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Q.1 The area between the curve x2 = 4y and line x + 2 = 4y is

(1) 9/8

(2) 9/4

(3) 9/2

(4) 5/4

Q.2

Q.3

(1) 10

(2) 15

(3) 20

(4) None

Q.4

Q.5 If xy = 4 and x2 = 4y. Then the common tangent is

(1) y = (–16)1/3x – (–16)2/3

(2) y = (16)1/3x –(16)2/3

(3) y = (–16)2/3x – (–16)1/3

(4) None of tese

Q.6 x2 + y2 + 6x – 8y – 103 = 0; A square inscribed in circle and sides of square are parallel to coordinate axes, then minimum distance of any vertex from origin is

(1) √37

(2) √41

(3) 5

(4) 4

Q.7 There are two circles of same radius they intersect at (0, 1) & (0, –1). Tangent at one point on circle passes through centre of other circle. Then distance between their centres is-

(1) 1

(2) 2

(3) 3

(4) 4

Q.8

(1) 85

(2) 6

(3) 91

(4) –6

Q.9 Straight line x + 2y = 1 cuts coordinates axes at points A and B. A circle passes through points A, B and origin. Then sum of length of perpendicular drawn from A and B on tangent at origin of given circle is

Q.10

Q.11

Q.12

Q.13

Q.14

Q.15

(1) –300

(2) –100

(3) 200

(4) 350

Q.16

(1) 0

(2) sin 4

(3) 4 – sin 4

(4) 2

Q.17 A = {1, 2, 3, ...., 11}, two numbers are selected and sum are even. Then the conditional probability that both numbers are even is

Q.18 Tangent drawn on ellipse 2x2 + y2 = 1 at any point (not in vertex) cut axis of coordinate at point A & B. Then locus of midpoint of AB is

Q.19
Q.19 x2 – c2 = y
x = sum of two sides
y = product of two sides
c = third side
Then circumradius is

Q.20

Q.21

(1) not differentiable at one point

(2) not differentiable at two points

(3) not differentiable at three points

(4) discontinuous in [–2, 2]

Q.22

Q.23

(1) 1

(2) 4

(3) 0

(4) 9

Q.24

Q.25

Q.26

Q.27 Two equal resistance consume power 60 W when connected in series. The value of power when both are connected in parallel

(1) 60 w

(2) 120 w

(3) 180 w

(4) 240 w

Q.28 Focal length of convex lens is 0.3 m. An object is at distance of 20 cm from lens at principle axis. When object is moving away from lens with velocity of 5 m/ then velocity of image will be

(1) 45 m/s away from lens

(2) 25 m/s towards to lens

(3) 45 m/s towards to lens

(4) 35 m/s away from lens

Q.29

Q.30 A particle is projected with speed of 10 m/s at an angle 60° to vertical. The radius of curvature of particle at t = 1 sec will be

Q.31 An electron is moving with speed 500 m/s in an uniform magnetic field B = 100 mT. Calculate radius of path of electron?

(1) 14.22 nm

(2) 28.44 nm

(3) 14.22 Å

(4) 28.44 Å

Q.32

Q.33 For the system as shown, if potential energy of charge system is zero. The value of Q will be-

Q.34

(1) 0.3 V

(2) 0.2 V

(3) 0.8 V

(4) 1 V

Q.35 A particle is moving in a circular path with speed 10 m/s. Change in velocity when it turns by angle 60º.

(1) 5 m/s

(2) 10 m/s

(3) 0 m/s

(4) 20 m/s

Q.36 The equation of plane progressive wave is given by y = 0.03 sin[450 t – 9x]. If mass per unit length of wire is 5 gm/m then find tension in wire-

(1) 25 N

(2) 12.5 N

(3) 6.25 N

(4) 45 N

Q.37 50 gm water at 40ºC is mixed with m gm of ice at –20ºC, 20 gm ice remain unmelted. Find m ?

(1) 20 gm

(2) 40 gm

3) 60 gm

(4) 80 gm

Q.38

Q.39 The moment of inertia of equilateral plane sheet about axis AA′ is I. If middle portion of this sheet which is also a equilateral plane sheet ; as shown in diagram is removed. Find the new moment of inertia of sheet about the same axis.

Q.40 Find current flowing through Zener diode.

(1) 10 mA

(2) 20 mA

(3) 5 mA

(4) 1 mA

Q.41

Q.42 A satellite if rotating near to the surface of earth. By what amount the speed should increased so that it can escape from gravitational field of earth.

Q.43 Find correct option related to given graph.

(1) Spherical shell V vs r

(2) Spherical shell E vs r

(3) Solid sphere V vs r

(4) Solid sphere E vs r

Q.44 At t = 0, switch S1 is closed. After some time 'S1' is opened and 'S2' is closed. Which of following graph represents the variation of current through inductor with time?

Q.45

Q.46

Q.47

(1) 0.74

(2) 0.85

(3) 0.50

(4) 0.25

Q.48 Two solenoids (as shown in figure) with radii r1 and r2 are given. Calculate ratio of self inductance of inner solenoid to mutual inductance of system.

Q.49

Q.50

Q.51

(1) 2

(2) 4

(3) 6

(4) 8

Q.52 Which of the following options is correct for given curve?

Q.53

(1) 9

(2) 9.4

(3) 5.2

(4) 5

Q.54 Which of the following is not correct about Henry’s law.

(1) On increasing temperature value of KH increases

(2) Value of KH increases solubility of gas increases

(3) Value of KH for two different gases at same temperature is not same

(4) None of these

Q.55 Time when concentration of A becomes half

(1) 1

(2) 10

(3) 100

(4) 5

Q.56

(1) 30.3 g

(2) 15.15 g

(3) 7.6 g

(4) 60.6 g

Q.57

Q.58 Given a mixture with 0.5 mole of gas A and X moles of gas B. Total pressure is 200 pa at 1000 k temperature in a vessel of volume 10m3. Then, find x. (R is universal gas constant).

Q.59 Which of the following are isotope of hydrogen

(1) Deutrium, Protium

(2) Deutrium, Tritium

(3) Deutrium, Tritium, Protium

(4) Protium

Q.60

(1) P > Q > R

(2) Q > P > R

(3) R > P > Q

(4) R > Q > P

Q.61

Q.62 Presence of which makes water unsuitable for drinking.

(1) Fe = 0.2 ppm

(2) Cu = 2 ppm

(3) Mn = 0.5 ppm

(4) Zn = 0.05 ppm

Q.63 Which of the following is strongest acid

Q.64 Which of the following alkaline earth metal nitrate does not crystalline with water of crystallization?

Q.65 Which of the following ore contains iron and copper

(1) Malachite

(2) Azurite

(3) Copper pyrite

(4) None of these

Q.66 Considering MOT comment on the stability:

67. Which of the following property in a group decrease down the group and increase down the group respectively.

(1) electronegativity and atomic radius

(2) electronegativity and electro gain enthalpy

(3) atomic radius and electronegativity

(4) electro gain enthalpy and electronegativity

Q.68

Q.69 Which of the following properties is/are true for a silicone polymer?

A) Thermally resistant and have low dielectric constant
B) Resistant towards oxidation and used in grease
C) Biocompalible
D) Hydrophobic in nature

(1 ) A & B

(2) A, B & C

(3) B, C, & D

(4) A, B, C & D

Q.70 Which of the following is a piezo electric material?

(1) Silica

(2) Quartz

(3) Mica

(4) Beryl

Q.71 Aluminium exist in +3 stable where as thallium exist in both +1 & +3 oxidation state. Reason for this is

(1) Inert pair effect

(2) Lanthanoid contraction

(3) Diagonal relationship

(4) None of these

Q.72 Maximum spin only magnetic moment for transition metal complex may be

(1) 5.92 BM

(2) 6.92 BM

(3) 4.89 BM

(4) 3.87 BM

Q.73 Match the following drugs with correct functional group test

A) Chloroxylenol P) Carbylamine
B) Penicillin Q) Baeyer’s reagent
C) Sulpha Pyridine R) FeCl3 test
D) Norethindrone S) Sodium hydrogen sulphate

(1) A → R, B → P, C → S, D → Q

(2) A → S, B → R, C → P, D → Q

(3) A → R, B → S, C → P, D → Q

(4) A → Q, B → R, C → P, D → S

Q.74 Arrange the following amino acids in order of their PKa order. Lysine, Aspartic acid, Arginine, Glycine.

(1) lys > Arg > Gly > Asp

(2) Arg > Lys > Asp > Gly

(3) Gly > Asp > Arg > Lys

(4) Arg > Lys > Gly > Asp

Q.75 Write the product of given reaction:

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