JEE Main Model Question Paper 2
Exam Duration: 180 Mins Total Questions : 75
Let \({ \triangle }_{ 1 }=\left| \begin{matrix} a & b & c \\ c & a & b \\ b & c & a \end{matrix} \right| \quad and \quad{ \triangle }_{ 2 }=\left| \begin{matrix} b+c & c+a & a+b \\ a+b & b+c & c+a \\ c+a & a+b & b+c \end{matrix} \right| \)
- (a)
\({ \triangle }_{ 1 }={ \triangle }_{ 2 }\)
- (b)
\({ \triangle }_{ 1 }={2 \triangle }_{ 2 }\)
- (c)
\({ \triangle }_{ 2 }={ 2\triangle }_{ 1 }\)
- (d)
none of these
If \(A=\left[ \begin{matrix} 1 & 3 \\ -1 & 2 \end{matrix} \right] ,\quad B=\left[ \begin{matrix} 5 & -7 \\ 6 & 4 \\ -1 & 2 \end{matrix} \right] \), then
- (a)
AB exists
- (b)
AB and BA both exists
- (c)
Neither Ab nor BA does not exists
- (d)
BA exist but AB does not exists
Area of the parallelogram formed by the lines y=mx, y=mx+1, y=nx, y=nx+1, is
- (a)
\(\frac { |m+n| }{ (m-n)^2 } \)
- (b)
\(\frac { 2 }{ (m+n) } \)
- (c)
\(\frac { 1 }{ (m+n) } \)
- (d)
\(\frac { 1 }{ (m-n) } \)
The vectors \(\vec { a } =xi+yj+zk,\quad \vec { b } =j\quad and\quad \vec { c } \) are such that \(\vec { a } ,\vec { c } ,\vec { b } \) form a right handed system, then \(\vec { c } =\)
- (a)
yj
- (b)
\(\vec { 0 } \)
- (c)
zi-xk
- (d)
-zi+xk
\(\begin{matrix} lim \\ x\rightarrow 0 \end{matrix}\int _{ 0 }^{ { x }^{ 2 } }{ \frac { sin\sqrt { x } }{ { x }^{ 3 } } } dx\) equals
- (a)
0
- (b)
\(\frac { 1 }{ 2 } \)
- (c)
1
- (d)
none of these
If P represents radiation pressure, C is speed of light Q the intensity of radiation, then non-zero integers x, y, z are if PxQyCz is a dimensionless quantity:
- (a)
+1, +1, -1
- (b)
+1, -1, +1
- (c)
-1, +1, +1
- (d)
+1, +1, +1
A projectile thrown with the speed \(\vartheta\) at an angle \(\theta\) has a range R on the surface of earth.For same \(\vartheta\) and \(\theta\) ,its range on the surface of moon will be
- (a)
\(\frac {R}{6} \)
- (b)
R
- (c)
6R
- (d)
36R
potentail energy of a system consisting of four equal- mass particles M located at the corners of a square having sides of length L is
- (a)
\(\frac { -{ GM }^{ 2 }(4+\sqrt { 2 } ) }{ d } \)
- (b)
\(-4\frac { { GM }^{ 2 } }{ d } \)
- (c)
\(\frac { -\sqrt { 2\quad { GM }^{ 2 } } }{ d } \)
- (d)
none of the above
a satellite S is moving in an elliptical orbit around the earth. the mass of the satellite is very small compared to the mass of the earth?
- (a)
the acceleration of S is always directed toward the centre of the earth
- (b)
the angular momentum of S about the centre of the earth changes in direction but its magnitude remains constant
- (c)
the total mechanical energy of S varies periodically with time
- (d)
the linear momentum of S remains constant in magnitude
If 'S' is stress and 'Y' is Young's modules of material of a wire,then the energy stored in the wire per unit volume is
- (a)
\(\frac{S^2}{2Y}\)
- (b)
\(\frac{2Y}{S^2}\)
- (c)
\(\frac{S}{2Y}\)
- (d)
\(2S^2Y\)
In the production of beats by two progressive waves of nearly the same frequency,
- (a)
the frequency of the beats is a function of time
- (b)
the frequency of the beats depends on the relative position of the listener
- (c)
the frequency of beats depends on the relative velocity between the source and listener
- (d)
the frequency of the beats can heard more distinctly if the frequency difference between the component waves is large
An ammeter connected in series with a silver. Voltmeter reads 0.810 A. If the weight of silver deposited in 20 minutes is 1.071 g, the error in the reading of ammeter is (Electro-chemical equivalent of silver is 1.118 X 10-3 gC-1)
- (a)
+0.12 A
- (b)
+0.012 A
- (c)
-0.012 A
- (d)
-0.12 A
The ratio of intensity of magnetisation and magnetising field is called
- (a)
permeability
- (b)
magnetic induction
- (c)
magnetic intensity
- (d)
magnetic susceptibility
Susceptibility is positive and large for a
- (a)
paramagnetic substance
- (b)
ferromagnetic substance
- (c)
diamagnetic substance
- (d)
non-magnetic substance
Electron emitted in beta radiation originates from
- (a)
inner orbits
- (b)
free electrons existing in nuclei
- (c)
decay of neutron in a nucleus
- (d)
photon escaping from the nucleus
The electronic configuration of nitrogen is 1s2, 2s2, 2px1, 2py1, 2pz1 because of
- (a)
Pauli's exclusion principle
- (b)
(n+1) rule
- (c)
Hund's rule
- (d)
uncertainity principle
What will be de Broglie wavelength of an electron moving with a velocity of \(1.20\times {10}^{5} m{s}^{-1}\)?
- (a)
6.068X10-9
- (b)
3.133X10-37
- (c)
6.626X10-9
- (d)
6.018X10-7
Which one of the following sets of quantum numbers is not possible?
- (a)
n = 3, l = 0, m = -1
- (b)
n = 3, l = 2, m = +1
- (c)
n = 3, l = 2, m = -1
- (d)
n = 3, l = 2, m = 0
Hydrogen bond is most extensive in
- (a)
ethanol
- (b)
diethyl ether
- (c)
ethyl chlorial
- (d)
triethylamine
The correct order of decreasing polarisable ion is
- (a)
\(C\overline{l},B\overline{r},\overline{I},\overline{F}\)
- (b)
\(\overline{F},\overline{I},B\overline{r},C\overline{l}\)
- (c)
\(\overline{I},B\overline{r},C\overline{l},\overline{F}\)
- (d)
\(\overline{F},C\overline{l},B\overline{r},\overline{I}\)
Gases deviate from ideal behaviour because their molecules
- (a)
posses negligible volume
- (b)
are polyatomic
- (c)
have forces of attraction between them
- (d)
exert no attraction no one another
Enthalpy of an element in its standard state at 25\(?\) and 1 atm pressure is always
- (a)
zero
- (b)
positive
- (c)
negative
- (d)
maximum
The solution of sodium carbonate has pH
- (a)
greater than 7
- (b)
less than 7
- (c)
equal to 7
- (d)
equal to zero
pH of a solution is defined by the exxpression
- (a)
log [H+]
- (b)
\(log\frac { 1 }{ \left[ { H }^{ + } \right] } \)
- (c)
\(\frac { 1 }{ log { H }^{ + } } \)
- (d)
\(-log\frac { 1 }{ { H }^{ + } } \)
The strongest reducing agent is
- (a)
K
- (b)
Mg
- (c)
Al
- (d)
Ne
Molarity of 98% \(H_2SO_4\) having density 1.95 g ml would be (given molecular weight = 98) :
- (a)
16.0
- (b)
17.0
- (c)
18.0
- (d)
19.5
Vapour pressure of a solution of 5 g of non-volatile compound in 100 g of water at temperature T is 2985 N \(m^-2\). Vapour pressure of pure water is 3000 N \(m^-2\). The molecular weight of solute is
- (a)
60
- (b)
120
- (c)
180
- (d)
240
Strongest acid form the following is
- (a)
HF
- (b)
H3P
- (c)
HBr
- (d)
H2S
The oxiding ability of perhalates follow th order:
- (a)
CIO4<BrO4>IO4
- (b)
CIO4<BrO4>IO4
- (c)
IO4<BrO4>ClO4
- (d)
None of the above
Solid K2Cr2O7 is used to detect the presence of which one of the following acid radicals in analytical chemistry?
- (a)
F
- (b)
Ci
- (c)
Br
- (d)
I
Angle between the tangents to the curve \(y=x^2-5x+6\) at the points (2,0) and (3,0) is
- (a)
\(\pi\over 2\)
- (b)
\(\pi\over 6\)
- (c)
\(\pi\over 4\)
- (d)
\(\pi\over 3\)
If \(\phi (x)={log\ sin\ x\over x}, x\neq n\pi, \ n\in I\) and \(\int^3_1{3\ log(sin\ x)\over x}dx=\phi(k)-\phi(1), then\) possible values of k is
- (a)
27
- (b)
18
- (c)
9
- (d)
36
Let f(x)=min{x+|x|,x-[x]}, where [x] denotes the greatest integer function, then \(\int^1_{-1}f(x)\) dx is equal to
- (a)
\(1\over2\)
- (b)
\(-{1\over2}\)
- (c)
1
- (d)
-1
The range of \(f(x)=\left| { 3tan }^{ -1 }x-{ cos }^{ -1 }(0) \right| { -cos }^{ -1 }(-1)\) is
- (a)
\([-\pi ,\pi )\)
- (b)
\((-\pi ,\pi )\)
- (c)
\([-\pi ,\pi ]\)
- (d)
\(\left[ -\frac { \pi }{ 2 } ,\frac { \pi }{ 2 } \right) \)
The variation of density inside a solid sphere, is given by \(\rho=\rho_o \ a/r\) where, \(\rho_o\) is density at the surface of the sphere and r denotes the distance from the centre. The value of gravitational field at distance 2a from the centre of the sphere is
- (a)
1/4\(\pi G\rho_oa\)
- (b)
2\(\pi G\rho_oa\)
- (c)
\(\pi G\rho_oa\)
- (d)
1/2\(\pi G\rho_oa\)
Statement I: For a mass M, kept at the centre of a cube of side a, the flux of gravitational field passing through its sides is \(4\pi\) GM.
Statement II: If the direction of a field due to a point source is radial and its dependence on the distance r from the source is given as \(1\over r^2\), its flux through a closed surface depends only on the strength of the source enclosed by the surface and not on the size or shape of the surface
- (a)
Statement I is true; Statement II is true; Statement II is not the correct explanation for statement I
- (b)
Statement I is true; statement II is false
- (c)
Statement I is false; Statement II is true
- (d)
Statement I is true; Statement II is true; Statement II is the correct explanation for statement I
A balloon is ascending at the ratio of 14 m/s at a height of 98 m above the ground, when a packet is dropped from the balloon. After how many time and what velocity does it reach to the ground?
- (a)
6.13 s, 47 m/s
- (b)
6.123 s, 46 m/s
- (c)
7 s, 49 m/s
- (d)
8 s, 50 m/s
If a simple pendulum has significant amplitude (upto a factor of 1/e of original) only in the period between t=0 sec to t=\(\tau\) sec, then \(\tau\) may be called the average life of the pendulum. When the spherical bob of the pendulum suffers a retardation proportional to its velocity with b as the constant of proportionality, the average life time of the pendulum is ( assuming damping is small) in seconds
- (a)
\(\frac{0.0693}{b}\)
- (b)
\(b\)
- (c)
\(\frac{1}{b}\)
- (d)
\(\frac{2}{b}\)
In the reaction, \(2A+4B\rightarrow 3C+4D;\) when 5 moles of A react with 6 moles of B, then calculate amount of C formed.
- (a)
10
- (b)
4.5
- (c)
3
- (d)
4
Which of the following has the highest value of lattice energy?
- (a)
MgO
- (b)
Al2O3
- (c)
CaO
- (d)
Na2O
The number of equidistance oppositely charged ions in sodium chloride crystal is
- (a)
2
- (b)
4
- (c)
6
- (d)
8
Which of the following requires maximum energy to undergo decomposition?
- (a)
O2
- (b)
C2
- (c)
O2+
- (d)
N2
Calomel (Hg2Cl2) on reaction with NH4OH gives
- (a)
HgO
- (b)
Hg2O
- (c)
NH2 - Hg - Hg - Cl
- (d)
HgNH2Cl
Of the five isomeric hexane, the isomer which can give two monochlorinated compounds, is
- (a)
2-methylpentane
- (b)
2,2-dimethylbutane
- (c)
2,3-dimethylbutane
- (d)
n-hexane
Fog is a colloidal system in which
- (a)
liquid dispersed in gas
- (b)
gas dispersed in liquid
- (c)
gas dispersed in solid
- (d)
solid dispersed in liquid
What is the equilibrium constant, K for the following reaction at 400K?
\(2NOCl(g)\rightleftharpoons 2NO(g)+Cl_{ 2 }(g)\); \(\Delta H=77.2kJmol^{-1}\) and \(\Delta S=122JK^{-1}mol^{-1}\) at 400K.
- (a)
-3.708
- (b)
1.95X10-4
- (c)
2.8X104
- (d)
1.67X10-5
Let an = \(\frac { { \left( 1000 \right) }^{ n } }{ n! } \) for \(n\varepsilon N\) Then an is greatest, when
- (a)
n = 998
- (b)
n = 999
- (c)
n = 1000
- (d)
n = 1001
Which of the following statements are possible , a, b, m and n being non-zero real numbers?
- (a)
\(4\sin ^{ 2 }{ \theta } =5\)
- (b)
\(\left( { a }^{ 2 }+{ b }^{ 2 } \right) \cos { \theta } =2ab\)
- (c)
\(\left( { m }^{ 2 }+{ n }^{ 2 } \right) \cos { ec\theta } ={ m }^{ 2 }-{ n }^{ 2 }\)
- (d)
\(\sin { \theta = } 2.375\)
The maximum value of the expression \(\left| \sqrt { \left( \sin ^{ 2 }{ x } +2{ a }^{ 2 } \right) } -\sqrt { \left( { 2a }^{ 2 }-1-\cos ^{ 2 }{ x } \right) } \right| \) , where a and x are real numbers is
- (a)
\(\sqrt{3}\)
- (b)
\(\sqrt{2}\)
- (c)
1
- (d)
\(\sqrt{5}\)
Two points A and B move on the x-axis and the y-axis respectively such that the distance between the two points is always-the same. The locus of the middle point of AB is
- (a)
a straight line
- (b)
a circle
- (c)
a parabola
- (d)
an ellipse
Let A and B are two independent events. The probability that both A and B happen is \(\frac { 1 }{ 2 } \) and the probability that neither A nor B happens is \(\frac { 1 }{ 2 } \) then
- (a)
\(P(A)=\frac { 1 }{ 3 } ,P(B)=\frac { 1 }{ 4 } \)
- (b)
\(P(A)=\frac { 1 }{ 2 } ,P(B)=\frac { 1 }{ 6 } \)
- (c)
\(P(A)=\frac { 1 }{ 6 } ,P(B)=\frac { 1 }{ 2 } \)
- (d)
\(P(A)=\frac { 1 }{ 4 } ,P(B)=\frac { 1 }{ 3 } \)
The Order of the differential equation is the order of the highest derivative appearing in the equation and the Degree of a differential equation which can be written as polynomial in the derivatives in the degree of the derivative of the highest order occuring in it, after it has been expressed in a form free from radicals and fractions and if differential equation can not be written as a polynomial in the derivatives, then degree deos not defined but order defined.
The degree of the differential equation \(\left( \frac { d^{ 3 }y }{ dx^{ 3 } } \right) ^{ 2/3 }+3\frac { d^{ 2 }y }{ dx^{ 2 } } +\frac { dy }{ dx } +5\) = 0 is
- (a)
1
- (b)
2
- (c)
3
- (d)
none of these
Solution of differential (x cos x - sin x) dx = \(\frac{x}{y}\) sin xdy is
- (a)
sin x = 1n I xy I + c
- (b)
\(1n\left| \frac { sinx }{ x } \right| =y+c\)
- (c)
\(\left| \frac { sinx }{ xy } \right| =c\)
- (d)
none of these
If ex+ef(x)=e, then for f(x)
- (a)
domain=(-\(\infty\),1)
- (b)
range=(-\(\infty\),1)
- (c)
domain=(-\(\infty\),0]
- (d)
range=(-\(\infty\),1]
If the equation ax2+bx+c=0 and x3+3x2+3x+2=0 have two common roots,then
- (a)
a=b≠c
- (b)
a≠b=c
- (c)
a=b=c
- (d)
a=-b=c
Which term of the sequence 4,9,14,19,....is 124 ?
- (a)
25th
- (b)
20th
- (c)
26th
- (d)
21st
The number of divisors of 72,2025 and 1568 are in
- (a)
A.P
- (b)
G.P.
- (c)
A.G.P.
- (d)
None of these
if the expansion of \(\left( \frac { 3\sqrt { x } }{ 7 } -\frac { 5 }{ 2x\sqrt { x } } \right) ^{ 13n }\) contains a term independent of x, then n should be a multiple of
- (a)
10
- (b)
5
- (c)
6
- (d)
4
Calculate the mean deviation from the mean of the following data:
| Marks | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 |
| Number of students | 4 | 6 | 1 | 20 | 10 | 6 | 4 |
- (a)
12.33
- (b)
11.33
- (c)
20
- (d)
13
The work done in dragging a stone of mass 100 kg up an inclined plane I in 100 through a distance of 10m is:
- (a)
zero
- (b)
980 J
- (c)
9800 J
- (d)
98 J
A spherical body of mass m and radius r is allowed to fall in a medium of viscosity η. The time in which the velocity of the body increases from zero to 0.63 times, the terminal velocity (v) is called time constant (ፒ). Dimensionally ፒ can be represented by:
- (a)
\(\frac { m{ r }^{ 2 } }{ 6\pi \eta } \)
- (b)
\(\sqrt { \left( \frac { 6\pi mr\eta }{ { g }^{ 2 } } \right) } \)
- (c)
\(\frac { m }{ 6\pi \eta r\upsilon } \)
- (d)
none of these
Consider a compound slab consisting of two different materials having equal thicknesses and thermal conductivities K and 2K respectively. The equivalent thermal conductivity of the slab is:
- (a)
\(\sqrt { 2 } K\)
- (b)
3 K
- (c)
4K/3
- (d)
2K/3
The sum to 20terms of the series 1x32+2x52+3x72+...... is
- (a)
18800
- (b)
188010
- (c)
188020
- (d)
188090
A pendulum of length I = I m is released from θ0 = 60° The rate of change of speed of the bob at θ = 30° is:
- (a)
\(5\sqrt3\)m/s2
- (b)
5m/s2
- (c)
10m/s2
- (d)
2.5m/s2
If the surface area ofthe filament of an incandescent lamp is 5 x 10-5. square metres, temperature 2000 K and relative emittence 0.85, then energy radiated per minute is: (Stefan's constant = 5.672 x 10-8Wm-2 K-4)
- (a)
2500 J
- (b)
2315 J
- (c)
2800 J
- (d)
3000 J
The moment of inertia of a solid cylinder about its axis is I. It is allowed to roll down an inclined plane without slipping. If its angular velocity at the bottom be to, then kinetic energy of the cylinder will be:
- (a)
\({1\over2}I\omega^2\)
- (b)
\(I\omega^2\)
- (c)
\({3\over2}I\omega^2\)
- (d)
2\(I\omega^2\)
The minimum number of vectors of equal magnitude required to produce a zero resultant is:
- (a)
2
- (b)
3
- (c)
4
- (d)
more than 4
If the system of equations x + ky - z = 0, 3x - ky - z = 0 and x - 3y + z = 0 has non-zero solution, then k is equal to
- (a)
-1
- (b)
0
- (c)
1
- (d)
2
Given that the displacement of an oscillating particle is given by y = A sin(Bx + Ct + D). The dimensional formula for ABCD is
- (a)
[M0L-1T0]
- (b)
[M0L0T-1]
- (c)
[M0L-1T-1]
- (d)
[M0L0T0]
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