193969_634618365995252500 (1)

IIT-JEE/AIEEE/PMT COMBINED TEST SERIES BY ATC | TEST -01 | PHYSICS+MATHS+CHEMISTRY+BIOLOGYTOTAL TIME: 3 HRS | TOTAL PRINTED PAGES : 10 | CHECK ALL PAGES ARE OK

INSTRUCTIONS:

IIT /PMT VERY SIMILAR TEST. EVERY CORRECT ANSWER WILL REWARD U 3 MARKS AND EVERY WRONG ANSWER WIL DEDUCT YOURS 1 MARK. SO BE CARE FULL.

SECTION-A | IIT-JEE (PHYSICS)

INSTRUCTIONS:

Q.1 If force, acceleration and time are taken as fundamental quantities, then the dimensions of length will be:(A) FT2 (B) F1 A2 T1 (C) FA2T (D) AT2

Q.2 The dimensions ML1 T2 can correspond to :(A) moment of a force or torque (B) surface tension(C) pressure (D) co-efficient of viscosity.

(useful relation are =

r x F , S = F/l , F = 6 r, where symbols have usual meaning)

Q.3 Which of the following can be a set of fundamental quantities(A) length, velocity, time (B) momentum, mass, velocity(C) force, mass, velocity (D) momentum, time, frequency

Q.4 Kinetic energy (K) depends upon momentum (p) and mass (m) of a body as K pa mb

(A) a =1; b =1 (B) a =2; b = –1 (C) a =2; b=1 (D) a =1; b =2

Q.5 If area (A) velocity (v) and density () are base units, then the dimensional formula of force can be represented as.

(A) Av (B) Av2 (C) Av2 (D) A2v

Q.6 The pressure of 106 dyne/cm2 is equivalent to(A) 105 N/m2 (B) 106 N/m2 (C) 107 N/m2 (D) 108 N/m2

Q.7 If 1 unit of mass = 4 kg; 1 unit of length = m and 1 unit of time = 5 sec, then 1 Joule = x units of energy in this system where x = (A) 100 units (B) 0.01 units (C) 200 units (D) 0.02 units

Q.8 In a certain system of units, 1 unit of time is 5 sec, 1 unit of mass is 20 kg and unit of length is 10 m. In this system, one unit of power will correspond to (A) 16 watts (B) watts (C) 25 watts (D) none of these

Q.9 In a book, the answer for a particular question is expressed as

b =

mak21

kma l

here m represents mass, a represents accelerations , l represents length. The unit of b should be

(A) m/s (B) m/s2 (C) meter (D) / sec.Q.10 If the resultant of two forces of magnitudes P and Q acting at a point at an angle of 60° is Q, then

P / Q is(A) 1 (B) 3 / 2 (C) 2 (D) 4

Q.11 The resultant of two forces F1 and F2 is P. If F2 is reversed, then resultant is Q. Then the value of (P2 + Q2) in terms of

F1 and F2 is

(A) 2(F12 + F2

2) (B) F12 + F2

2 (C) (F1 + F2)2 (D) none of these

Q.12 A man moves towards 3 m north then 4 m towards east and finally 5m towards 37° south of west. His displacement from origin is(A) (B) 0 m (C) 1 m (D) 12 m

Q.13 Three forces P, Q & R are acting at a point in the plane . The angle between P & Q and Q & R are 150º & 120º respectively, then for equilibrium, forces P, Q & R are in the ratio

(A) 1 : 2 : 3 (B) 1 : 2 : 3 (C) 3 : 2 : 1 (D) : 2 : 1

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Q.14 A man rows a boat with a speed of 18km/hr in northwest direction. The shoreline makes an angle of 15° south of west. Obtain the component of the velocity of the boat along the shoreline.

(A) 9 km/hr (B) 18

32 km/hr (C) 18 cos15°km/hr (D) 18 cos75° km/hr

Q.15 A bird moves from point (1, 2, 3) to (4, 2, 3) . If the speed of the bird is 10 m/sec, then the velocity vector of the bird is :(A) 5 (B) 5 (C) (D)

Q.16 The motion of a body is given by the equation

d v td t

( )

= 6.0 3 v(t) ; where v (t) is the speed in

m/s & t in sec., if the body has v = 0 at t = 0 then(A) the terminal speed is 2.0 m/s (B) the magnitude of the initial acceleration is 6.0 m/s²

(C) the speed varies with time as v(t) = 2 (1 e-3t) m/s (D) the speed is 1.0 m/s when the acceleration is half the initial value. [JEE ’1995]

Q.17 A ball is dropped vertically from a height d above the ground it hits the ground and bounces up vertically to a height d/2. Neglecting subsequent motion and air resistances, its velocity v varies with the height h above the ground as

[JEE'2000 (Scr)]

(A) (B) (C) (D) [JEE'1996]

Q.18 A small block slides without friction down an inclined plane starting from rest. Let Sn be the distance travelled from time t = n - 1 to t = n. Then is [JEE' 2004 (Scr)]

(A) n21n2

(B) (C) (D)

Q.19 In 1.0 sec. a particle goes from point A to point B moving in a semicircle of radius 1.0 m. The magnitude of average velocity is : [JEE '99](A) 3.14 m/sec (B) 2.0 m/sec

(C) 1.0 m/sec (D) zero

Q.20 The co-ordinates of a particle moving in a plane are given by x (t) = a cos (t) and y (t) = b sin (t) where a, b (< a) & are positive constants of appropriate dimensions.(A) the path of the particle is an ellipse (B) the velocity & acceleration of the particle are normal to each other at t = /(2)(C) the acceleration of the particle is always directed towards a focus(D) the distance travelled by the particle in time interval t = 0 o t = /(2) is a . [JEE '1999]

Q.21 A ball is dropped vertically from a height d above the ground it hits the ground and bounces up vertically to a height d/2. Neglecting subsequent motion and air resistances, its velocity v varies with the height h above the ground as

[JEE'2000 (Scr)](A) (B) (C) (D)

Q.22 A particle starts from rest. Its acceleration a) versus time (t) is as shown in the figure. The maximum speed of the particle will be

[JEE' 2004 (Scr)]------------------------------------------------------------------------------------------------------------------------------------------------------------------

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2


BC

OA45o

45o

150oP Q

R12

OF

A

E D

C

B


(A) 110 m/s (B) 55 m/s (C) 550 m/s (D) 660 m/s

Q.23 Find the resultant of three vectors OA , OB and

OC shown in the following figure. Radius of the circle is R.

(a) 2R (b)R(1+√2) (c)R√2 (d)R(√2−1 )

Q.24 If |A−B|=|A|=|B|, the angle between A and

B is(a) 60° (b) 0° (c) 120° (d) 90°

Q.25 At what angle must the two forces (x + y) and (x – y) act so that the resultant may be √( x2+ y2 )

(a)cos−1(− x2+ y2

2( x2− y2) )(b)

cos−1(−2( x2− y2)x2+ y2 )

(c)cos−1(− x2+ y2

x2− y2)(d)

cos−1(− x2− y2

x2+ y2 )

Q.26 . Let the angle between two nonzero vectors A and

B be 120° and resultant be C

(a)C must be equal to |A−B| (b)

C must be less than |A−B|

(c)C must be greater than |A−B| (d)

C may be equal to |A−B|

Q. 27. Fig. shows ABCDEF as a regular hexagon. What is the value of AB+AC+AD+AE+AF

(a)AO (c) 4AO

(b) 2AO (d)6AO

P, Q and Q.28 There are three coplanar forces acting at a point and are in equilibrium. Given P = 1.9318 kg wt, sin θ1=0.9659, the value of R is ( in kg wt)

[CET 1998]

(a) 0.9659(b) 2(c) 1

(d)

12

Q.29 A man can swim with velocity v relative to water. He has to cross a river of width d flowing with a velocity u (u > v). The distance through which he is carried down stream by the river is x. Which of the following statement is correct

(a) If he crosses the river in minimum time x=du

v

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(b) x can not be less than

duv

(c) For x to be minimum he has to swim in a direction making an angle of

π2+sin−1( v

u ) with the direction of

the flow of water

(d) x will be max. if he swims in a direction making an angle of

π2+sin−1 v

u with direction of the flow of water

Q.30 . A stone tied to a string of length L is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude of the change in its velocity as it reaches a position where the string is horizontal is

[IIT-JEE 1998; CBSE PMT 2004]

(a) √u2−2 gL (b) √2 gL (c)√u2−gl (d) √2(u2−gL) SECTION-B | IIT-JEE (Maths)

Differentiation

1. A function f is differentiable in the interval 0 ≤ x ≤ 5 such that f(0) = 4 and f(5)=-1. if , then there exists some ‘c’ in 0 < c < 5 such that equals :

(a) (b) (c) (d) None

2. All the points on the curve at which the tangent is parallel to the x-axis lie on the curve.

(a) y2 = 4ax (b) y2 = 4a2 sin (c) x2 = 4ay(d) x2 + y2 = a2

3. The set onto which the derivative of the function f(x) = x (log x – 1) maps the ray [1, ) is :(a) [0, ) (b) [1, )(c) (0, ) (d) None of these

4. Let (x) = f(x) + f(1 - x) and in 0 ≤ x ≤ 1, then :(a) (x) decreases in (0, 1/2)(b) (x) increases in (0, 1)(c) (x) decreases in (0, 1)(d) None of these

5. The value of as n is equal to :

(a) 4 e (b) 2 e (c) (d) 6. If f(x) = | x – a| + | x + b|, x R, Rb > a > a. Then :

(a) (b) (c) (d) 7. In the interval 0 < x < 2, the function f(x) = | sin 2x | is not differentiable at :

(a) (b) (c) (d) ------------------------------------------------------------------------------------------------------------------------------------------------------------------


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8. For the function f() = 1, which of the following statements are true :

(a) f( - 0) = - 1 (b) f( + 0) = 1(c) f(x) is continuous at x = (d) f(x) is differentiable at x = .

9. If f(x) = sin x, g(x) = x2 and h(x) = logex if f(x) = h(g(f(x))) then equals :(a) – 2 cosec2x (b) 2 cosec3x

(c) 2 cotx2 – 4x2 cosec2 x2 (d)

10. Suppose f and g are functions having second derivatives and everywhere, if f(x) . g(x) = 1 for

all x and and are never zero then equals :

(a) (b) (c) (d)

11. If and then is equal to :

(a) (b) (c) (d)

Passage – 1

The successive derivative of certain functions follow a pattern. We can find the derivative of any order by following this pattern. Methods of induction can also be used in finding nth derivative of functions.

12. The nth derivative of long x must be :

(a) (b) (c) (d) 13. The nth derivative of sinx must be :

(a) (b) (c) (d) 14. In n leaves remainder 3 when divided by 4 then value of nth derivative of tan-1 x at x = 0 must be :

(a) 0 (b) n!(c) (n – 1)!(d) – (n – 1)!

15. (0 < x < 1) is

(a) 0 (b) (c) (d) None of these

16. if y = sin1 , x > 0, then is equal to

(a) 1 (b) 0(c) (d) None of these------------------------------------------------------------------------------------------------------------------------------------------------------------------


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17. Derivative of tan w.r.t. is

(a) sec2 x (b) sec2 (c) (d) None of these18. Let f(x +y) = f(x) + f(y) x, y R. Suppose that f(6) = 5 and f(0) = 1, then f(6) is equal to

(a) 1 (b) 30 (c) 25 (d) None of these

19. If x sin (a + y) = sin y, then is equal to

(a) (b) (c) (d)

20. If y = , then is equal to

(a) (b) (c) (d) None of these

21. If y2 = ax2 + b, then is equal to


22. If x = at2, y = 2 at, then is equal to

(a) 0 (b) (c) (d) None of these

23. If x = f(t) and y = g(t), then is equal to

(a) (b)

(c) (d) None of these

24. If y = a sin mx + b cos mx, then is equal to(a) m2y (b) m2y (c) m(d) None of these

25. If then y6 =


26. is equal to

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(a) (b)

(c) (d) None of these27. Differential coefficient of a function f(g(x)) w.r.t. the function g(x) is

(a) f (g(x)) (b) f(g(x)) g(x)(c) (d) None of these

28. is equal to

(a) (b) (c) cosec x (d) None of these29. If y = emx, then yn, n N, is

(a) emx (b) mnemx(c) mn emx (d) None of these

30. If f(x) = tan1 x and g(x) = tan1 , the(a) f (x) = g(x) (b) Df = Dg(c) f(x) = g(x) (d) None of these

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