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KVPY Mock Test – SB / SX (Short)
Number of questions  60 
Type of questions  Multiple Choice Question with single answer correct 
Time limit (duration of exam)  90 minutes (1.5 hours) 
Mock Test for  KVPY SB/SX Stream 
Marks for correct answer in Part I  +1 
Marks for correct answer in Part II  +2 
Maximum Marks  80 
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Question 1 of 60
1. Question
Category: MathsThe sum of nonreal roots of the polynomial equation x^{3} + 3x^{2} + 3x + 3 = 0.

Question 2 of 60
2. Question
Category: MathsLet n be a positive integer such that
log_{2}log_{2}log_{2}log_{2}log_{2}(n) < 0 < log_{2}log_{2}log_{2}log_{2}(n).
Let l be the number of digits in the binary expansion of n. Then the minimum and the maximum possible values of l are 
Question 3 of 60
3. Question
Category: MathsLet ω be a cube root of unity not equal to 1. Then the maximum possible value of  a + bw + cw^{2}  where a, b, c ∈ {+1, ñ1} is

Question 4 of 60
4. Question
Category: MathsIf a, b are positive real numbers such that the lines ax + 9y = 5 and 4x + by = 3 are parallel, then the least possible value of a + b is

Question 5 of 60
5. Question
Category: MathsTwo line segments AB and CD are constrained to move along the x and y axes, respectively, in such a way that the points A, B, C, D are concyclic. If AB = a and CD = b, then the locus of the centre of the circle passing through A, B, C, D in polar coordinates is

Question 6 of 60
6. Question
Category: MathsConsider a triangle ABC in the xy plane with vertices A = (0,0), B = (1,1) and C = (9, 1). If the line x = a divides the triangle into two parts of equal area, then a equals

Question 7 of 60
7. Question
Category: MathsLet ABC be an acuteangled triangle and let D be the midpoint of BC. If AB =AD, then tan(B)/tan(C) equals

Question 8 of 60
8. Question
Category: MathsThe angles α, β, γ of a triangle satisfy the equations 2sinα + 3cosβ = 3√2 and 3sinβ + 2cosα = 1. Then angle γ equals

Question 9 of 60
9. Question
Category: MathsLet f : R → R be a function such that f(x) = M > 0. Then which of the following is false?

Question 10 of 60
10. Question
Category: MathsFor x, t ∈ R let
p_{t}(x) = (sint)x^{2}(2cost)x + sint
be a family of quadratic polynomials in x with variable coefficients. Let A(t) = pt(x)dx Which of the following statements are true?
(I) A(t) < 0 for all t.
(II) A(t) has infinitely many critical points.
(III) A(t) = 0 for infinitely many t.
(IV) A(t) < 0 for all t. 
Question 11 of 60
11. Question
Category: PhysicsConsider an initially neutral hollow conducting spherical shell with inner radius r and outer radius 2r. Apoint charge +Q is now placed inside the shell at a distance r/2 from the centre. The shell is then grounded by connecting the outer surface to the earth. P is an external point at a distance 2r from the point charge +Q on the line passing through the centre and the point charge +Q as shown in the figure.
The magnitude of the force on a test charge +q placed at P will be

Question 12 of 60
12. Question
Category: PhysicsConsider the circuit shown in the figure below :
All the resistors are identical. The charge stored in the capacitor, once it is fully charged, is 
Question 13 of 60
13. Question
Category: PhysicsA nuclear decay is possible if the mass of the parent nucleus exceeds the total mass of the decay particles. If M(A, Z) denotes themass of a single neutral atom of an element with mass numberAand atomic number Z, then the minimal condition that the β decay
will occur is (m_{e} denotes the mass of the β particle and the neutrino mass m_{v} can be neglected) :

Question 14 of 60
14. Question
Category: Physics“The equation of state of n moles of a nonideal gas can be approximated by the equation
(P + n^{2}a/V^{2}) (V – nb) = nRT
where a and b are constants characteristic of the gas.Which of the following can represent the equation of a quasistatic adiabat for this gas (Assume that C_{V}, themolar heat capacity at constant volume, is independent of temperature)?”

Question 15 of 60
15. Question
Category: PhysicsAblackbox (BB) whichmay contain a combination of electrical circuit elements (resistor, capacitor or inductor) is connected with other external circuit elements as shown below in the figure (a). After the switch (S) is closed at time t = 0, the current (I) as a function of time (t) is shown in the figure (b).
From this we can infer that the blackbox contains

Question 16 of 60
16. Question
Category: PhysicsIn a photocell circuit the stopping potential, V_{0}, is a measure of the maximum kinetic energy of the photoelectrons. The following graph shows experimentally measured values of stopping potential versus frequency v of incident light.
The values of Planks constant and the work function as determined from the graph are (taking the magnitude of electronic charge to be e = 1.6 × 10^{19} C)

Question 17 of 60
17. Question
Category: PhysicsAn engine moving away from a vertical cliff blows a born at a frequency f. Its speed is 0.5% of the speed of sound in air. The frequency of the reflected sound received at the engine is

Question 18 of 60
18. Question
Category: PhysicsAn arangement with a pair of quarter circular coils of radii r and R with a common centre C and carrying a current I is shown.
The permeability of free space is μ_{0}. The magnetic field at C is

Question 19 of 60
19. Question
Category: PhysicsThe circuit shown has been connected for a long time. The voltage across the capacitor is

Question 20 of 60
20. Question
Category: PhysicsA wheel of radius R with an axle of radius R/2 is shown in the figure and is free to rotate about a frictionless axis through its centre and perpendicular to the page. Three forces (F, F, 2F) are exerted tangentially to the repective rims as shown in the figure.
The magnitude of the net torque acting on the system is nearly 
Question 21 of 60
21. Question
Category: ChemistryAmong the following, the set of isoelectronic ions is

Question 22 of 60
22. Question
Category: ChemistryFor a zeroorder reaction with rate constant k, the slope of the plot of reactant concentration against time is

Question 23 of 60
23. Question
Category: ChemistryThe compound which reacts with excess bromine to produce 2, 4, 6tribromophenol, is

Question 24 of 60
24. Question
Category: ChemistryEthyl acetate reacts with NH_{2}NHCONH_{2} to form

Question 25 of 60
25. Question
Category: ChemistryThe variation of solubility of four different gases (G1, G2, etc.) in a given solvent with pressure at a constant temperature is shown in the plot.
The gas with the highest value of Henrys law constant is

Question 26 of 60
26. Question
Category: ChemistryFor the reaction A ⇔ B, the concentration of Adecreases from 0.06 to 0.03mol L^{1} and that of B rises from 0 to 0.06 mol L^{1} at equilibrium. The values of n and the equilibrium constant for the reaction, respectively, are

Question 27 of 60
27. Question
Category: ChemistryThe reaction of ethyl methyl ketone with Cl_{2}/excess OH^{} gives the following major product

Question 28 of 60
28. Question
Category: ChemistryThe compound that readily tautomerizes is

Question 29 of 60
29. Question
Category: ChemistryHydrolysis of BCl3 gives X which on treatment with sodium carbonate produces Y, X and Y, respectively, are

Question 30 of 60
30. Question
Category: ChemistryThe numbers of lone pair(s) on Xe in XeF_{2} and XeF_{4}are, respectively,

Question 31 of 60
31. Question
Category: BiologyHuman fetal haemoglobin differs from the adult haemoglobin in that it has

Question 32 of 60
32. Question
Category: BiologyNucleolus is an organelle responsible for the production of

Question 33 of 60
33. Question
Category: BiologyThe sequences of four DNAmolecules are given below:
i.TATATATATATATA ii. TTTCCCGGGAAA
ATATATATATATAT AAAGGGCCCTTT
iii.TTGCGTTGCCC iv.GCCGGATCCGGC
AACGCAACGGG CGGCCTAGGCCG
Which one of these DNAmoelcules will have the highestmelting temperature (T_{m})? 
Question 34 of 60
34. Question
Category: BiologyIf DNA codons are ATG GAA, insertion of thymine after the first codon results in,

Question 35 of 60
35. Question
Category: BiologyGenetic content of a cell reduces to half during

Question 36 of 60
36. Question
Category: BiologyWhich one of the following techniques is used for the detection of proteins ?

Question 37 of 60
37. Question
Category: BiologyFission yeasts are

Question 38 of 60
38. Question
Category: BiologyIn green leaves, the light and dark reactions occur in

Question 39 of 60
39. Question
Category: BiologyAccording to Mendel, ………………………………. segregate and ……………………… assort independently

Question 40 of 60
40. Question
Category: BiologyThe two enzymatic activities associated with RUBISCO are

Question 41 of 60
41. Question
Category: Maths IILet f(x) be a nonconstant polynomial with real coefficients such that f(1/2) = 100 and f(x) ≤ 100 for all real x. Which of the following statements is NOT necessarily true ?

Question 42 of 60
42. Question
Category: Maths IILet a, b, c, d be real numbers such that
for every natural number n. Then  a  +  b  +  C  +  d  is equal to

Question 43 of 60
43. Question
Category: Maths IIThe vertices of the base of an isosceles triangle lie on a parabola y^{2} = 4x and the base is a part of the line y = 2x  4. If the third vertex of the triangle lies on the xaxis, its coordinates are

Question 44 of 60
44. Question
Category: Maths IIIn a triangle ABC, let G denote its centroid and let M, N be points in the interiors of the segments AB, AC, respectively, such that M, G, N are collinear. If r denotes the ratio of the area of triangle AMN to the area of ABC then

Question 45 of 60
45. Question
Category: Maths IILet XY be the diameter of a semicircle with centre O. Let A be a variable point on the semicircle and B another point on the semicircle such that AB is parallel to XY. The value of ∠BOY for which the inradius of triangle AOB is maximum, is

Question 46 of 60
46. Question
Category: Physics IIA bullet of mass m is fired horizontally into a large sphere of mass M and radius R resting on a smooth horizontal table.
The bullet hits the sphere at a height h from the table and sticks to its surface. If the sphere starts rolling without slippng immediately on impact, then

Question 47 of 60
47. Question
Category: Physics IIA small boy is throwing a ball towards a wall 6 in front of him. He releases the ball at a height of 1.4 m from the ground. The ball bounces from the wall at a height of 3 m, rebounds from the ground and reaches the boys hand exactly at the point of release. Assuming the two bounces (one from the wall and the other from the ground) to be perfectly elastic, how far ahead of the boy did the ball bounce from the ground?

Question 48 of 60
48. Question
Category: Physics IIIn the PV diagram below the dashed curved line is an adiabat.
For a process that is described by a straight line joining two points X and Y on the adiabat (solid line in the diagram) heat is : (hint : Consider the variations in temperature from X to Y along the straitght line)

Question 49 of 60
49. Question
Category: Physics IIA singly ionized helium atom in an excited state (n = 4) emits a photon of energy 2.6 eV. Given that the ground state energy of hydrogen atom is  13.6 eV, the energy (E_{t}) and quantum number (n) of the resulting state are respectively,

Question 50 of 60
50. Question
Category: Physics IIThe figure below shows a circuit and its input voltage v_{i} as function of time t.
Assuming the diodes to be ideal, which of the following graphs depicts the output voltage v_{0} as function of time t ?

Question 51 of 60
51. Question
Category: Chemistry IIThe major product obtained in the reaction of aniline with acetic anhydride is

Question 52 of 60
52. Question
Category: Chemistry IIThe maximum number of isomers that can result from monobromination of 2methyl2pentene with Nbromosuccinimide in boiling CCl_{4} is

Question 53 of 60
53. Question
Category: Chemistry IIThe compound X (C_{7}H_{9}N) reacts with benzensulfonyl chloride to give Y (C_{13}H_{13}NO_{2}S) which is insoluble in alkali. The compound X is

Question 54 of 60
54. Question
Category: Chemistry IIIn 108 g of water, 18 g of a nonvolatile compound is dissolved.At 100°C the vapor pressure of the solution is 750mm Hg.Assuming that the compound does not undergo association or dissociation, themolar mass of the compound in g mol^{1} is

Question 55 of 60
55. Question
Category: Chemistry IIThe standard electrode potential of Zn^{2+}/Zn is 0.76 V and that of Ca^{2+}/Cu is 0.34 V. The emf (V) and the free energy change (kJ mol^{1}), respectively, for a Daniel cell will be

Question 56 of 60
56. Question
Category: Biology II10^{9} bacteria were spread on an agar plate containing penicillin.After incubation overnight at 37°C, 10 bacterial colonies were observed on the plate. That the colonies are likely to be resistant to penicillin can be tested by

Question 57 of 60
57. Question
Category: Biology IIWatson and Crick model of DNA is

Question 58 of 60
58. Question
Category: Biology IIEco RI and Rsa I restriction endonucleases require 6 bp and 4 bp sequences respectively for cleavage. In a 10 kb DNA fragment howmany probable cleavage sites are present for these enzymes

Question 59 of 60
59. Question
Category: Biology IIFrom an early amphibian embryo the cells that would give rise to skin in adults were transplanted into the developing brain region of another embryo. The transplanted cells developed into brain tissue in the recipient embryo.What do you infer from this experiment?

Question 60 of 60
60. Question
Category: Biology IIPresence of plastids in Plasmodium suggests