FULL SYLLABUS TEST-2 KISHORE VAIGYANIK PROTSAHAN YOJANA (KVPY) | STREAM (SA)_XI ® Time: 3 Hours Max. Marks : 100. Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose. INSTRUCTIONS 1. Immediately fill the particulars on this page of the Test Booklet with Blue / Black Ball Point Pen. Use of pencil is strictly prohibited. 2. The question paper consists of two parts (both contain only multiple choice questions) for 100 marks. There will be four sections in Part-A (each containing 15 questions) and four sections in Part-B (each containing 5 questions). 3. There are Two parts in the question paper. The distribution of marks subjectwise in each part is as under for each correct response. MARKING SCHEME : PART-A : MATHEMATICS Question No. 1 to 15 consist of ONE (1) mark for each correct response & – 0.25 for incorrect response. PHYSICS Question No. 16 to 30 consist of ONE (1) mark for each correct response & – 0.25 for incorrect response. CHEMISTRY Question No. 31 to 45 consist of ONE (1) mark for each correct response & – 0.25 for incorrect response. BIOLOGY Question No. 46 to 60 consist of ONE (1) mark for each correct response & – 0.25 for incorrect response. PART-B : MATHEMATICS Question No. 61 to 65 consist of TWO (2) marks for each correct response & – 0.5 for incorrect response. PHYSICS Question No. 66 to 70 consist of TWO (2) marks for each correct response & – 0.5 for incorrect response. CHEMISTRY Question No. 71 to 75 consist of TWO (2) marks for each correct response & – 0.5 for incorrect response. BIOLOGY Question No. 76 to 80 consist of TWO (2) marks for each correct response & – 0.5 for incorrect response. 4. No deduction from the total score will be made if no response is indicated for an item in the Answer sheet. 5. No candidate is allowed to carry any textual material, printed or written, bits of papers, paper, mobile phone, any electronic device, etc., except the Admit Card inside the examination hall/room. 6. Rough work is to be done on the space provided for this purpose in the Test Booklet only. This space is given at the bottom of each page. 7. On completion of the test, the candidate must hand over the Answer Sheet to the Invigilator on duty in the Room/Hall. However, the candidates are allowed to take away this Test Booklet with them. 8. Do not fold or make any stray marks on the Answer Sheet. Resonance Eduventures Limited REGISTERED & CORPORATE OFFICE : CG Tower, A-46 & 52, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.) - 324005 Ph.No. : 0744-2777777, 0744-2777700 | Toll Free : 1800 258 5555 | FAX No. : +91-022-39167222 | 73400 10333 Website : www.resonance.ac.in | E-mail : [email protected]| CIN: U80302RJ2007PLC024029 Name of the Candidate : I have read all the instructions and shall abide by them ....................................... Signature of the Candidate Roll Number : I have verified all the information filled by the candidate. ........................................ Signature of the Invigilator
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FULL SYLLABUS TEST-2
KISHORE VAIGYANIK PROTSAHAN YOJANA
(KVPY) | STREAM (SA)_XI
®
Time: 3 Hours Max. Marks : 100.
Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.
INSTRUCTIONS
1. Immediately fill the particulars on this page of the Test Booklet with Blue / Black Ball Point
Pen. Use of pencil is strictly prohibited.
2. The question paper consists of two parts (both contain only multiple choice questions) for 100 marks. There will be four sections in Part-A (each containing 15 questions) and four sections in Part-B (each containing 5 questions).
3. There are Two parts in the question paper. The distribution of marks subjectwise in each part is as under for each correct response.
MARKING SCHEME :
PART-A :
MATHEMATICS
Question No. 1 to 15 consist of ONE (1) mark for each correct response & – 0.25 for incorrect
response. PHYSICS
Question No. 16 to 30 consist of ONE (1) mark for each correct response & – 0.25 for incorrect response.
CHEMISTRY
Question No. 31 to 45 consist of ONE (1) mark for each correct response & – 0.25 for incorrect response.
BIOLOGY
Question No. 46 to 60 consist of ONE (1) mark for each correct response & – 0.25 for incorrect response.
PART-B :
MATHEMATICS
Question No. 61 to 65 consist of TWO (2) marks for each correct response & – 0.5 for incorrect response.
PHYSICS
Question No. 66 to 70 consist of TWO (2) marks for each correct response & – 0.5 for incorrect response.
CHEMISTRY
Question No. 71 to 75 consist of TWO (2) marks for each correct response & – 0.5 for incorrect response.
BIOLOGY
Question No. 76 to 80 consist of TWO (2) marks for each correct response & – 0.5 for incorrect response.
4. No deduction from the total score will be made if no response is indicated for an item in the Answer sheet.
5. No candidate is allowed to carry any textual material, printed or written, bits of papers, paper, mobile phone, any electronic device, etc., except the Admit Card inside the examination hall/room.
6. Rough work is to be done on the space provided for this purpose in the Test Booklet only. This space is given at the bottom of each page.
7. On completion of the test, the candidate must hand over the Answer Sheet to the Invigilator on duty in the Room/Hall. However, the candidates are allowed to take away this Test Booklet with them.
8. Do not fold or make any stray marks on the Answer Sheet.
Resonance Eduventures Limited REGISTERED & CORPORATE OFFICE : CG Tower, A-46 & 52, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.) - 324005
1. A 5-digit number abcde, when multiplied by 9, gives the 5-digit number edcba. The sum of the digits in
the number is (A) 18 (B) 27 (C) 36 (D) 45
2. Let x and y be two positive real numbers such that x + y = 1. Then the minimum value of y
1
x
1 is
(A) 2 (B) 2
5 (C) 3 (D) 4
3. Suppose p,q,r are positive rational numbers such that rqp is also rational. Then
(A) r,q,p are irrational
(B) qr,pr,pq are rational, but r,q,p are irrational
(C) r,q,p are rational
(D) qr,pr,pq are irrational
4. Let x, y be real numbers such that x > 2y > 0 and 2log(x – 2y) = logx + logy
Then the possible value(s) of y
x
(A) is 1 only (B) are 1 and 4 (C) is 4 only (D) is 8 only 5. Let p1(x) = x3 – 2020x2 + b1x + c1 and p2(x) = x3 – 2021x2 + b2x + c2 be polynomials having two common
roots and . Suppose there exist polynomials q1(x) and q2(x) such that p1(x)q1(x) + p2(x)q2 (x) = x2 – 3x + 2. Then the correct identity is
(A) p1(3) + p2(1) + 4028 = 0 (B) p1(3) + p2(1) + 4026 = 0 (C) p1(2) + p2(1) + 4028 = 0 (D) p1(1) + p2(2) + 4028 = 0 6. Let ABCD be a quadrilateral such that there exists a point E inside the quadrilateral satisfying
AE = BE = CE = DE. Suppose DAB, ABC,BCD is an arithmetic progression. Then the median of
the set {DAB, ABC, BCD} is
(A) 6
(B)
4
(C)
3
(D)
2
7. Let r be the remainder when 20212020 is divided by 20202. Then r lies between (A) 0 and 5 (B) 10 and 15 (C) 20 and 100 (D) 107 and 120 8. In the integers from 1 to 2021 are written as single integer like 123…91011…20202021, then the 2021st
digit (counted from the left) in the resulting number is (A) 0 (B) 1 (C) 6 (D) 9
9. In a triangle ABC, a point D is chosen on BC such that BD : DC = 2:5. Let P be a point on the
circumcircle ABC such that PDB = BAC. Then PD : PC is
(A) 5:2 (B) 2 : 5 (C) 2 : 7 (D) 7:2
10. Let [x] be the greatest integer less than or equal to x, for a real number x. Then the following sum
16
16
15
15
14
14
13
13
12
122018
2020
2018
2020
2018
2020
2018
2020
2018
2020
is (A) 80 (B) 85 (C) 90 (D) 95 11. Let M = 230 – 215 + 1, and M2 be expressed in base 2. The number of 1's in this base 2 representation of
M2 is: (A) 29 (B) 30 (C) 59 (D) 60
12. In a triangle ABC, the altitude AD and the median AE divide A into three equal parts. If BC = 28, then
the nearest integer to AB + AC is (A) 38 (B) 37 (C) 36 (D) 33 13. The number of permutations of the letters a1, a2, a3, a4, a5 in which the first letter a1 does not occupy the
first position (from the left) and the second letter a2 does not occupy the second position (from the left) is
(A) 96 (B) 78 (C) 60 (D) 42 14. There are m books in black cover and n books in blue cover and all books are different. The number of
ways these (m + n) books can be arranged on a shelf so that all the books in black cover are put side by side is
(A) m!n! (B) m!(n + 1)! (C) (n + 1)! (D) (m + n)! 15. Let [x] be the greatest integer less than or equal to x, for a real number x. Then the equations [x2] = x + 1 has (A) two solution (B) one solution (C) no solution (D) more than two solution
PHYSICS
16. A frictionless wire AB is placed on a fixed smooth sphere of radius R. The length of the wire is adjustable along the surface of the sphere. A very small spherical bead slips on this wire as shown in
the figure. The time taken by the bead to slip from A to B after release varies with (if 0 < /2) as :
17. A ball is thrown upward at an angle of 30° with the horizontal and lands on the top edge of a building
that is 20 m away. The top edge is 5m above the throwing point. The initial speed of the ball in metre/second is (take g = 10 m/s2) :
(A) 10 m/s (B) 20 m/s (C) 25 m/s (D) 30 m/s 18. A swimmer wants to cross a river and reach point B directly from A. The speed of the swimmer in still
river and that of river flow are same. The dotted line AN is normal to flow direction of river. For swimmer
to reach point B, the angle his velocity relative to river will make with line AN is given by . Then the
value of is :
(A) 60° (B) 30° (C) 45° (D) 0°
19. Two blocks of masses m1 = 8 kg and m2 = 7 kg are connected by a light string passing over a light frictionless pulley. The mass m1 is at rest on the inclined plane and mass m2 hangs vertically. The angle of inclination is 30º. Therefore, the force of friction acting on m1 is
(A) 30 N up the plane (B) 30 N down the plane (C) 40 N up the plane (D) 40 N down the plane
20. Kinetic energy of a particle moving in a straight line varies with time as K = 4t2. The force acting on the particle.
(A) is constant (B) is increasing (C) is decreasing (D) first increases and then decreases 21. Two blocks A and B each of same mass are attached by a thin inextensible string through an ideal
pulley. Initially block B is held in position as shown in figure. Now the block B is released. Bolck A will slide to right and hit the pulley in time tA. Block B will swing and hit the surface in time tB. Assume the surface as frictionless.
(A) tA = tB (B) tA < tB (C) tA > tB (D) data are not sufficient to get relationship between tA and tB.
22. Two identical disks are positioned on a vertical axis as shown in the fig. The bottom disk is rotating at
an angular velocity o and has rotational kinetic energy k
o. The top disk is initially at rest. It allowed to
fall and sticks to the bottom disk. The change in the rotational kinetic energy of the system after the collision is:
23. The figure shows four progressive waves A, B, C & D. It can be concluded from the figure that with respect to wave A:
(A) the wave C is ahead by a phase angle of /2 & the wave B lags behind by a phase angle /2
(B) the wave C lags behind by a phase angle of /2 & the wave B is ahead by a phase angle of /2
(C) the wave C is ahead by a phase angle of& the wave B lags behind by the phase angle of
(D) the wave C lags behind by a phase angle of & the wave B is ahead by a phase angle of 24. Which of the following will have maximum average total kinetic energy at temperature 300 K. (A) 1 kg of H
2 (B) 1 kg of He
(C) 1
2 kg of H
2 +
1
2 kg of He (D)
1
4 kg of H
2 +
3
4 kg of He
25. An ideal gas follows a process described by PV2 = C from (P1, V1, T1) to (P2, V2, T2) (C is a constant). Then
(A) if P1 > P2 then T2 > T1 (B) if V2 > V1 then T2 < T1 (C) if V2 > V1 then T2 > T1 (D) If P1 > P2 then V1 > V2
26. In the figure shown a hole of radius 2 cm is made in a semicircular disc of radius 6 cm at a distance 8 cm from the centre C of the disc. The distance of the centre of mass of this system from point C is:
(A) 4 cm (B) 8 cm (C) 6 cm (D) 12 cm
27. The intensity of sound during the festival season increased by 100 times. This could imply a decibel
level rise from (A) 20 to 120 dB (B) 70 to 72 dB (C) 100 to 10000 dB (D) 80 to 100 dB 28. A man stands at rest in front of a large wall. A sound source of frequency 400 Hz is placed between him and the wall. The source is now moved towards the wall at a speed of 1 m/s. The number of beats heard per second will be(speed of sound in air is 345 m/s) (A) 0.8 (B) 0.58 (C) 1.16 (D) 2.32
29. During the head on collision of two masses 1 kg and 2 kg the maximum energy of deformation is 100
3J.
If before collision the masses are moving in the same direction, then their velocity of approach before the collision is :
33. The correct order of increasing pH values of the aqueous solutions of baking soda, rock salt,
washing soda and slaked lime is:
(A) Baking Soda < Rock Salt < Washing Soda < Slaked lime
(B) Rock Salt < Baking Soda < Washing Soda < Slaked lime
(C) Slaked lime < Washing Soda < Rock Salt < Baking Soda
(D) Washing Soda < Baking Soda < Rock Salt < Slaked lime
34. The weight of oxalic acid required to neutralize 100 mL of normal NaOH is : (A) 6.3 g (B) 126 g (C) 530 g (D) 63 g 35. Which has the highest e/m ratio ? (A) He2+ (B) H+ (C) He+ (D) D+
36. Which of the following compound is planar and non-polar? (A) XeO4 (B) SF4 (C) XeF4 (D) CF4
37. The oxidant which cannot act as reducing agent is: (A) SO2 (B) NO2 (C) CO2 (D) C1O2
38. The value of Planck's constant is 6.63 × 10–34 Js. The velocity of light is 3.0 × 108 m s–1. Which value is
closest to the wavelength in nanometers of a quantum of light with frequency of 8 × 1015 s–1 ? (A) 3 × 107 (B) 2 × 10–25 (C) 5 × 10–18 (D) 4 × 101 39. The closed containers of the same capacity and at the same temperature are filled with 44 g of H2
in one and 44 g of CO2 in the other. If the pressure of carbon dioxide in the second container is 1atm, then pressure of hydrogen in the first container would be:
(A) 1 atm (B) 10 atm (C) 22 atm (D) 44 atm 40. The bond order in N2
+ is: (A) 1.5 (B) 3.0 (C) 2.5 (D) 2.0 41. Which of the underlined atoms in the molecules shown below have sp-hybridization?
(u) CH2CHCH3
(w) CH3CH2+
(y) CH3CN
(v) CH2CCHCl
(x) H — C C — H (z) (CH3)2CNNH2
(A) x and z (B) x, y and z (C) u, w and x (D) v, x and y 42. What is the IUPAC name of the compound ?
MATHEMATICS 61. Consider a regular 10-gon with its vertices on the unit circle. With one vertex fixed. draw straight lines to
the other 9 vertices. Cell them L1, L2, ….., L9 and denote their lengths by 1, 2, ,,,,,9 respectively then
the product 1, 2, ,,,,,9 is
(A) 10 (B) 10 3 (C) 3
50 (D) 20
62. Let ABC be triangle such that AB = 4. BC = 5 and CA = 6. Choose points D, E, F on AB, BC, CA
respectively. such that AD = 2, BE = 3, CF = 4. Then ABCarea
DEFarea
is
(A) 4
1 (B)
15
3 (C)
15
4 (D)
30
7
63. For [0,]. Let f() = sin(cos and g() = cos(sin) . Let a = fmax
0, b =
fmin
0 ,
c = gmax
0and d =
gmin
0 . The correct inequalities satisfied by a, b, c, d are
(A) b < d < c < a (B) d < b < a < c (C) b < d < a < c (D) b < a < d < c 64. A bottle in the shape of a right-circular cone with height h contains some water. When its base is placed
on a flat surface, the height of the vertex from the water level is a units. When it is kept upside down,
the height of the base from the water level is 4
a units. Then the ratio
a
h is
(A) 4
851 (B)
8
851 (C)
4
651 (D)
8
651
65. Consider the following two statements: I. If n is a composite number, then n divides (n –1)!. II. There are infinitely many natural numbers n such that n3 + 2n2 + n divides n!. Then (A) I and II are true (B) I and II are false (C) I is true and II is false (D) I is false and II is true
PHYSICS
66. At the instant a motor bike starts from rest in a given direction, a car overtake the motor bike, both moving in the same direction The speed time graphs for motor bike and the car are represented by OAB and CD respectively. Then
C
A B
D
60
40
20
O 27 18 12
speed
(m/s)
s.
(A) at t = 18 s the motorbike and car are 180 m apart.
(B) at t = 18 s the motor bike and car are 720 m apart
(C) the relative distance between motor bike and car always remains same.
67. A bullet of mass m moving with velocity v0 just grazes (bullet does not slip on the disc during the contact
with the disc) the top of a uniform circular disc of mass M and radius R resting on a rough horizontal surface as shown in figure. Assuming that the disc rolls without slipping, find the velocity of the bullet just after it grazes the disc :
(A) M3m8
mu4
(B)
M3m8
mu8
(C)
M3m4
mu8
(D)
M3m4
mu4
68. Two pendulums differ in lengths by 22 cm. They oscillate at the same place so that one of them makes
30 oscillations and the other makes 36 oscillations during the same time. The lengths (in cm) of the pendulum are :
(A) 72 and 50 (B) 60 and 38 (C) 50 and 28 (D) 80 and 58 69. Four identical beakers contain same amount of water as shown below. Beaker 'a' contains only water.
A lead ball is held submerged in the beaker 'b' by string from above. A same sized plastic ball, say a table tennis (TT) ball, is held submerged in beaker 'c' by a string attached to a stand from outside. Beaker 'd' contains same sized TT ball which is held submerged from a string attached to the bottom of the beaker. These beakers (without stand) are placed on weighing pans and register reading Wa, Wb, Wc and Wd for a, b, c and d, respectively. (Effects of the mass and volume of the stand and string are to be neglected.)
a
b
lead
c
TT
d
TT
(A) Wa = Wb = Wc = Wd (B) Wb = Wc > Wd > Wa
(C) Wb = Wc > Wa > Wd (D) Wb > Wc > Wd > Wa
70. 540 g of ice at 0ºC is mixed with 540 g of water at 80ºC. The final temperature of the mixure is (A) 0ºC (B) 40ºC (C) 80ºC (D) 100°C
CHEMSITRY
71. Which of the following metal sulphides has maximum solubility in water?
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(A) tA = tB (B) tA < tB (C) tA > tB
(D) lwpuk vi;kZIr gS blfy, tA rFkk tB esa laca/k iznf'kZr ugha fd;k tk ldrkA
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xfrt ÅtkZ ko gSA Åij okyh pdrh izkjEHk esa fojkekoLFkk esa gSA Åij okyh pdrh dks fxjus ds fy;s NksM+k x;k gSA
;g uhps okyh pdrh ij fpid tkrh gSA VDdj ds ckn fudk; dh ?kw.kZu xfrt ÅtkZ esa ifjorZu gksxk:
(A) ko/2 (B) (1/2) k
o (C) (1/4) k
o (D) k
o/4
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(A) rjax C, /2 dyk dks.k ls vkxs rFkk rjax B, /2 dyk dks.k ls ihNs gS (B) rjax C, /2 dyk dks.k ls ihNs rFkk rjax B, /2 dyk dks.k ls vkxs gS (C) rjax C, dyk dks.k ls vkxs rFkk rjax B, dyk dks.k ls ihNs gS (D) rjax C, dyk dks.k ls ihNs rFkk rjax B, dyk dks.k ls vkxs gS
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39. leku {kerk okys ik=kksa esa] leku rki ij] ,d ik=k esa H2 ds 44 g rFkk vU; ik=k esa CO2 ds 44 g Hkjh x;h gSA ;fn f}rh; ik=k esa dkcZuMkbZvkWDlkbM dk nkc 1atm gS rc izFke ik=k esa gkbMªkstu dk nkc gksxk&