Important Questions for Iit-jee

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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

Q.2

If force, acceleration and time are taken as fundamental quantities, then the dimensions of length will be: (A) FT2 (B) F1 A2 T1 (C) FA2T (D) AT2 The dimensions ML1 T2 can correspond to : (A) moment of a force or torque (B) surface tension (C) pressure (useful relation are

 

(D) co-efficient of viscosity.   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) Av2 (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

ma  2 kl   1  k  ma 

b= 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 F1 and F2 is (A) 2(F12 + F22)

(B) F12 + F22

(C) (F1 + F2)2

(P 2 + Q2) in terms of

(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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IIT-JEE/AIEEE/PMT COMBINED TEST SERIES BY ATC | TEST -01 | PHYSICS+MATHS+CHEMISTRY+BIOLOGY TOTAL TIME: 3 HRS 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.

3 2 (B) 18 km/hr

(A) 9 km/hr Q.15

Q.16

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(C) 18 cos15°km/hr

(D) 18 cos75° km/hr

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)

The motion of a body is given by the equation 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 v (t ) dt = 6.0  3 v(t) ; where v (t) is the speed in

[JEE ’1995]

(D) the speed is 1.0 m/s when the acceleration is half the initial value. 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) Q.18

(C)

(D) [JEE'1996]

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)

Q.19

(B)

2n  1 2n

(B)

(C)

(D)

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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Find the resultant of three vectors OA, OB and OC shown in the following figure. Radius of the circle is R. C (b) R(1 

(a) 2R

(d) R( 2  1)

(c) R 2

2)

O

45o o 45

B A

Q.24 If | A  B | | A | | B |, the angle between A and B is (a) 60° Q.25

(b) 0°

(c) 120°

(d) 90°

At what angle must the two forces (x + y) and (x – y) act so that the resultant may be

  

1 (a) cos  

 2(x 2  y 2 )    x 2  y 2  

x 2  y 2  2(x 2  y 2 ) 

 x2  y2 cos  1    x2  y2 

1 (b) cos  

(c)

 x2  y2 cos  1    x2  y2 

   

(x 2  y 2 ) (d)

   

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 |

Q.

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

(a)

AO

150o

P

(b) 2 AO

(d) C may be equal to | A  B |

2

(c)

Q

1

4 AO

(d) 6 AO

R

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 1  0.9659, the value of R is ( in kg wt) (a) 0.9659 (b) 2 (c) 1 (d)

1 2

D

E F

C

O A

B

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  (b) x can not be less than

du v

du v



(c) For x to be minimum he has to swim in a direction making an angle of 2  sin

1  v

   with the direction u

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

v

1 (d) x will be max. if he swims in a direction making an angle of 2  sin 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 (a)

u 2  2 gL

2 gL (c) u 2  gl

(b)

(d)

2(u 2  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.

then there exists some ‘c’ in 0 < c < 5 such that (a)

2.



5 6

(b)

All the points on the curve



f '(c)

if

g(x) 

f(x) , x 1

equals :

1 6

(c)

1 6

(d) None

x  y2  4a x  a sin  at which the tangent is parallel to the a 

x-axis

lie on the curve. (a) y2 = 4ax

(b) y2 = 4a2 sin

x a

(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 (a) [0,  ) (b) [1,  )(c) (0,  ) (d) None of these

4.

Let  (x) = f(x) + f(1 - x) and

f "(x)  0

[1,

 ) is :

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.

 |__ 2n The value of  n  |nn  _ (a) 4 e

6.

true :

9.

f '(b)  0

(b)

(c)

2 e

 R, Rb > a > a. Then : (c) f '(a)  1 f '(b)  1

(d)

4 e

(d)

f '(a)  0

In the interval 0 < x < 2, the function f(x) = | sin 2x | is not differentiable at : (a)

8.

(b) 2 e

If f(x) = | x – a| + | x + b|, x (a)

7.

1

n   is equal to :  as n  

 4

For the function

(b)

 2

f(x)  (  x)

(a) f( - 0) = - 1 (c) f(x) is continuous at x = 

cos x ;x  , | sin x |

(c) 

3 2

f() = 1, which of the following

statements

are

(b) f( + 0) = 1 (d) f(x) is differentiable at x = .

If f(x) = sin x, g(x) = x2 and h(x) = logex if f(x) = h(g(f(x))) then (a) – 2 cosec2x

(d)

d2 f dx2

equals :

(b) 2 cosec3x

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(c) 2 cotx2 – 4x2 cosec2 x2 (d) 10. all x and

11.



2 1  cos2 x

Suppose f and g are functions having second derivatives

f'

and

(a)

2

If

g'

f "(x) g"(x)  f '(x) g'(x) 2g'(x) g(x)

are never zero then

f '(x) f(x)

(b)

x  (t) and y  (t) then

(a)

 '  "  '  " '

(b)

2

d2 y

and

g"

everywhere, if

f(x) . g(x) = 1 for

equals :

f '(x) f(x)

(c)



(c)

" "

(d)

2

f '(x) f(x)

is equal to :

dx2  '  "  '  " '

f"

3

(d)

" '

2



 '.  " '3

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)

13.

15.

16.

xn 1   sin  x  (n  1)  2  

19.

xn

(c)

(1)n(n  1)!

(b)

  sin  x  (n  1)  2  



(d)

xn 1

(1)n 1(n  1)! xn

(c)

n   sin  x  2  

(d)

n   sin  x  2  

if y = sin1

(c)

1 x 1x

(d) None of these

 x 1  x  1 dy 1 is equal to    s ec   , x > 0, then dx  x  1  x 1  (b) 0(c) (d) None of these 2

Derivative of tan

x2  1 w.r.t.

Let f(x +y) = f(x) + f(y) (a) 1

x2  1 is

(b) sec2

x2  1

sin a

(c)

  x  sec2   2   x 1

(d) None of these

 x, y  R. Suppose that f(6) = 5 and f(0) = 1, then f(6) is equal to (b) 30

(c) 25

dy If x sin (a + y) = sin y, then is equal to dx sin2  a  y  sin a (a)

x = 0 must be :



d sin1 1  x  cos1 x (0 < x < 1) is dx 1 (a) 0 (b)  x 1x

(a) sec2 x 18.

(1)n(n!)

In n leaves remainder 3 when divided by 4 then value of nth derivative of tan-1 x at (a) 0 (b) n!(c) (n – 1)!(d) – (n – 1)!

(a) 1

17.

(b)

The nth derivative of sinx must be : (a)

14.

(1)n 1(n  1)!

(b)

2

sin

a  y 

(c)

(d) None of these

sin  a  y  sin a

(d)

sin a sin  a  y 

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21.

d2 y

If y2 = ax2 + b, then (a)

22.

dx2

ab x

If x = at2, y = 2 at, then

(c)

25.

If

1 t

(c)

2

d2 y dx2



1

(d) None of these

2at3

is equal to

(b)

g''  t  f '  t   g'  t  f ''  t 

g''  t  f '  t   g'  t  f ''  t 

f ' t 

3

(d) None of these

 f '  t 

2

d2 y

is equal to

dx2

(b) m2y (c) m(d) None of these

1x then y6 = 1x 2.6!

1  x 

7

(b)

2.6!

1  x 

7

(c)

6!

(d) None of these

1  x 7

sin x  is equal to 3

dx4

3 34 cos 3x 3 sin x  34 sin3x cos x  (b) 4 4 4 3 34 cos 3x sin x  (d) None of these 4 4

Differential coefficient of a function f(g(x)) w.r.t. the function g(x) is (a) f (g(x))

29.

(d) None of these

y2

is equal to

f ''  t 

d4

(c)

28.

ab

y

(a)

27.

y

dx2

g ''  t 

(c)

3

If y = a sin mx + b cos mx, then

(a)

26.

ab

d2 y

(b)

(a) m2y

(d) None of these

is equal to

If x = f(t) and y = g(t), then

(a)

24.



(b)

3

(a) 0

23.



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x 1 dy x2  1  log x  x2  1 , then If y = is equal to 2 2 dx 1 2 2 (a) 2 x  1 (b) x  1 (c) 2 x 1

(b) f(g(x)) g(x)(c)

d  x   log tan  is equal to dx  2 2 1 (a) (b) (c) cosec x x sin x tan 2 If y = emx, then yn, n  N, is (a) emx (b) mnemx(c) mn emx



f ' g x g'  x 



(d) None of these

(d) None of these

(d) None of these

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If f(x) = tan1 x and g(x) = tan1 (a) f (x) = g(x)

 x  1  x  1  , the  

(b) Df = Dg(c) f(x) = g(x) (d) None of these SECTION-C | IIT-JEE (CHEMISTRY) Solutions

1.

Which of the following is not correct for an ideal solution : (a) Raoult’s law is obeyed for entire concentration range (b) Hmix = 0 (c) Vmix = 0(d) Smix = 0

2.

What is the normality of 1 M H3PO2 solution : (a) 0.5 N (b) 1.0 N(c) 2.0 N

3.

1 mole of heptane (V.P. = 82 mm Hg) was mixed with 4 moles of octane (V.P. = 31 mm Hg). The V.P. of resulting ideal solution is : (a) 46.2 mm Hg (b) 40.0 mm Hg (c) 41.2 mm Hg (d) none of these

4.

The vapour pressure of a pure liquid A is 70 mm at 27°C. If forms an ideal solution with another liquid B. The mole fraction of B is 0.2 and total pressure of the solution is 84 mm at 27°C. The vapour pressure of pure liquid B at 27°C is : (a) 14 (b) 56 (c) 70 (d) 140

5.

A strong electrolyte A gives 3 ions and B is a non-electrolyte. If 0.1 M solution of B produces an osmotic pressure of P, then 0.05 M solution of A will produce an osmotic pressure of : (a) 1.5 P (b) 3.0 P (c) 0.5 P (d) 0.75 P

6.

Which solution will exert highest osmotic pressure : (a) 1 M glucose solution (b) 1 M urea solution (c) 1 M alum solution (d) 1 M NaCl solution

7.

Which of the following salts will have the same value of the Van’t Hoff factor as that of K4[Fe(CN)6] : (a) Al2(SO4)3 (b) NaCl (c) Na2SO4 (d) Al(NO3)3

8.

When HgI2 is added to the aqueous solution of KI : (a) boiling point does not change (c) boiling point is elevated

9.

The elevation in boiling point of a solution of 10 g of binary electrolyte (Molar mass 100) in water is Tb. The value of Kb for water is : (a)

Tb 2

(b) Tb

(d) 3.0 N

(b) freezing point is elevated (d) freezing point is lowered

(c) 10 Tb

100 g of

(d) 2Tb

10.

The molal freezing point constant for water is 1.86 K kg mol-1. Therefore, the freezing point of 0.1 M NaCl solution in water is expected to be : (a) 0.186°C (b) – 0.186°C (c) – 0.372°C (d) 0.372°C

11.

Assuming the salts to be completely ionized in solution, which of the following solution has highest osmotic pressure : (a) 1% CsCl (b) 1% RbCl (c) 1% KCl (d) Same for all

12.

Mole fraction of glycerol in a solution of 36 g of water and 46 g of glycerol is : (a) 0.46 (b) 0.20 (c) 0.36

13.

1 kg aqueous solution of CaCO3 contains 10 g of CaCO3. Concentration of solution is : (a) 10 ppm (b) 100 ppm (c) 1000 ppm (d) 10000 ppm

14.

Elevation in boiling point is 0.52°C when 60g of a compound X was dissolved in 100 g of water Molar mass of X is (Kb(water) 0.52°C kg mol-1) : (a) 120 (b) 60(c) 600 (d) 180

15.

The Van’t Hoff factor for 0.1 M Ba(NO3)2 solution is 2.74. The degree of dissociation is : (a) 91.3% (b) 87%(c) 74%(d) none of these

16.

Benzoic acid undergoes dimerisation in benzene solution. The Van’t Hoff factor (i) is related to the degree of association () of the acid as :

(d) 0.40

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17.

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i 1

 2

(d)

Glucose is added to 1 L of water ( = 1 g cm-3) to such an extent that the ratio of

i 1

 2

Tf becomes 10-3. The Kf

mass of glucose added is : (a) 180 g (b) 18 g(c) 1.8 g(d) 0.18 g 18.

Glucose solution is 25% by weight of solution, Its percentage concentration by weight of solvent is : (a) 20% (b) 25%(c) 33.3% (d) none of these

19.

At a given temperature total vapour pressure (in mm) of a mixture of volatile components A and B is given by P = 120 – 75 XB. Hence, vapour pressure of pure A and B respectively (in mm) are : (a) 120, 75 (b) 120, 195(c) 120, 45 (d) 75, 45

20.

In the following equilibrium N2O4(g) 2NO2(g), NO2 is 50% of the total volume. Hence, Van’t Hoff factor (i) is : (a) 1.5 (b) 1.25(c) 1.33(d) none of these

21. Co-ordination number of Na+ in NaCl is a) 4 b) 3 c) 6 d) 5 22. Which has no rotation symmetry? a) Hexagonal b) Orthorhombic c) Cubic d) Triclinic 23. The hardest substance among the following: a) BeC b) Graphite c) Ti d) SiC 24. The number of molecules in a unit cell of fluorite is a) 2

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b) 4 c) 6 d) 8 25. The coordination number of calcium fluoride type structure is a) 8:4 b) 4:8 c) 4:4 d) 8:8 26. The structure of sodium chloride is a) hexagonal b) octahedral c) rhombohedral d) tetrahedral 27. Which of the following will not adopt CsCl structure a) CsBr b) CsCN c) CsC d) CsF 28. The arrangement of first two layers, one above the other , in hcp and ccp arrangements is a) exactly same in both cases b) partly same and partly different c) different from each other d) nothing definite 29. The number of atoms present in a unit cell of a monoatomic substance of a simple cubic lattice , body – centered cubic respectively a) 8,9, and 14 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------www.anuragtyagiclasses.com | call us @ 09818777-622 | centres at: VASUNDHRA | SAHIBABAD

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b) 1,2 and 4 c) 4,5 and 6 d) 2,3 and 5 30. Antiflourite structure is derived from fluorite structure by a) Heating fluorite crystal lattice b) Subjecting fluorite structure to high pressure c) Inter changing the position of cations and anions in the lattie d) None of these. SECTION-D | PMT (BIOLOGY) 1.

2.

3.

4.

5.

Meiosis can be observed in a) megaspore b) micro mother cell c) microspore d) anther wall the number of microsporangia present in anther is a) 1 b) 2 c) 3 d) 4 filiform apparatus is located at a) tip of microsporangium b) tip of filament c) tip of megasporangium d) pericarp Sexual reproduction in plants was reported by a) Camererius b) Hofmeister c) Strasburger d) Nawaschin Triple fusion means, fusion of A. two polar bodies and male gametes B. two eggs with male gametes C. two male gametes and one egg D. two male gametes and one egg and secondary nucleus

6.

Angiosperms are characterized by A. fertilisationwithout gametes B. double fertilization C. simple fertilization D. parthenocarpy

7.

Which of the following is the reproductive organ of plants? A. Flower B. Pistil C. Stamen D. Anther 8.

Assertion - Reason questions Direction. a) if both assertion and reason are correct and reason is true explanation of assertion. b) if both assertion and reason aretrue but reason is not correct explanation of assertion c) If assertion is true but reason is false d) if assertion is false but reason is true.

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A. Two sperms in a pollen tube often change their shape. R. the sperms are released in the synergids as intact cells but only their nuclei migrate.

A. a condensed rhizome is corm. 11. R. Zinjiber stem is rrhizome.

12.

The volume of semen released per ejaculation is ..... in man A. 2-4 ml B. 2-8 ml C. 1-2 ml D. 6-7 ml

13.

The head of the sperm serves two functions A. assembly and activating B. genetic and activating C. genetic and cleavage D. genetic and energy

14.

Spermioteleosis is A. B. C. D.

15.

Ovary is attached with the back to body wall by A. mesorchium B. mesosalpinx C. mesovarium D. ovarian ligament

16.

Menarche is the stage when A. first delivery occurs B. first menstrual cycle starts C. when first ejaculation occurs D. first month of menopause

17.

One oogonium forms A. 1 ovum and 3 polar bodies B. 1 ovum and 1 polar body C. 1 ovum without centriole and 3 polar bodies D. single ovum

18.

Semen consist of an enzyme A. seminase B. hyaulonidase C. vasciulase D. ligase

19.

The phase of menstrual cycle when fertilization is possible A. follicular B. leuteal C. bleeding phase D. none of these

20.

Parturition is controlled by A. oxytocin B. FSH C. relaxin D. Oestrogen

21.

Probable fertility period of menstrual cycle is from ..... day to ..... day A. 5 - 8 B. 9 - 12 C. 13 - 16 D. 17 - 20

22.

50 primary spermatocytes give rise to A. 220 spermatocytes

another name of maturation of ovum spermatogenesis spermiogenesis degeneration of sperms

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During a woman's life she produces about A. 4000 eggs B. 365 - 800 eggs C. 40 eggs D. 400 - 500 eggs

24.

This is a method of A. B. C. D.

25.

Assertion -Reason (For direction refer to those given in Ques. 23) A. During ovulation the oocyte has released one polar body. R. When oocyte is in fallopian tube it is in second metaphase state.

26.

Temporary and 100% effective method to control birth in males is A. tubal ligation B. vasectomy C. oral contraceptives D. mating rhythm control

27.

Sperm maturation A. B. C. D.

28.

Sperm releases lysozyme because it A. aids to fertilization B. dissolves oocyte membrane C. increase sperm motility D. delays fertilization

29.

birth control IUDs GIFT HTF IVF-ET

in man occurs in vasa differentia epididymis rete testis vasa efferentia

Estrogen level is highest on A. 14th day B. 12th day C. 21st day D. 5th day 30. Amphimixis is a) reaction of antifertilizin and fertilizin b) formation of reception cone by ovum c) fusion of male and female pronuclei d) penetration of sperms into ovum

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