MOCK TEST – BIT-SAT - XtraEdge_2010

3 (B) 2π

k 4

m 3

3 (D) 2π

k 2

m 3

5. The displacement of two identical particles executing SHM are represented by equations

x1 = 4 sin 



 



 +π t 6

10 and x2 = 5 cos ωt

For what value of ω energy of both the particles is same ?

(A) 16 unit (B) 6 unit (C) 4 unit (D) 8 unit

6. A solid sphere of mass M and radius R is placed on a smooth horizontal surface. It is given a horizontal impulse J at a height h above the centre of mass and sphere starts rolling then, the value of h and speed of centre of mass are –

M C R µ = 0 h

(A) h = 5

2 R and v = M

(B) h = 5

2R and v = 5 2

M J

7R and v = 5 7

M J

(D) h = R 5

7 and v = M

MOCK TEST – BIT-SAT

Time : 3 Hours Total Marks : 450

Instructions :

• This question paper contains 150 questions in Physics (40) Chemistry (40), Mathematics (45), Logical Reasoning (10) & English (15). There is Negative Marking

• Each question has four option & out of them, ONLY ONE is the correct answer. There is – ve marking.

• +3 Marks for each correct & – 1 Mark for the incorrect answer.

7. As shown in figure, wheel A of radius rA = 10 cm is coupled by belt B to wheel C of radius rC = 25 cm. The angular speed of wheel A is increased from rest at a constant rate of 1.6 rad/s². Time after which wheel C reaches a rotational speed of 100 rpm, assuming the belt does not slip, is nearly-

A C

(A) 4 sec (B) 8 sec

8. Let r

R ) Q r (

P ₄

=π be the charge density distribution for a solid sphere of radius R and total charge Q. For a point ‘p’ inside the sphere at distance r1 from the centre of the sphere, the magnitude of electric field is-

(A) 0 (B) ₂

1 0 r 4

∈

0 12

R 4

r Q

∈

π (D) ₄

0 12

R 3

r Q

∈

9. An isolated and charged spherical soap bubble has a radius 'r' and the pressure inside is atmospheric. If 'T' is the surface tension of soap solution, then charge on drop is -

(A)

rT 2 2

∈ (B) 8 π r 2rT∈ ₀ (C) 8 π r rT∈ (D) ₀ 8 π r

rT 2

∈

10. Current versus time and voltage versus time graphs of a circuit element are shown in figure.

4.0 sec 1.0

amp

t(s) I(A)

4.0 Volt

t(s) V(Volt)

4.0 sec The type of the circuit element is : (A) capacitance of 2 F

(B) resistance of 2Ω (C) capacitance of 1 F

(D) a voltage source of e.m.f 1 V

11. Three identical metal plates of area 'A' are at distance d1 & d2 from each other. Metal plate A is uncharged, while plate B & C have respective charges +q & – q.

If metal plates A &C are connected by switch K

through a consumer of unknown resistance, what energy does the consumer give out to its surrounding?

Assume d1 = d2 = d A B C

+q –q

K (A)

A 4

d q

0 2

ε (B) A

d q

0 2

ε (C) A 2

d q

0 2

ε (D)

A d q 2

0 2

ε 12. Consider the network of equal resistances (each R)

shown in Figure. Then the effective resistance between points A an B is –

(A) (5/3) R (B) (5/6) R (C) (5/12) R (D) None of these

13. A current of 2 ampere flows in a system of conductors as shown in the following figure. The potential difference (VA – VB) will be - (in volt)

2Ω 3Ω

3Ω 2Ω

2 amp

B D C

(A) +2 (B) +1

14. Consider a toroid of circular cross-section of radius b, major radius R much greater than minor radius b, (see diagram) find the total energy stored in magnetic field of toroid –

(A)

0 2 2 2

2 R b B

π (B)

0 2 2 2

4 R b B

µ π

(C)

0 2 2 2

8 R b B

π (D)

0 2 2

2 b R

B µ

15. AB and CD are smooth parallel rails, separated by a distance L and inclined to the horizontal at an angle θ. A uniform magnetic field of magnitude B, directed vertically upwards, exists in the region. EF is a conductor of mass m, carrying a current I. For EF to be in equilibrium:

A θ

C θ

B E

(A) I must flow from E to F (B) BIL = mg cos θ (C) BIL = mg sin θ (D) BIL = mg

16. In the circuit shown the cell is ideal. The coil has an inductance of 4H and zero resistance. F is a fuse of zero resistance and will blow when the current through it reaches 5A.The switch is closed at t = 0.

The fuse will blow - + –

2V S

F L=4H

(A) after 5 sec (B) after 2 sec (C) after 10 sec (D) almost at once

17. In the circuit shown X is joined to Y for a long time and then X is joined to Z. The total heat produced in R2 is –

Z R2

X Y R1

Fig.

(A) ₂

1 2

R 2

LE (B) ₂

2 2

R 2 LE

(C)

2 1

R R 2

LE (D) ₃

1 2 2

R 2

R LE

18. A step down transformer reduces 220 V to 110 V.

The primary draws 5 ampere of current and secondary supplies 9 ampere. The efficiency of transformer is -

(A) 20% (B) 44%

19. Of the following transitions in hydrogen atom, the one which gives emission line of minimum frequency is -

(A) n = 1 to n = 2 (B) n = 3 to n = 10 (C) n = 10 to n = 3 (D) n = 2 to n = 1

20. In uranium (Z = 92) the K absorption edge is 0.107 Å and the Kα line is 0.126 Å the, wavelength of the L absorption edge is -

(A) 0.7 Å (B) 1 Å (C) 2 Å (D) 3.2 Å

21. A material whose K absorption edge is 0.15 Å is irradiated with 0.1 Å X-rays. The maximum kinetic energy of photoelectrons that are emitted from K-shell is-

(A) 41 KeV (B) 51 KeV (C) 61 KeV (D) 71 KeV

22. The element which has Kα X-ray line whose wavelength is 0.18 nm is –

(A) Iron (B) Cobalt (C) Nickel (D) Copper

23. The momentum of a photon having energy equal to the rest energy of an electron is:

(A) zero

(B) 2.73 × 10^–22 kg ms^–1 (C) 1.99 × 10^–24 kg ms^–1 (D) infinite

24. A parallel beam of uniform, monochromatic light of wavelength 2640 Å has an intensity of 100 W/m². The number of photons in 1 mm³ of this radiation are –

(A) 222 (B) 335

25. The figure shows the variation of photo current with anode potential for a photo-sensitive surface for three different radiations. Let Ia, Ib and Ic be the intensities and fa, fb and fc be the frequencies for the curves a, b and c respectively -

b a c

Anode potential O Photo current

(A) fa = fb and Ia ≠ I_b (B) fa = fc and Ia = Ic

(D) fb = fc and Ib = Ic

26. The internal resistance of a cell is determined by using a potentiometer. In an experiment, an internal resistance of 100 Ω is used across the given cell.

When the key K2 is closed, the balance length on the potentiometer decreases from 90 cm to 72 cm.

Calculate the internal resistance of the cell - (A) 100Ω (B) 75Ω

27. In the potentiometer arrangement shown, the driving cell D has e.m.f. E and internal resistance r. The cell C whose e.m.f. is to be measured has e.m.f. E/2 and internal resistance 2r. The potentiometer wire is 100 cm long. If the balance is obtained the length AP = l, then-

D(E,r)

P B

C (E/2, 2r) G (A) l = 50 cm (B) l > 50 cm (C) l < 50 cm

(D) Balance will not obtained

28. The figure shows a metre-bridge circuit, with AB = 100 cm, X = 12 Ω and R = 18 Ω, and the jockey J in the position of balance.

R – +

A J B

If R is now made 8 Ω, through what distance will J have to be moved to obtain balance?

(A) 10 cm (B) 20 cm (C) 30 cm (D) 40 cm

29. The pitch of a screw gauge is 0.1 cm. The number of divisions on its circular scale is 100. In the measurement of diameter of a wire with this screw gauge the linear scale reading is 'N' cm and the number of division on the reference line is n. Then the radius of the wire in cm will be -

(A) N + 0.01 n (B) N + 0.001 n (C) 0.5 N + 0.001 n

(D) 5(0.1 N+0.0001 n)

30. When ⁶₃Liis bombarded with 4 MeV deutrons, one reaction that is observed is the formation of two α-particles, each with 13.2 MeV of energy. The Q-value for this reaction is -

(A) 13.2 MeV (B) 26.4 MeV (C) 22.4 MeV (D) 4 MeV

31. In a radioactive decay, let N represent the number of residual active nuclei, D the number of daughter nuclei, and R the rate of decay at any time t. Three curves are shown in Fig. The correct ones are –

(1)t

N N

(2)t t

(3) D

(A) 1 and 3 (B) 2 and 3 (C) 1 and 2 (D) all three

32. Young's double slit experiment is made in a liquid. The 10^th bright fringe in liquid lies where 6^th dark fringe lies in vacuum. The refractive index of the liquid is approximately-

(A) 1.8 (B) 1.54

33. A particle moves in a circle of diameter 1 cm with a constant angular velocity. A concave mirror of focal length 10 cm is placed with its principal axis passing through the centre of the circle and perpendicular to its plane. The distance between the pole of the mirror and the centre of the circle is 30 cm. The ratio of acceleration of image to that of object is -

(A) 2

1 (B)

1 (C) 2 (D) 4

34. A concave mirror of focal length 15 cm forms an image having twice the linear dimensions of the object. The position of the object when the image is virtual will be-

(A) 22.5 cm (B) 7.5 cm (C) 30 cm (D) 45 cm

35. A telescope has focal length of objective and eye-piece as 200 cm and 5 cm. What is the magnification of telescope ?

(A) 40 (B) 80 (C) 50 (D) 101 36. A compound microscope has magnifying power as 32

and magnifying power of eye-piece is 4, then the magnifying power of objective is -

(A) 8 (B) 10 (C) 6 (D) 12

37. Two blocks are connected by a massless string through an ideal pulley as shown. A force of 22N is applied on block B when initially the blocks are at rest. Then speed of centre of mass of block A and block B, 2 sec, after the application of force is (masses of A and B are 4 kg and 6 kg respectively and surfaces are smooth) –

A 4kg

6kg F = 22 N

(A) 1.4 m/s² (B) 1 m/s² (C) 2 m/s² (D) None of these

38. A chain of length 1.5 πR and mass ‘m’ is put on a mounted half cylinder as shown in figure. Chain is pulled by vertically downward force 2 mg. Assuming surfaces to be friction less, acceleration of chain is –

F = 2mg

(A) 2g (B)

3 g

2 (C)

g (D)

3 g 5

39. In hydraulic press radii of connecting pipes r1 and r2

are in ratio 1 : 2. In order to lift a heavy mass M on larger piston, the small piston must be pressed through a minimum force f equal to -

(A) Mg (B) Mg/2

40. A uniform rod of length 2.0 m specific gravity 0.5 and mass 2 kg is hinged atone end to the bottom of a tank of water (specific gravity = 1.0) filled upto a height of 1.0 m as shown in figure. Taking the case θ ≠ 0º the force exerted by the hinge on the rod is : (g = 10 m/s²) –

θ 1.0 m

(A) 10.2 N upwards (B) 4.2 N downwards (C) 8.3 N downwards (D) 6.2 N upwards

CHEMISTRY

1. According to Bohr’s theory, angular momentum of an electron in fourth orbit is -

(A) 2π

h (B)

π 4

h (C)

π h

2 (D)

π h 4

2. 1.25g of a solid dibasic acid is completely neutralized by 25 ml. of 0.25 molar Ba(OH)2 solution. Molecular mass of the acid is -

(A) 100 (B) 150 (C) 120 (D) 200

3. Rates of effusion of hydrogen and deuterium under similar conditions are in the ratio -

(A) 1 : 1 (B) 2 : 1 (C) 2 : 1 (D) 1 : 4 4. For equilibrium NH4HS(s) NH³(g) + H2S(g)

KC = 1.8 × 10^–4 at 298 K. The value of Kp at 298 K is-

(A) 0.108 (B) 4.4 × 10^–3 (C) 1.8 × 10^–4 (D) 4.4 × 10^–4

5. Given that H2O (l) → H2O(g) ; ∆H = + 43.7 kJ H2O (s) → H₂O (l) ; ∆H = + 6.05 kJ

∆Hsublimation of ice is -

(A) 49.75 kJ mol^–1 (B) 37.65 kJ mol^–1 (C) 43.7 kJ mol^–1 (D) – 43.67 kJ mol^–1 6. Which of the following is a Lewis base ? (A) CO2 (B) BF3

7. The solubility product Ksp of sparingly soluble salt Ag2CrO4 is 4 × 10^–12. The solubility of the salt is - (A) 1 × 10^–12 M (B) 2 × 10^–6 M

8. Which of the following chemical reactions depicts the oxidising behaviour of H2SO4 ?

(A) 2HI + H2SO4 → I₂ + SO2 + 2H2O (B) Ca(OH)2 + H2SO4 → CaSO₄ + 2H2O

(D) 2PCl5 + H2SO4 → 2POCl3 + 2HCl + SO2Cl2

9. Potassium has a bcc structure with nearest neighbour distance of 4.52 Å. If atomic mass of potassium is 3a, its density is -

(A) 454 kg m^–3 (B) 804 kg m^–3 (C) 852 kg m^–3 (D) 900 kg m^–3

10. If E⁰_Zn2+_/_Zn = – 0.763 V and E⁰_Cd2+_/_Cd= – 0.403 V, the emf of the cell

Zn | Zn²⁺||Cd²⁺|Cd (a = 0.004), (a = 0.2) will be given by -

(A) E = – 0.36 + 2 059 . 0 log

2 004 . 0

(B) E = + 0.36 + 2 059 .

0 log 2

04 . 0

004 . 0

2 . 0

(D) E = + 0.36 + 2 059 . 0 log

004 . 0

2 . 0

11. The value of P° for benzene of certain temperature is 640 mm of Hg. The vapour pressure of solution containing 2.5 g of a certain substance ‘A’ in 39.0 g of benzene is 600 mm of Hg. The molecular mass of A is -

(A) 65.25 (B) 130 (C) 40 (D) 80 12. For adsorption, ∆H is -

(A) + ve (B) – ve

13. A reaction which is of first order w.r.t. reactant A, has a rate constant 6 min^–1. If we start with [A] = 0.5 mol L^–1, when would [A] reach the value of 0.05 mol L^–1 ?

(A) 0.384 min (B) 0.15 min (C) 3 min (D) 3.84 min

14. The number of molecules present in 1 cm³ of water is (density of H2O = 1 g cm^–3)

(A) 2.7 × 10¹⁸ (B) 3.3 × 10²² (C) 6.02 × 10²⁰ (D) 1000

15. CH3NH2 + CHCl3 + KOH → Nitrogen containing compound + KCl + H2O

Nitrogen containing compound is –

(A) CH3 – C ≡ N (B) CH3 – NH – CH3

16. 4-methyl benzene sulphonic acid react with sodium acetate to give –

(A) CH3

SO3Na

; CH3COOH

(B) COONa

CH3

; SO3

(D)

SO2 – O – C – CH3

CH3

; NaOH

17. The product(s) obtained via oxymercuration (HgSO4 + H2SO4) of 1-butyne would be –

(A) CH3CH2COCH3

(B) CH3CH2CH2CHO (C) CH3CH2CHO + HCHO (D) CH3CH2COOH + HCOOH

18. Acetophenone is prepared by the reaction of which of the following in the presence of AlCl3 catalyst – (A) Phenol and acetic acid

(B) Benzene and acetone (C) Benzene and acetyl chloride (D) Phenol and acetone

19.

OCH3

CH3

heat 2

NaOH / Br . 1 ₂

− 



 →



(A) OCH3

CH3

Br (B)

OCH3

CH3

(C)

OCH3

CH3

(D)

OCH3

CH3

20. Phenol ^NaNO²^/^H²^SO⁴→ B  →^H²^O C  →^NaOH D Name of the above reaction is –

(A) Libermann's reaction (B) Phthalein fusion test

21.

CCl3



 →

¹^eqv^.^of^Br²^/^Fe A. Compound A is -

(A) CCl3

(B) CCl3

(C)

CCl3

Br Br

(D)

CCl3

Br 22. In a reaction

CH2 = CH2 acid us Hypochloro

 →

 M →^R

CH2 – OH CH2 – OH

where M = molecule R = Reagent M and R are

(A) CH3CH2Cl and NaOH

(B) CH2Cl – CH2OH and aq. NaHCO3

23. Which of the following will have least hindered rotation about carbon-carbon bond –

(A) Ethane (B) Ethylene

24. Which is least reactive towards nucleophilic substitution (SN2)

(A) CH2 = CH2 – CH2 – Cl (B)

CH3

CH3 – C – Cl CH3

(D) Cl CH3 – CH – CH3

25. Among the following the least stable reasonance structure is –

(A) _- ^-_N

- O

O -

(B) _- ^-_N ^O O -

- O

O -

- (D) -

-- N-

-26. Homolytic fission of C–C bond in ethane gives an intermediate in which carbon is -

(A) sp³ hybridised (B) sp² hybridised (C) sp hybridised (D) sp²d hybridised

27. The IUPAC name of the compound is – (A) (2E, 4E)-2, 4-hexadiene

(B) (2Z, 4Z)-2, 4-hexadiene (C) (2Z, 4E)-2, 4-hexadiene (D) (2E, 4Z)-4, 2-hexadiene

28. The brown ring test for NO and ⁻₂ NO is due to the ⁻₃ formation of complex ion with the formula –

(A) [Fe(H2O)6]²⁺ (B) [Fe(NO)(CN)5]²⁺

29. The correct order for the wavelength of absorption in the visible region is –

(A) [Ni (NO2)6]^4– < [Ni(NH3)6]²⁺ < [Ni(H2O)6]²⁺

(B) [Ni (NO2)6]^4–< [Ni(H2O)6]²⁺< [Ni(NH3)6]²⁺

(D) [Ni(NH3)6]²⁺ < [Ni(H2O)6]²⁺<[Ni (NO2)6]^4–

30. In nitroprusside ion,, the iron and NO exists as Fe (II) and NO⁺ rather than Fe(III) and NO these forms can be differentiated by –

(A) Estimating the concentration of iron (B) Measuring the concentration of CN^–

(C) Measuring the solid state magnetic moment (D) Thermally decomposing the compound 31. Four reactions are given below

I 2Li + 2H2O → 2LiOH + H₂ II 2Na + 2H2O → 2NaOH + H₂ III 2LiNO3  →^heat 2LiNO2 + O2

IV 2NaNO3  →^heat 2NaNO2 + O2

Which of the above if any is wrong

(A) IV (B) III

32. Name of the structure of silicates in which three oxygen atoms of [SiO4]^4– are shared is –

(A) Pyrosilicate (B) Sheet silicate (C) Linear chain silicate (D) Three dimensional silicate

33. The metallic lusture exhibited by sodium is explained by –

(A) Diffusion of sodium ions (B) Oscillation of loose electron (C) Excitation of free protons

(D) Existence of body centred cubic lattice

34. Hydrogen is evolved by the action of cold dil. HNO3

on –

(A) Fe (B) Mn

35. 'Lapis-Lazuli' is a blue coloured precious stone. It is mineral of the class –

(A) Sodium alumino silicate (B) Zinc-cobaltate

36. In which of the following arrangements the order is not according to the property indicating against it – (A) Al³⁺ < Mg²⁺ < Na⁺ < F^– (increasing ionic size)

(B) B < C < N < O (increasing first I.E.) (C) I < Br < F < Cl

(increasing electron gain enthalpy (–ve)) (D) Li < Na < K < Rb (increasing metallic radius) 37. Which set of hybridisation is correct for the

following compound NO2, SF4, PF ₆⁻

(A) sp, sp², sp³ (B) sp, sp³d, sp³d² (C) sp², sp³, d²sp³ (D) sp³, sp³d², sp³d²

38. The increasing order of atomic radius for the elements Na, Rb, K and Mg is –

(A) Mg < Na < K < Rb (B) K < Na < Mg < Rb (C) Na < Mg < K < Rb (D) Rb < K < Mg < Na

39. Which of the following ion forms a hydroxide highly soluble in water –

(A) Ni²⁺ (B) K⁺ (C) Zn²⁺ (D) Al³⁺

40. When CO2 is bubbled into an aqueous solution of Na2CO3 the following is formed –

(A) NaOH (B) NaHCO3

MATHEMATICS

1. y = 2x² – log | x | passes - (A) two minima & one maxima (B) Two maxima and one minima (C) Only two minima (B) is strictly decreasing in (0, π/2) (C) is strictly increasing in (0, π/2) (D) has global maximum value 2

3. If the radius of a spherical balloon is measured with in 1 % the error (in percent) in the volume is – choices from the following is -

(i) reflexive (ii) symmetric (iii) Transitive (iv) anti symmetric

(A) 1 (B) 2 (C) 3 (D) 4 be distributed among 5 people such that each person gets at least 3 rupee is –

(A) 26 (B) 63 (C) 125 (D) None 10. The total number of six digit number x1 x2 x3 x4 x5 x6

have the property that

x1 < x2 ≤ x₃ < x4 < x5 ≤ x₆ is equal to –

12. The term independent of x in

19. Solution of the differential equation xdx + zdy + (y + 2z)dz = 0 is –

(A) x² + 2yz + 2z² = c (B) x² + yz + z² = c (c) x² + 2yz + z² = c (D) None of these

20. The slope of the tangent to the curve y = f(x) at (x, f(x)) is (2x + 1). If the curve passes through the point (1, 2), then the area bounded by the curve, x-axis and the lines x = 1, x = 0 is –

(A) 5/6 (B) 6/5 (C) 6 (D) 1

21. The maximum area of a rectangle whose two consecutive vertices lie on the x-axis and another two lie on the curve point (x′, y′) which is contained between the co-ordinate axes is bisected at the point –

(A) (–x′, y′) (B) (y′, x′) the origin and equally inclined with axes the equation of the plane perpendicular to OP and passing through P cuts the intercepts on axes the sum of whose reciprocals is –

(A) a (B) 3/2a (C) 3a/2 (D) 1/a 26. If ar= piˆ+5jˆ+17kˆ and br=2 qiˆ+13jˆ+kˆ

have equal magnitude and p, q are positive integer ∈ [1, 1000] then the total number of ordered pair (p, q) is – (A) 33 (B) 32 (C) 31 (D) None 28. The equation

a point where it is intersected by line y = x – 1 is –

(A) π/6 (B) π/3 (C) π/4 (D) π/2 30. Consider four circles (x ± 1)² + (y ± 1)² = 1 equation

of smaller circle touching these four circles is – (A) x² + y² = 3 – 2 (B) x² + y² = 6 – 3 2 (C) x² + y² = 5 – 2 2 (D) x² + y² = 3 – 2 2

31. If the point P(a, a²) lies completely inside the triangle formed by the lines x = 0, y = 0 and x + y = 2 then exhaustive range of 'a' is –

(A) a ∈ (0, 1) (B) a ∈ (1, 2 ) (C) a ∈ ( 2 – 1, 2 ) (D) a ∈ ( 2 – 1, 1)

32. The distance between the orthocentre and the circumcentre of the triangle with vertices (0, 0) (0, a) and (b, 0) is – solution then K belongs to –

(A)  (A) One point of minimum

(B) One point of maximum (C) No extreme point (D) Two point of maximum 36. If solution of the equation

where [.] and {.} denote the integral part and fractional part respectively, is given by –

(A) 1 (B) 2 Where [.] denotes the greatest integer function respectively –

(A) [ 1, ∞), [0, tangent not parallel to x-axis at the point (a, 0) through which the graph passes, then

43. If (a + bx)e^y/x = x then y2

1 (xy1 – y)² =

(Α) x³ (B) 3x² (C) 1/x³ (D) None 44. If f(x) is continuous function such that

∫

⁺¹ ⁼

In document XtraEdge_2010_03 (Page 81-91)