and F2 can be compared in terms of 9. ortho and para form of hydrogen have 10. The structure of H2O2 is 11. Match the species in Column I with their types in Column II.
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.tg td{b 12. In which pair or pairs is the stronger bond found in the first species?
I. O$$_2^{2 - }$$, O2; II. N2, N$$_2^{+ }$$; III 13. Select the correct statement about the complex [Co(NH3)5SO4] Br. 14. A certain metal sulphide, MS2, is used extensively as a high temperature lubricant. If MS2 is 40.06% by mass sulphur, me 15.
X and Y are 16. Ge (II) compounds are powerful reducing agents whereas Pb (IV) compounds are strong oxidants. It can be because 17. Which compound has antifluorite structure? 18. 100 mL of 2 M of formic acid (pKa = 3.74) is neutralise by NaOH, at the equivalence point pH is 19. The reaction of C6H5CH = CHCH3 with HBr produces 20. The number of 3C$$-$$2e$$-$$ bonds present in diborane is 21. Standard entropy of X2, Y2 and XY2 are 60, 40 and 50 JK$$-$$1mol$$-$$1, respectively. For the reaction, $$\frac{1}{2}$$X 22. The total number of P$$-$$OH bonds for pyrophosphoric acid 23. Using the standard electrode potential, find out the pair between which redox reaction is not feasible.
E$$^\Theta $$ va 24. What is [NH$$_{4}^+$$] in a solution that is 0.02 M NH3 0.01 M KOH ? [Kb(NH3) = 1.8 $$\times$$ 10$$-$$5] 25. For an isomerisation reaction A $$\rightleftharpoons$$ B, the temperature dependence of equilibrium constant is given by 26. In an adiabatic process, no transfer of heat takes place between system and surrounding. Choose the correct option for f 27. The given graph represents the variation of compressibility factor (Z) = $$\frac{pV}{nRT}$$, for three real gases A, B a 28. Which one of the following statements in relation to the hydrogen atom is correct? 29. In the molecules CH4, NF3, NH$$_4^ + $$ and H2O 30. 0.20 g of an organic compound gave 0.12 g of AgBr. By using Carius method, the percentage of bromine in the compound wil
English Proficiency
1. $$\underline {Forthrightness} $$ in speech may not always be a desirable quality. 2. The $$\underline {inexorable} $$ demands of the workers brought the company to a closure. 3. Then her face was bowed. 4. The complex form of the sentence given below would be
Spare the rod and spoil the child. 5. The attack on the freedom of the press is a $$retrograde$$ step. 6. The leader might have had some $$covert$$ reason for the change of his political affiliations. 7. Regard for other as a principle of action or selflessly. 8. Code of diplomatic etiquette and precedence is 9. (A) Now under liberated economy they are learning to compete domestically and globally.
(B) In India corporations until 10. (A) Recovery was given inadequate attention and consequently some bank branches regularly incurred heavy losses and thei
Logical Reasoning
1. Select the figure that can replace the question mark (?) in the following series.
2. '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 3. Three different positions of the same dice are shown, the six faces of which are numbered from 1 to 6. Select the number 4. Select the option in which the given figure X is embedded (rotation is not allowed).
5. Selecty the letter-cluster that can replace the question mark (?) in the following series.
TULG, WRPC, ZOTY, CLXU, ? 6. How many triangles are there in the given figure?
7. The average marks of 50 students in a class was found to be 64. If the marks of two students were incorrectly entered as 8. Select the correct mirror image of the given figure when the mirror is placed on the right of the figure.
9. 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 s 10. 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 11. In the following question, complete the missing segment by selecting the appropriate figure from the given alternatives, 12. In each of the following question, find out which of the answer figures (a), (b), (c) and (d) completes the figure matri 13. Statements
60% of government employees went on strike.
Mr. Gopal is a government employee.
Conclusions
I. Mr. Gopal went 14. Statements
Lawyers marry only fair girls.
Shobha is very fair.
Conclusions
I. Shobha is married to a lawyer.
II. Shobha 15. In the question given below, find out which of the figures can be formed from the pieces given in the problem figure.
16. Select the option in which the words share the same relationship as that shared by the given pair of words.
Barometer : 17. Select the option in which the words share the same relationship as that shared by the given set of words.
Cat : Lion : 18. 'Needle' is related to 'Sew' in the same way as 'Microscope' is related to '...........' . 19. Select the option that is related to the fifth number in the same way as the second number is related to the first numbe 20. Select the letter-cluster that can replace the question mark (?) in the following series.
TXB, QWE, NVH, KUK, ?
Mathematics
1. If $$\alpha$$ be a root of the equation $$4{x^2} + 2x - 1 = 0$$, then the other root of the equation is 2. 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 3. If $$|w| = 2$$, then the set of points $$z = w - {1 \over w}$$ is contained in or equal to the set of points z satisfyin 4. The value of $$\mathop {\lim }\limits_{x \to 0} {{1-\cos (1 - \cos x)} \over {{x^4}}}$$ is 5. 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 6. The number of terms in the expansion of $${(1 + 5\sqrt {2x} )^9} + {(1 - 5\sqrt {2x} )^9}$$ is 7. The number of different seven-digit numbers that can be written using only the three digits 1, 2 and 3 with the conditio 8. Given 2x $$-$$ y + 2z = 2, x $$-$$ 2y - z = $$-$$4, x + y + $$\lambda$$z = 4, then the value of $$\lambda$$ such that th 9. Let $$A = \left[ {\matrix{
1 & { - 1} & 1 \cr
2 & 1 & { - 3} \cr
1 & 1 & 1 \cr
} } \right]$$ and $$10B 10. If $$x \in \left( {0,{\pi \over 2}} \right)$$, then the value of $${\cos ^{ - 1}}\left( {{7 \over 2}(1 + \cos 2x) + \sq 11. 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-ci 12. $$\left( {{{dy} \over {dx}}} \right)\tan x = y{\sec ^2}x + \sin x$$, find general solution 13. If the straight line $$y = mx + c$$ touches the parabola $${y^2} - 4ax + 4{a^3} = 0$$, then c is 14. A normal is drawn at the point P to the parabola $${y^2} = 8x$$, which is inclined at 60$$^\circ$$ with the straight lin 15. The value of $$\int {{1 \over {{{[{{(x - 1)}^3}{{(x + 2)}^5}]}^{{1 \over 4}}}}}dx} $$, is 16. What is the area enclosed by the parabola described by $${(y - 2)^2} = (x - 1)$$, its tangent line at the point (2, 3), 17. $$\widehat u$$ and $$\widehat v$$ are two non-collinear unit vectors such that $$\left| {{{\widehat u + \widehat v} \ove 18. A six faced die is a biased one. It is thrice more likely to show an odd numbers than show an even number. It is thrown 19. The sum of all the solution of the equation $$\cos \theta \cos \left( {{\pi \over 3} + \theta } \right)\cos \left( {{\p 20. Let $$\alpha$$ be the solution of $${16^{{{\sin }^2}\theta }} + {16^{{{\cos }^2}\theta }} = 10$$ in $$\left( {0,{\pi \o 21. For each parabola y = x2 + px + q, meeting coordinate axes at 3-distinct points, if circles are drawn through these poin 22. The number of ways of arranging letters of the word HAVANA so that V and N do not appear together is 23. Let a1, a2, a3 .... be a harmonic progression with a1 = 5 and a20 = 25. The least positive integer n for which an 24. If the plane $$3x + y + 2z + 6 = 0$$ is parallel to the line $${{3x - 1} \over {2b}} = 3 - y = {{z - 1} \over a}$$, then 25. Let a, b be the solutions of x2 + px + 1 = 0 and c, d be the solution of x2 + qx + 1 = 0. If (a $$-$$ c) (b $$-$$ c) and 26. If $$\left[ {\matrix{
1 & { - \tan \theta } \cr
{\tan \theta } & 1 \cr
} } \right]{\left[ {\matrix{
1 & { 27. The value of $$\mathop {\lim }\limits_{x \to 0} {{{{(1 + x)}^{{1 \over x}}} - e + {1 \over 2}ex} \over {{x^2}}}$$ is 28. The locus of the mid-point of the chord if contact of tangents drawn from points lying on the straight line $$4x - 5y = 29. Let $$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 30. 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 ot 31. 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 co 32. 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
33. If g(x) = x2 + x $$-$$ 2 and $$\frac{1}{2}gof(x)=2x^2-5x+2$$, then f(x) is equal to 34. The smallest positive integral value of n such that $${\left[ {{{1 + \sin {\pi \over 8} + i\cos {\pi \over 8}} \over { 35. Given that a house forms a right angle view from a window of another house, and the angle of elevation from the base of 36. A spherical balloon is filled with 4500$$\pi$$ cubic meters of helium gas. If a leak in the balloon causes the gas to es 37. If in a $$\Delta$$ABC, 2b2 = a2 + c2, then $$\frac{\sin 3B}{\sin B}$$ is equal to 38. If the sum of the coefficients in the expansion of (x + y)n is 1024, then the value of the greatest coefficient in the e 39. The area enclosed by the curves $$y = \sin x + \cos x$$ and $$y = |\cos x - \sin x|$$ over the interval $$\left[ {0,{\pi 40. If $$\alpha,\beta,\gamma \in[0,\pi]$$ and if $$\alpha,\beta,\gamma$$ are in AP, then $${{\sin \alpha - \sin \gamma } \o
Physics
1. The stopping potential (V0) versus frequency $$\nu $$ of a graph for photoelectric effect in a metal. From the graph, th 2. In a resonance coloum first and second resonance are obtained at depths 24 cm and 78 cm the third resonance will be obta 3. A submarine A travelling at 17 m/s is being chased along the line of its velocity by another submarine B travelling at 3 4. Transverse waves of the same frequency are generated in two steel wires A and B. The diameter of A is twice that of B an 5. In the diagram shown below, both the strings AB and CD are made of same material and have same cross-section. The pulley 6. What will be the acceleration due to gravity at a depth d, where g is acceleration due to gravity on the surface of eart 7. A direct current of 6 A is superimposed on an alternating current I = 10 sin $$\omega$$t flowing through a wire. The eff 8. Which one of the following graphs represents the variation of electric potential with distance r from the centre of a no 9. For an insulator, the forbidden energy gap is 10. A machine gun fires 300 bullets per min if the mass of each bullet is 10 g and the velocity of the bullets is 600 ms$$-$ 11. 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 remainin 12. A particle of mass m is projected with velocity v at an angle $$\theta$$ with the horizontal. At its highest point, it e 13. In the circuit shown assume the diode to be ideal. When Vi increases from $$-$$2V to 6V, the change in current is (in mA 14. The de-Broglie wavelength of an electron moving with a velocity $$\frac{c}{3}$$ (c = 3 $$\times$$ 108 m/s) is equal to t 15. In the circuit shown in the figure, the AC source gives a voltage V = 20 cos (2000t) neglecting source resistance, the v 16. An electromagnetic wave is propagating along X-axis. At x = 1 cm and t = 18s, its electric vector |E| = 8 V/m, then the 17. In the following circuit the equivalent resistance between X and Y is ......... $$\Omega$$
18. A monoatomic gas of molar mass m is kept in a insulated container. Container is moving with velocity v. If the container 19. A projectile is projected with the velocity of $$(3\widehat i + 4\widehat j)$$ m/s. The horizontal range of the projecti 20. A transistor is connected in common-emitter (CE) configuration. The collector supply is 8V and the voltage drop across a 21. 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 cha 22. 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 c 23. 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 24. A mosquito O is sitting infront of a glass rod having spherical end of radius of curvature 40 cm. The image would be for 25. One mole of an ideal diatomic gas undergoes a process as shown in the figure. The molar specific heat of the gas in the 26. A capillary tube is attached horizontally to a constant heat arrangement. If the radius of the capillary tube is increas 27. In the arrangement shown in figure, when the switch S2 is open, the galvanometer, shows no deflection for $$l$$ = 50 cm 28. In a young's double slit arrangement fringes are produced using light of wavelength 4000 $$\mathop A\limits^o $$. One sl 29. An electric current I enters and leaves a uniform circular wire of radius r through diametrically opposite points. A cha 30. An achromatic convergent doublet of two lenses in contact has a power of +5 D. The power of converging lens is +6 D. The
1
BITSAT 2022
MCQ (Single Correct Answer)
+3
-1
$$\left( {{{dy} \over {dx}}} \right)\tan x = y{\sec ^2}x + \sin x$$, find general solution
A
$$y = \tan x(\log |{\mathop{\rm cosec}\nolimits} x - \cot x| + \cos x + c)$$
B
$$y = {\sec ^2}x + \tan x + c$$
C
$$y = \log |\sec x + \tan x| + {\mathop{\rm cosec}\nolimits} \,x + c$$
D
$$y = {\tan ^2}x + \sin x + c$$
2
BITSAT 2022
MCQ (Single Correct Answer)
+3
-1
If the straight line $$y = mx + c$$ touches the parabola $${y^2} - 4ax + 4{a^3} = 0$$, then c is
A
$$am + {a \over m}$$
B
$$am - {a \over m}$$
C
$${a \over m} + {a^2}m$$
D
$${a \over m} - {a^2}m$$
3
BITSAT 2022
MCQ (Single Correct Answer)
+3
-1
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
A
$$2x + y - 12 - 4\sqrt 3 = 0$$
B
$$2x - y - 12 + 4\sqrt 3 = 0$$
C
$$2x - y - 12 - 4\sqrt 3 = 0$$
D
None of these
4
BITSAT 2022
MCQ (Single Correct Answer)
+3
-1
The value of $$\int {{1 \over {{{[{{(x - 1)}^3}{{(x + 2)}^5}]}^{{1 \over 4}}}}}dx} $$, is
A
$${4 \over 3}{\left( {{{x + 1} \over {x - 2}}} \right)^{{1 \over 4}}} + C$$
B
$${3 \over 4}{\left( {{{x - 1} \over {x + 2}}} \right)^{{1 \over 4}}} + C$$
C
$${4 \over 3}{\left( {{{x - 1} \over {x + 2}}} \right)^{{1 \over 4}}} + C$$
D
$${1 \over 3}{\left( {{{2x - 1} \over {4x - 3}}} \right)^{{1 \over 4}}} + C$$
Paper analysis
Total Questions
Chemistry
30
English Proficiency
10
Logical Reasoning
20
Mathematics
40
Physics
30
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