JEE Main Model Question Paper

Exam Duration: 180 Mins Total Questions : 75

1 )

The value of \(arg(z)+arg(\overline { z } )\) is

(a)
\(n\pi \)
(b)
\(-n\pi \)
(c)
\(2n\pi \)
(d)
\(-2n\pi \)

2 )

If \(1,\omega ,{ \omega }^{ 2 }\) are the cube roots of unity, then

\(\triangle =\left| \begin{matrix} 1 & { \omega }^{ n }\quad & { \omega }^{ 2n } \\ { \omega }^{ n } & { \omega }^{ 2n } & 1 \\ { \omega }^{ 2n } & 1 & { \omega }^{ n } \end{matrix} \right| \) is equal to

(a)
\(0\)
(b)
\(1\)
(c)
\(\omega \)
(d)
\({ \omega }^{ 2}\)

3 )

Let the three digit numbers A28,3B9,62C, where A,B,C are integers between 0 and 9, be divisible by a fixed integer k; then the determinant

\(\left| \begin{matrix} A & 3 & 6 \\ 8 & 9 & C \\ 2 & B & 2 \end{matrix} \right| \) is divisible by

(a)
k+1
(b)
k-1
(c)
k
(d)
k²

4 )

The number of numbers greater than million that can be formed with the digits 2, 3, 0, 3, 4, 2, 3 is

(a)
380
(b)
420
(c)
360
(d)
960

5 )

The sum of the series \(\frac { m-n }{ m+n } +\frac { 1 }{ 3 } { \left( \frac { m-n }{ m+n } \right) }^{ 3 }+\frac { 1 }{ 5 } { \left( \frac { m-n }{ m+n } \right) }^{ 5 }+...\infty \) is

(a)
\(log\left( \frac { m }{ n } \right) \)
(b)
\(log\left( \frac { m-n }{ m+n } \right) \)
(c)
\(log\left( \frac { n }{ m } \right) \)
(d)
NONE OF THESE

6 )

A weight of 26 N is suspended by two light inelastic strings of length 5m and 12m from two points at the same level 13m apart. Then tensions in the strings are

(a)
24N,10N
(b)
28N,12N
(c)
24N,16N
(d)
None of these

7 )

Cosmic ray particles from outer space enter the earth's atmosphere. On entering the earth's magnetic field, the negatively charged particles in the cosmic rays will get deflected towards

(a)
North
(b)
South
(c)
East
(d)
West

8 )

In L-C-R series A.C. circuit, the phase angle between current and voltage is

(a)
any angle between 0 and \(\pm \pi /2\)
(b)
\(\pi /2\)
(c)
\(\pi\)
(d)
any angle between 0 and \(\pi /2\)

9 )

In young's double slit experiment, the intensity on screen at a point where path difference is \(\lambda\), is k. what will be intensity at the point where path difference is \(\lambda\)/4?

(a)
K/4
(b)
K/2
(c)
K
(d)
zero

10 )

Solid paraffin and sulphur have

(a)
metalic binding forces
(b)
ionic binding forces
(c)
covalent binding forces
(d)
van der Wala's binding forces

11 )

Which of the following solids make the best mirrors?

(a)
ionic solids
(b)
covalent solids
(c)
metallic solids
(d)
dielectric solids

12 )

Arrange in order of increasing sizes \(C\overset { - }{ I } ,B\overset { - }{ r } ,\overset { - }{ F } ,\overset { - }{ I } \)

(a)
\(\overset { - }{ I } <C\overset { - }{ I } <B\overset { - }{ r } <\overset { - }{ F } \)
(b)
\(\overset { - }{ I } <C\overset { - }{ I } >B\overset { - }{ r } >\overset { - }{ F } \)
(c)
\(\overset { - }{ F } <C\overset { - }{ I } <B\overset { - }{ r } <\overset { - }{ I } \)
(d)
\(\overset { - }{ F } =C\overset { - }{ I } =\overset { - }{ I } <B\overset { - }{ r } \)

13 )

Types of solids which generally have low melting points are those composed of

(a)
atoms
(b)
small symmetrical molecules
(c)
small anions and small cations
(d)
positive ions and mobile electrons

14 )

A substance A_xB_y crystallises in a face centred cubic (FCC) lattice in which atoms A occupy each corner of the cube and atoms B occupy the centres of each face of the cube. Identify the correct composition of the substance A_xB_y.

(a)
AB₃
(b)
A₄B₃
(c)
A₃B
(d)
Composition cannot be specified

15 )

Which of the following defects in the crystals lower its density?

(a)
Schottky
(b)
Frenkel
(c)
Interstitial
(d)
F-centres

16 )

In the reaction \(Zn+{ H }_{ 2 }{ SO }_{ 4 }\longrightarrow Zn{ SO }_{ 4 }+{ H }_{ 2 }\)

(a)
Zn is oxidised
(b)
Zn is reduced
(c)
\({ H }_{ 2 }{ SO }_{ 4 }\) is oxidised
(d)
\(Zn{ SO }_{ 4 }\) is reduced

17 )

The reaction:

\({ N }_{ 2 }{ O }_{ 5 }(in\quad CC{ l }_{ 4 })\rightarrow 2N{ O }_{ 2 }(g)+\frac { 1 }{ 2 } { O }_{ 2 }(g)\)

is first order in N₂O₅ with rate constant 6.2X10^-4s^-1. What is the value of rate of reaction when [ N₂O₅] = 1.25 mol L^-1?

(a)
7.75 X 10^-4 mol L^-1 s^-1
(b)
6.65 X 10^-3 mol L^-1 s^-1
(c)
5.15 X 10^-5 mol L^-1 s^-1
(d)
3.85 X 10^-4 mol L^-1 s^-1

18 )

Which one of the following statements is true?

(a)
Nuclei having 2, 8, 20, 28, 50, 82, or 126 protons or neutrons are stable; these are called magic numbers.
(b)
one curie=3.7X10¹⁰Bcquerel (or dps).
(c)
a breeder reactor is the one which non-fissionable U-238 is convered into fissionable plutonium.
(d)
ALL OF THE ABOVE

19 )

Insert the missing figure in the following \(_{ 25 }^{ 55 }{ Mn }\) (n, \(\gamma\) ) \(\rightarrow \)

(a)
\(_{ 25 }^{ 56 }{ Mn }\)
(b)
\(_{ 24 }^{ 55 }{ Cr }\)
(c)
\(_{ 25 }^{ 55 }{ Mn }\)
(d)
\(_{ 24 }^{ 56 }{ Cr }\)

20 )

The activity of a sample is defined as the number of disintegrations per unit time. If \(\lambda \) represents the decay or disintegration constant, the activity of the sample is given by

(a)
N/N_o
(b)
\(\lambda\)N
(c)
N/\(\lambda\)
(d)
None of these

21 )

The number of oxygen atoms in 4.4 g of CO₂ is approx.

(a)
1.2 x 10²³
(b)
6 x 10²²
(c)
6 x 10²³
(d)
12 x 10²³

22 )

Hydrogen gas will not reduce

(a)
heated cupric oxide
(b)
heated ferric oxide
(c)
heated stannic oxide
(d)
heated aluminium oxide

23 )

KMnO₄ is a powerful

(a)
reducing agent
(b)
oxidising agent
(c)
hydrating agent
(d)
dehydrating agent

24 )

It is not true:

(a)
Phosphorous is less reactive than nitrozen
(b)
PH₃ is more stable than NH₃
(c)
HNO₃ is a stronger acid than H₃PO₃
(d)
Nitrozen is more electronegative than phosphorus

25 )

How many isomers are possible for the compounds having molecular formula C₃H₅Br₃?

(a)
5
(b)
4
(c)
6
(d)
8

26 )

To find out whether C₃H₄ contains two double bonds or a triple bond,the test performed would be treating it with

(a)
bromine water
(b)
Bayer's reagent
(c)
Fehling's solution
(d)
Ammoniacal silver nitrate

27 )

Alkyl isocyanides contain \(\sigma \) and \(\pi \) bounds

(a)
\(9\sigma \quad and\quad 3\pi \)
(b)
\(9\sigma \quad and\quad 9\pi \quad \)
(c)
\(3\sigma \quad and\quad 4\pi \)
(d)
\(5\sigma \quad and\quad 7\pi \)

28 )

Observe the following columns.

Column I		ColumnII
A.	If a, b, c, d are four non zero real numbers such that (d + a - b)² + (d + b - c)² = 0 and roots of the equation a(b - c)x² + b (c - a)x + c(a - b) = 0 are real and equal, then	p.	\(a+b+c\neq 0\)
B.	If a, b, c are three non - zero real numbers such that the roots of the equation (b - c) x² + (c - a) x + (a - b) = 0 are real and equal, then	q.	a, b, c are in AP
C.	If the three equations x² + px + 12 = 0, x² + qx + 15 = 0 and x² + (p + q) x + 36 = 0 have a common positive root and a, b, c be their other roots, then	r.	a, b, c are in GP
		s.	a, b, c are in HP
		t.	a = b = c

(a)

A B C

(p,q,r,s,t) (p,q) (p)
(b)

A B C

(p,q,r) (p,q,r,s,t) (p,r)
(c)

A B C

(p,q,s) (p,q,r) (q,t)
(d)
None of the above

29 )

A box contains 2 white balls, 3 black balls and 4 red balls. The number of ways of drawing 3 balls from the box, if atleast one black ball is included, is

(a)
36
(b)
42
(c)
56
(d)
64

30 )

The set S={1,2,3,....12} is to be partioned into three sets A,B and C of equal size.
Thus \(A\cup B\cup C=S\\ A\cap B=B\cap C\\ =A\cap C=\phi \)
The number of ways to partition S is

(a)
\(12!\over {3!(4!)^3}\)
(b)
\(12!\over 3!(3!)^4\)
(c)
\(12!\over (4!)^3\)
(d)
\(12!\over (3!)^4\)

31 )

A straight line L on the XY-plane bisects the angle between OX and OY. What are the direction cosines of L?

(a)
\(<({1\over \sqrt2}),({1\over\sqrt2}),0>\)
(b)
\(<({1\over2}),({\sqrt3\over2}),0>\)
(c)
<0,0,1>
(d)
\(<({2\over3}),({2\over3}),({1\over3})>\)

32 )

A bag contains 17 tickets numbered 1 to 17. A ticket is drawn and replaced, then one more ticket is drawn and replaed. Probability that first number drawn id even and second is odd, is

(a)
82/289
(b)
72/289
(c)
64/289
(d)
None of the above

33 )

If \({ log }_{ a }X,{ log }_{ b }X\) and \({ log }_{ c }X\) are in HP, then a,b and c are in

(a)
AP
(b)
HP
(c)
GP
(d)
None of the above

34 )

Match the laws given in Column I, with their formula in column II and select the correct option in the choices given below.

	Column I		Column II
A.	Newton's law of cooling	1.	\({ \lambda }_{ m }.T=constant\)
B.	Calorimetry	2.	\(\frac { dQ }{ dt } =K\Delta T\)
C.	Wein's displacement law	3.	\({ m }_{ 1 }{ s }_{ 1 }\left( { \theta }_{ 1 }-\theta \right) ={ m }_{ 2 }{ s }_{ 2 }\left( \theta -{ \theta }_{ 2 } \right) \)

(a)

A B C

3 1 2
(b)

A B C

1 2 3
(c)

A B C

2 3 1
(d)

A B C

3 2 1

35 )

A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is v, then the maximum area around the fountain that gets wet is

(a)
\(\pi{v^4\over g^2}\)
(b)
\({\pi v^4\over 2g^2}\)
(c)
\(\pi{v^2\over g^2}\)
(d)
\(\pi{v^2\over g}\)

36 )

A damped oscillator of frequency v₁ is driven by an external periodic force of frequency v₂. when steady state is reached, frequency of oscillator will be

(a)
\(v_{2}\)
(b)
\(v_{1}\)
(c)
\(\frac{v_1+v_2}{2}\)
(d)
\(\sqrt{v_1+v_2}\)

37 )

When p-n junction diode is forward biased, then

(a)
the depletion region is reduced and barrier height is increased
(b)
the depletion region is widened and barrier height is reduced
(c)
both the depletion region and barrier height are reduced
(d)
both the depletion region and barrier height are increased

38 )

For coherent sources

(a)
amplitude must be same
(b)
a constant phase difference is required
(c)
Both (a) and (b) are correct
(d)
Both (a) and (b) are incorrect

39 )

Two students A and B report the weight of the same substance as 4.0 and 4.00 g respectively. Which of the following statements is correct?

(a)
Both are equally accurate
(b)
A is more accurate than B
(c)
B is more accurate than A
(d)
Both are inaccurate scientifically

40 )

What is the concentration of sugar (C₁₂H₂₂O₁₁) in mol L^-1 if its 20 g are dissolved in enough water to make a final volume upto 2 L?

(a)
0.0292 M
(b)
0.0120 M
(c)
0.0391 M
(d)
0.0200 M

41 )

Mathc the following and choose the correct option.

Type of packing	Voild volume
A. hcp	p. 0.38
B. sc	q. 0.48
C. bcc	r. 0.22
D. dc(diamond cubic)	s. 0.66

(a)

A B C D

p r q s
(b)

A B C D

r q p s
(c)

A B C D

r p q s
(d)

A B C D

p q r s

42 )

Phosphine is not formed when

(a)
white phosphorus is boiled with a strong solution of Ba(OH)₂
(b)
phosphorus acid is heated
(c)
calcium hypophosphite is heated
(d)
metaphosphoric acid is heated

43 )

Cellulose is a polymer of

(a)
glucose
(b)
fructose
(c)
sucrose
(d)
ribose

44 )

In context with the industrial preparation of hydrogen from water gas \((CO+H_2)\). Which of the following is the correct statement?

(a)
CO and \(H_2\) are fractionally separated using differences in their densities
(b)
CO is removed by absorption in aqueous \(Cu_2Cl_2\) solution
(c)
\(H_2\) is removed through occlusion with Pd.
(d)
CO is oxidised to \(CO_2\) with steam in the presence of a catalyst followed by absorption of \(CO_2\) in alkali

45 )

The standard electrode potentials for the reactions,
\({ Ag }^{ + }(aq)+{ e }^{ - }\longrightarrow Ag(s)\) \({ S }n^{ 2+ }(aq)\ +\ 2{ e }^{ - }\longrightarrow Sn(s)\) at \({ 25 }^{ \circ }C\) are 0.80 V and -0.14 V, respectively.

The emf of the cell, \(Sn\ |\ { S }n^{ 2+ }(1M)\ ||\ Ag^{ + }(1M)\ |Ag\ \) is

(a)
0.48 V
(b)
0.80 V
(c)
1.08 V
(d)
0.94 V

46 )

Four species are listed below.

I.\({HCO}^{-}_{3}\) II. \(H_{3}O^{+}\)
III. \({HSO}^{-}_{4}\) IV. \(HSO_{3}F\)
Which one of the following is the correct sequence of their acid strength?

(a)
IV < II < III < I
(b)
II < III < I < IV
(c)
I < III < II < IV
(d)
III < I < IV < II

47 )

The number of positive integers with the property that they can be expressed as the sum of the cubes of 2 positive integers in two different ways is

(a)
1
(b)
100
(c)
infinite
(d)
0

48 )

The number of ways of arranging seven persons (having A, B, C and D among them ) in a row so that A, B, C and D are always in order A-B-C-D (not necessarily together) is

(a)
10
(b)
5040
(c)
6 X ⁷C₄
(d)
⁷P₃

49 )

The sum of the last ten coefficients in the expansion of (1 + x)¹⁹, when expanded in ascending powers of x is

(a)
2¹⁸
(b)
2¹⁹
(c)
2¹⁸ - ¹⁹C₁₀
(d)
none of these

50 )

If a_i > 0, i=1,2,3,....,n and m₁,m₂,m₃,...m_n be positive rational numbers, then
\(\left( \frac { { m }_{ 1 }{ a }_{ 1 }+{ m }_{ 2 }{ a }_{ 2 }+...+{ m }_{ n }a_{ n } }{ { m }_{ 1 }+{ m }_{ 2 }+....+{ m }_{ n } } \right) \ge ({ a }_{ 1 }^{ { m }_{ 1 } }{ a }_{ 2 }^{ { m }_{ 2 } }....{ a }_{ n }^{ { m }_{ n } })^{ 1/({ m }_{ 1 }+{ m }_{ 2 }+...+{ m }_{ n }) }\)
\(\ge \frac { ({ m }_{ 1 }+{ m }_{ 2 }+....+{ m }_{ n }) }{ \frac { { m }_{ 1 } }{ { a }_{ 1 } } +\frac { { m }_{ 2 } }{ { a }_{ 2 } } +...+\frac { { m }_{ n } }{ { a }_{ n } } } \) is called weighted mean theorem
where \({ A }^{ * }=\frac { { m }_{ 1 }{ a }_{ 1 }+{ m }_{ 2 }{ a }_{ 2 }+....+{ m }_{ n }{ a }_{ n } }{ { m }_{ 1 }+{ m }_{ 2 }+...+{ m }_{ n } } \)
= Weighted arithmetic mean
\({ G }^{ * }=({ a }_{ 1 }^{ { m }_{ 1 } }{ a }_{ 2 }^{ { m }_{ 2 } }....{ a }_{ n }^{ { m }_{ n } })^{ 1/({ m }_{ 1 }+{ m }_{ 2 }+...+{ m }_{ n }) }\)
=Weighted geometric mean
and \({ H }^{ * }=\frac { { m }_{ 1 }+{ m }_{ 2 }+....+{ m }_{ n } }{ \frac { { m }_{ 1 } }{ { a }_{ 1 } } +\frac { { m }_{ 2 } }{ { a }_{ 2 } } +...\frac { { m }^{ n } }{ { a }_{ n } } } \)= Weighted harmonic mean
ie ., \(A^{ * }\ge { G }^{ * }\ge { H }^{ * }\)
Now, let a+b + c = 5(a,b,c > 0) and x²y³ = 6(x>0,y>0)
The least value of 3x + 4y is

(a)
5
(b)
7
(c)
10
(d)
17

51 )

Let \(\vec { a } \) and \(\vec { b } \) are two vectors making angles \(\theta \) with each other, then unit vectors along bisector of \(\vec { a } \) and \(\vec { b } \) is

(a)
\(\pm \frac { \hat { a } +\hat { b } }{ 2 } \)
(b)
\(\pm \frac { \hat { a } +\hat { b } }{ 2\cos { \theta } } \)
(c)
\(\pm \frac { \hat { a } +\hat { b } }{ 2\cos { \theta /2 } } \)
(d)
\(\pm \frac { \hat { a } +\hat { b } }{ \left| \hat { a } +\hat { b } \right| } \)

52 )

If \(\hat { i } \times \left( \vec { a } \times \hat { i } \right) \times \hat { j } \times \left( \vec { a } \times \hat { j } \right) \times \hat { k } \times \left( \vec { a } \times \hat { k } \right) =.........\left\{ \left( \vec { a } .\hat { i } \right) \hat { i } +\left( \vec { a } .\hat { j } \right) \hat { j } +\left( \vec { a } .\hat { k } \right) \hat { k } \right\} \)

(a)
-1
(b)
0
(c)
2
(d)
none of these

53 )

\(\lim _{ x\rightarrow 0 }{ \frac { x\sqrt { { y }^{ 2 }-(y-x)^{ 2 } } }{ \left( \left( \sqrt { (8xy-{ 4x }^{ 2 } } \right) +\sqrt { (8xy)^{ 3 } } \right) } } \) is equal to

(a)
1/4
(b)
1/2
(c)
\(1/2\sqrt { 2 } \)
(d)
none of these

54 )

If we rotate the axes of the rectangular hyperbola x² -y² = a² through an angle \(\pi/4\) in the clockwise direction, then the equation x² - y² = a² reduces to xy \(=\frac { { a }^{ 2 } }{ 2 } ={ \left( \frac { a }{ \sqrt { 2 } } \right) }^{ 2 }={ c }^{ 2 }\) (say) Since x = ct, y = \(\frac {c}{t}\) satisfies.xy = c². \(\therefore\) ( x, y ) = \((ct,\frac{c}{t})\)\((t\neq0)\) is called a "t' point on the rectangular hyperbola. If e₁ and e₂ are the eccentricities of the hyperbolas xy = 9 and x²- y² = 25, then (e1,e2) lie on a circle C₁ with centre origin then the (radius)² of the director circle of C1 is

(a)
2
(b)
4
(c)
8
(d)
16

55 )

Let α, β be any two positive values of x for which 2 cos x, I cos x| and 1- 3 cos² x are in GP. The minimum value of |α - β| is

(a)
\(\pi\over3\)
(b)
\(\pi\over4\)
(c)
\(\pi\over2\)
(d)
none of these

56 )

Which of the following sets is an infinite set?

(a)
Set of concentric circles in a plane
(b)
Set of all lines in a plane
(c)
{x∊N : x<200}
(d)
All of these

57 )

A rope ladder with a length I carrying a man with a mass m at its end is attached to the basket of a balloon with a mass M. The entire system is in equilibrium in the air. As the man climbs up the ladder into the balloon, the balloon descends by a height h. Then the potential energy of the man:

(a)
increases by mg(l-h)
(b)
increases by mgl
(c)
increases by mgh
(d)
increases by mg(2l-h)

58 )

A car is moving on a straight horizontal road with a speed v. If the coefficient of friction between the tyres and the road is \(\mu\), the shortest distance in which the car can be stopped is:

(a)
\(\frac { { v }^{ 2 } }{ 2\mu g } \)
(b)
\(\frac { { v }^{ 2 } }{ \mu g } \)
(c)
\({ \left( \frac { v }{ \mu g } \right) }^{ 2 }\)
(d)
\( \frac { { v }^{ 2 } }{ \mu } \)

59 )

In a carbon monoxide molecule, the carbon and the oxygen atoms are separated by a distance 1.12x 10^-10 m . The distance of the centre of mass from the carbon atom is:

(a)
0.48 x 10^-10 m
(b)
0.51x 10^-10 m
(c)
0.56 x 10^-10 m
(d)
0.64 x 10^-10 m

60 )

The fractional change in internal energy when a gas is cooled from 927°C to 27°C is:

(a)
0.25
(b)
4
(c)
0.97
(d)
none of these

61 )

The sine of the angle between the straight line \(\frac { x-2 }{ 3 } =\frac { y-3 }{ 4 } =\frac { z-4 }{ 5 } \)and the plane 2x-2y+z=5 is

(a)
\(\frac{10}{6\sqrt5}\)
(b)
\(\frac{4}{5\sqrt2}\)
(c)
\(\frac { 2\sqrt { 3 } }{ 5 } \)
(d)
\(\frac { {\sqrt2 } }{ 5 } \)

62 )

A vessel is partly filled with a liquid. Coefficients of cubical expansion of material of the vessel and liquid are \(\gamma\)v and \(\gamma\)L respectively. lfthe system is heated, then volume unoccupied by the liquid will necessarily:

(a)
remain unchanged if \(\gamma\)v = \(\gamma\)L
(b)
increase if \(\gamma\)v = \(\gamma\)L
(c)
decrease if \(\gamma\)v =\(\gamma\)L
(d)
none of the above

63 )

A ball thrown by one player reaches the other in 2 sec. The maximum height attained by the ball above the point of projection will be about

(a)
2.5 m
(b)
5 m
(c)
7.5 m
(d)
10 m

64 )

Two projectiles are projected with the same velocity. If one is projected at an angle of 30° and the other at 60° to the horizontal, then the ratio of maximum heights reached is:

(a)
3:1
(b)
1:3
(c)
1:2
(d)
2:1

65 )

Let us define the sum of cubic numbers is \(\sum n^{3}=[{n(n+1)\over2}]^2\)
Statement-I : Sum of the series 1³ - 2³ + 3³- 4³ + ... + 11³ = 756
Statement-II: For any odd integer 1 n \(\ge\) 1, n³ - (n -1)³ + ... + (-1)^n-1 1³= \(1\over4\)(2n -1)(n + 1)².

(a)
If both Statement-I and Statement-II are true and Statement-II is the correct explanation of Statement -1.
(b)
If both Statement-I and Statement-II are true but Statement-II is not the correct explanation of Statement -1.
(c)
If Statement-I is true but Statement-II is false.
(d)
If Statement-I is false and Statement-II is true.

66 )

A body is projected vertically upwards with a velocity' u'. It crosses a point in its journey at a height' h' twice, just after 1 and 7 seconds. The value of u (in ms^-1) is

(a)
50
(b)
40
(c)
30
(d)
20

67 )

An artificial satellite moves in a circular orbit around the earth. Total energy of the satellite is given by E. The potential energy ofthe satellite is:

(a)
-2 E
(b)
-2 E
(c)
2E/3
(d)
-2E/3

68 )

Assuming the sun to be a spherical body of radius R at a temperature of TK, evaluate the total radiant power, incident on the earth, at a distance r from the sun, is:

(a)
\(\frac { { R }^{ 2 }\sigma { T }^{ 4 } }{ { r }^{ 2 } } \)
(b)
\(\frac { 4\pi { r }_{ 0 }^{ 2 }{ R }^{ 2 }\sigma { T }^{ 4 } }{ { r }^{ 2 } } \)
(c)
\(\frac { \pi { r }_{ 0 }^{ 2 }{ R }^{ 2 }\sigma { T }^{ 4 } }{ { r }^{ 2 } } \)
(d)
\(\frac { { r }_{ 0 }^{ 2 }{ R }^{ 2 }\sigma { T }^{ 4 } }{ 4\pi { r }^{ 2 } } \)

69 )

A big particle of mass (3 + m) kg blasts into 3 pieces, such that a particle of mass 1 kg moves along x-axis, with velocity 2 m/s and a particle of mass 2 kg moves with velocity 1m/s perpendicular to direction of 1 kg particle. If the third particle moves with velocity \(\sqrt { 2 } \) m/s, then m is:

(a)
2 kg
(b)
1 kg
(c)
\(2\sqrt { 2 } \) kg
(d)
none of these

70 )

The mass of a lift is 2000 kg. When the tension in the supporting cable is 28000 N, then its acceleration is:

(a)
4 ms^-2 upwards
(b)
4 ms^-2 downwards
(c)
14 4 ms^-2 upwards
(d)
30 ms^-2 downwards

71 )

The velocity of a particle (v) at an instant t is given by: v = at + bt². The dimension of b is:

(a)
[L]
(b)
[LT^-1]
(c)
[Lr^-2]
(d)
[LT^-3]

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Exam Duration: 180 Mins Total Questions : 75

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A	B	C
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