jee main online paper 5 cbse sample paper
TRANSCRIPT
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Sri Chaitanya IIT Academy, India JEE-MAIN_ONLINE P5_Prepared by CBSE BOARD
Sri Chaitanya IIT Academy., India.A right Choice for the Real Aspirant
Central Office , Madhapur – Hyderabad
Jee-Main_Online_Paper-5PHYSICS
1. The amount of heat produced in an electric circuit depends upon the
current (I), resistance (R) and time (t). if the error made in the
measurements of the above quantities are 2%, 1% and 1% respectively
then the maximum possible error in the total het produced will be.
1) 1% 2) 2% 3) 3% 4) 6%
2. A goods train accelerating uniformly on a straight railway track,
approaches an electric pole standing on the side of track. Its engine passes
the pole with velocity u and the guard’s room passes with velocity . The
middle wagon of the train passes the pole with a velocity.
1)u + υ
2 2) uυ 3) 2 2
1u + υ
2 4)
2 2u + υ2
3. Sand is being dropped on a conveyor belt at the rate of 2 kg per second.
The force necessary to keep the belt moving with a constant speed of
13 ms will be.
1) 6 N 2) 12 N 3) 18 N 4) Zero
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Sri Chaitanya IIT Academy, India JEE-MAIN_ONLINE P5_Prepared by CBSE BOARD4. A block of weight W rests on a horizontal floor with coefficient of static
friction . It is desired to make the block move by applying minimum
amount of force. The angle from the horizontal which the force should
be applied and the magnitude F of the force is
1) θ = 0,F = μW 2) -12
µWθ = tan μ ,F =
1 + µ
3)
-1
2
1 µWθ = tan ,F =
µ 1 + µ 4)
-1 µ µWθ = tan ,F =1 + µ 1 + µ
5. A moving particle of mass m,. makes a head on elastic collision with
another particle of mass 2m, which is initially at rest. The percentage loss
in energy of the colliding particle on collision, is close to
1) 90% 2) 67% 3) 33% 4) 10%
6. A ring is suspended from a point S on its rim as shown in the figure.
When displaced from equilibrium, it oscillates with time period of 1
second. The radius of the ring is (take 2 g )
1) 1.5 m 2) 0.5 m 3) 0.15 m 4) 1.0 m
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Sri Chaitanya IIT Academy, India JEE-MAIN_ONLINE P5_Prepared by CBSE BOARD7. Two point masses of mass 1 m fM and 2 1 1 m f M f are in
outer space (far from gravitational influence of other objects) at adistance R from each other. They move in circular orbits about theircentre of mass with angular velocities 1 for 1 m and 2 for 2 m . In that
case
1) 1 2f ω = 1 - f ω 2) 1 21 - f ω = fω
3) 1 2ω = ω and depend on f 4) 1 2ω = ω and independ on f
8. A steel wire can sustain at the most 100 kg weight without breaking. Ifthe wire is cut into equal parts, each part can sustain at the most a weightof
1) 200 kg 2) 100 kg 3) 50 kg 4) 400 kg
9. A large number of droplets, each or radius, r coalesce to form a biggerdrop of radius, R. an engineer designs a machine so that the energyreleased in this process is converted into the kinetic energy of the drop.Velocity of the drop is (T = Surface Tension; density)
1)
12T 1 1
ρ r R 2)
2
12T 1 1
ρ r R
3)3
12T 1 1
ρ r R 4)
6
12T 1 1
ρ r R
10. A large cylindrical rod of length L is made by joining two identical rods
of copper and steel of length (L/2) each. The rods are completely
insulated from the surroundings. If the free end of the copper rod is
maintained at 0100 C and that of steel at 00 C then the temperature of
junction is (thermal conductivity of copper is 9 times that of steel)
1) 10°C 2) 50°C 3) 90°C 4) 67°C
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Sri Chaitanya IIT Academy, India JEE-MAIN_ONLINE P5_Prepared by CBSE BOARD11. This question has Statement 1, Statement 2. Of the four choices given after the
Statement, choose the one that best described the two statements.
Statement 1: An inventor claims to have constructed an engine that has an
efficiency of 30% when operated between the boiling and freezing points of
water. This is not possible
Statement 2: The efficiency of a real engine is always less than the efficiency of
a Carnot engine operating between the same two temperatures.
1) statement 1 is true, Statement 2 is true. Statement 2 is the correct
explanation of Statement 1.
2) Statement 1 is false, Statement 2 is true
3) statement 1 is true, Statement 2 is true. Statement 2 is not correct
explanation of Statement 1.
4) Statement 1 is true, Statement 2 is false.
12. The pressure of an ideal as varies with volume as P V , where is a
constant. One mole of the gas is allowed to undergo expansion such that
its volume becomes ‘m’ times its initial volume. The work done by the gas
in the process is
1) 2αV m -12
2) 2α m - 12V
3) 2
2αV m -12
4) 2 2
2α V m - 12
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Sri Chaitanya IIT Academy, India JEE-MAIN_ONLINE P5_Prepared by CBSE BOARD
13. The displacement sin y t A t of a pendulum for23
is
represented correctly by
1) 2)
3) 4)
14. A uniform tube of length 60.5 cm is held vertically with its lower end
dipped in water. A sound source of frequency 500 Hz sends sound waves
into the tube. When the length of tube above water is 16 cm and again
when it is 50 cm, the tube resonates with the source of sound. Two lowest
frequencies (in Hz), to which tube will resonate when it is taken out of
water, are (approximately)
1) 281, 562 2) 281, 843 3) 276, 552 4) 272, 544
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Sri Chaitanya IIT Academy, India JEE-MAIN_ONLINE P5_Prepared by CBSE BOARD15. The flat base of a hemisphere of radius a with no charge inside it lies in a
horizontal plane. A uniform electric field E
is applied at an angle 4
with the vertical direction. The electric flux through the curved surface of
the hemisphere is:
1)
2π + 2 πa E2 2
2) 2πa E
3)
2πa E2 2
4)2
2πa E
16. A charge of total amount Q is distributed over two concentric hollow
spheres of radii r and R(R>r) such that the surface charge densities on
the two spheres are equal. The electric potential at the common centre is
1) 2 20
R - r Q14πε R + r
2) 2 20
R r Q14πε 2 R + r
3) 2 20
R - r Q14πε 2 R + r
4) 2 20
R r Q14πε R + r
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Sri Chaitanya IIT Academy, India JEE-MAIN_ONLINE P5_Prepared by CBSE BOARD17. A 6.0 volt battery is connected to two light bulbs as shown in figure. Light
bulb 1 has resistance 3 Ohm while light bulb 2 has resistance 6 Ohm.
Battery has negligible internal resistance. Which bulb will glow more?
1) Bulb 1
2) Bulb 2
3) Both glow equally
4) Bulb 1 will glow more first and then its brightness will become less
than bulb 2
18. A proton and a deuteron are both accelerated through the same potential
difference and enter in a magnetic field perpendicular to the direction of
the field. If the deuteron follows a path of radius R, assuming the neutron
and proton masses are nearly equal, the radius of the proton’s path will
be
1) R2
2) R 3) 2 R 4) R 2
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Sri Chaitanya IIT Academy, India JEE-MAIN_ONLINE P5_Prepared by CBSE BOARD19. This question has Statement 1, Statement 2. Of the four choices given
after the Statement, choose the one that best describes the two statements.
Statements 1: Self inductance of a long solenoid of length L, total number
of turns N and radius r is less than2 2
0 N r
L
Statement 2: The magnetic induction in the solenoid in Statement 1
carrying current I is 0 NI L
in the middle of the solenoid but becomes less
as we move towards its ends
1) statement 1 is true, Statement 2 is true. Statement 2 is the correct
explanation of Statement 1.
2) Statement 1 is false, Statement 2 is true
3) statement 1 is true, Statement 2 is true. Statement 2 is not correct
explanation of Statement 1.
4) Statement 1 is true, Statement 2 is false.
20. A generator has armature resistance of 0.1 and develops an induced
emf of 120 V when driven at its rated speed. Its terminal voltage when a
current of 50 A is being drawn is,
1) 120 V 2) 70 V 3) 115 V 4) 5 V
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Sri Chaitanya IIT Academy, India JEE-MAIN_ONLINE P5_Prepared by CBSE BOARD21. A coil of self inductance L is connected at one end of two rails as shown in
figure. A connector of length l, mass m can slide freely over the two
parallel rails. The entire set up is placed in a magnetic field of induction B
going into the page. At an instant t = 0 an initial velocity 0 is imparted to
it and as a result of that it starts moving along x axis. The displacement of
the connector is represented by the figure.
1) 2)
3) 4)
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Sri Chaitanya IIT Academy, India JEE-MAIN_ONLINE P5_Prepared by CBSE BOARD22. An electromagnetic wave with frequency and wavelength travels in
the +y direction. Its magnetic field is along +x axis. The vector equation
for the associated electric field (of amplitude 0 E ) is
1) ˆ 0
2πE = E cos ωt - y zλ 2) ˆ
0
2πE = E cos ωt y zλ
3) ˆ 0
2πE = E cos ωt - y x
λ 4) ˆ
02π
E = E cos ωt y xλ
23. A glass prism of refractive index 1.5 is immersed in water (refractiveindex 4/3) as shown in the figure. A light beam incident normally on theface AB is totally reflected to reach the face BC, if
1) sin θ > 8 / 9 2) 2 3sin θ > / 3) 5 9sin θ > / 4) 1 3sin θ > /
24. Two coherent plane light waves of equal amplitude make a small angle
1 with each other. They fall almost normally on a screen. If is
the wavelength of light waves, the fringe width x of interference
patterns of the two sets of waves on the screen is:
1) λ / α 2) λ / 2α 3) 2λ / α 4) λ α
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Sri Chaitanya IIT Academy, India JEE-MAIN_ONLINE P5_Prepared by CBSE BOARD25. This question has Statement 1, Statement 2, of the four choices given after
the Statement, choose the one that best describes the two statements.
Statement 1: A metallic surface is irradiated by a monochromatic light of
frequency 0v v (the threshold frequency). If the incident frequency is
now doubled, the photocurrent and the maximum kinetic energy are also
doubled.
Statement 2: The maximum kinetic energy of photoelectrons emitted
from a surface is linearly dependent on the frequency of the incident
light. The photocurrent depends only on the intensity of the incident light.
1) Statement 1 is true, Statement 2 is false.
2) Statement 1 is true, Statement 2 is true. Statement 2 is the correct
explanation of Statement 1.
3) Statement 1 is true, Statement 2 is true. Statement 2 is not the correctexplanation of Statement 1.
4) Statement 1 is false, Statement 2 is true.
26. The decay constants of a radioactive substance for and emission are
and respectively. If the substance emits and simultaneously,
then the average half life of the material will be.
1) α β1 T + T2 2) α βT + T 3)α β
α β
T T
T + T 4)
2 α β
α β
T T
T + T
27. Ionisation energy of Li (Lithium) atom in ground state is 5.4 eV. Binding
energy of an electron in Li ion in ground state is 75.6 eV. Energy
required to remove all three electrons of Lithium (Li) atom is
1) 81.0 eV 2) 156.6 eV 3) 203.4 eV 4) 135.4 eV
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Sri Chaitanya IIT Academy, India JEE-MAIN_ONLINE P5_Prepared by CBSE BOARD28. Which one of the following is the Boolean expression for NOR Gate?
1) Y = A . B 2) Y = A + B 3) Y = A 4) Y = A . B
29. Given the electric field of a complete amplitude modulated wave as
ˆ 1 cos cos m c m c c
E E iE t t
E
Where the subscript c stands for the carrier wave and m for the
modulating signal. The frequencies present in the modulated wave are
1) c mω and ω 2)2 2
c c mω and ω + ω
3) c c mω and ω ω 4) c c m c mω , ω + ω ,ω - ω
30. N divisions on the main scale of a vernier calipers coincide with (N+1)
divisions of the vernier, scale. If each division of main scale is ‘a’ units,
then the least count of the instrument is
1)a
N + 1 2) a 3)
N×a
N + 1 4)
aN
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Sri Chaitanya IIT Academy, India JEE-MAIN_ONLINE P5_Prepared by CBSE BOARDCHEMISTRY
1. When 2CO g is passes over red hot coke it partially gets reduced to
CO(g). upon passing 0.5 litre of 2CO g over red hot coke, the total
volume of the gases increased to 700 mL. the composition of the gaseousmixture at STP is:
1) 2CO = 200mL;CO = 500mL
2) 2CO = 350mL;CO = 350mL
3) 2CO = 300mL;CO = 400mL
4) 2CO = 0.0mL;CO = 700mL
2. An open vessel at 300 K is heated till 2/5 th of the air in it is expelled.
Assuming that the volume of the vessel remains constant, the temperature
to which vessel is heated, is:
1) 400 K 2) 750 K 3) 1500 K 4) 500 K
3. Ammonium chloride crystallizes in a body centred cubic lattice with edge
length of unit cell of 390 pm. If the size of chloride ion is 180 pm, the zie
of ammonium ion would be:
1) 158 pm 2) 142 pm 3) 126 pm 4) 174 pm
4. If the kinetic energy of an electron is increased four times, the wavelength
of the de-Broglie wave associated with it would become:
1) Half 2) One fourth 3) Two times 4) Four times
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Sri Chaitanya IIT Academy, India JEE-MAIN_ONLINE P5_Prepared by CBSE BOARD5. The compound of Xenon with zero dipole moment is :
1) 4XeOF 2) 2XeO 3) 3XeO 4) 4XeF
6. The enthalpy of neutralization of 4NH OH with HCl is151.46 kJ mol
and the enthalpy of neutralization of NaOH with HCl is 155.90 kJ mol .
The enthalpy of ionization of 4 NH OH is :
1) 14.44 kJ mol 2) 14.44 kJ mol
3)1
107.36 kJ mol 4)1
107.36 kJ mol
7. Liquids A and B form an ideal solution. At 030 C , the total vapour
pressure of a solution containing 1 mol of A and 2 mols of B is 250 mm
Hg. The total vapour pressure becomes 300 mm Hg when 1 more mol of
A is added to the first solution. The vapour pressures of pure A and B atthe same temperature
1) 450, 150 mm Hg 2) 150, 450 mm Hg
3) 250, 300 mm Hg 4) 125, 150 mm Hg
8. The value of Kp for the equilibrium reaction 2 4 22 N O g NO g is 2.
Is percentage dissociation of 2 4 N O g at a pressure of 0.5 atm is :
1) 71 2) 25 3) 50 4) 88
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Sri Chaitanya IIT Academy, India JEE-MAIN_ONLINE P5_Prepared by CBSE BOARD9. If sp K of 2CaF at
025 C is 101.7 10 , the combination amongst the
following which gives a precipitate of 2CaF is :
1) 3 2 51 10 and 1 10 M Ca M F
2) 4 2 41 10 and 1 10 M Ca M F
3) 2 2 31 10 and 1 10 M Ca M F
4) 2 2 51 10 and 1 10 M Ca M F
10. The standard potentials of 2 22 / , / 2 , / Ag Ag Hg Hg Cu Cu and
2
/ Mg Mg electrodes are 0.80, 0.79, 0.34 and –2.37 V, respectively. Anaqueous solution which contains one mole per litre of the salts of each of
the four metals is electrolyzed. With increasing voltage, the correct
sequence of deposition of the metals at the cathode is:
1) Mg, Cu, Hg, Ag 2) Ag, Hg, Cu, Mg
3) Ag, Hg, Cu only 4) Cu, Hg, Ag only
11. For a reaction A Products, a plot of 12
log t versus 0log a is shown in the
figure. If the initial concentration of A is represented by 0 a , the order ofthe reaction is:
1) One 2) Two 3) Three 4) Zero
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Sri Chaitanya IIT Academy, India JEE-MAIN_ONLINE P5_Prepared by CBSE BOARD12. On addition of 1 mL of 10% NaCl solution to 10 mL gold sol in the
presence of 0.025 g of starch, the coagulation is just prevented. Starch
has gold number :
1) 0.025 2) 0.25 3) 2.5 4) 25
13. Which pair of elements with the given atomic numbers is expected to
have similar properties?
1) 11, 12 2) 20, 36 3) 40, 72 4) 10, 28
14. Extraction of zinc from zinc blende is achieved by
1) roasting followed by self-reduction
2) electrolytic reduction
3) roasting followed by reduction with another metal
4) roasting followed by reduction with carbon
15. Square-planar geometry is shown by:
1)2
4 NiCl
2) 4 MnO 3)24CrO 4) 2 3 2 PtCl NH
16. Which one of the following will react most vigorously with water?
1) Li 2) K 3) Na 4) Rb
17. Which of the following has the square planar structure?
1) 4 NH 2) 4CCl 3) 4 XeF 4) 4 BF
18. Which of the following paramagnetic ions would exhibit a magnetic
moment (spin only) of the order of 5 BM?
(At Nos. Mn = 25, Cr = 24, V = 23, Ti = 22)
1) 2 n M 2) 2Cr 3) 2V 4) 2Ti
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Sri Chaitanya IIT Academy, India JEE-MAIN_ONLINE P5_Prepared by CBSE BOARD19. The correct order of ligands in the Spectrochemical series is :
1) CN en NCS Cl 2) NCS CN Cl en
3) en CN Cl NCS 4) Cl en CN NCS
20. Fog is a colloidal solution of :
1) liquid particles dispersed in gas
2) gaseous particles dispersed in a liquid
3) solid particles dispersed in a liquid
4) slid particles dispersed in gas
21. Among the following the molecule with the lowest dipole moment is :
1) 3CH Cl 2) 2 2CH Cl 3) 3CHCl 4) 4CCl
22. The IUPAC name of the following compound is :
1) (E) – 5 – hepten – 3- yne 2) (Z) – 5 – hepten – 3- yne
3) (E) – 2 – hepten – 3- yne 4) (Z) – 2 – hepten – 3- yne
23. The major product obtained in the photobromination of 2-methyl butane
is:
1) 1 – bromo – 2 – methylbutane
2) 1 – bromo – 3 – methylbutane
3) 2 – bromo – 3 – methylbutane
4) 2 – bromo – 2 – methylbutane
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Sri Chaitanya IIT Academy, India JEE-MAIN_ONLINE P5_Prepared by CBSE BOARD24. The product of the reaction between ethyl benzene and N-bromo
succinamide is:
1) 2)
3) 4)
25. Reagent used to convert allyl alcohol to acrolein is:
1) 4 KMnO 2) 2 2 H O 3) 2 MnO 4) 4OsO
26. The order of basicity of the compounds:
Is :
1) I >III > II > IV 2) IV > I > III > II
3) III > I > IV > II 4) II > I > III > IV
27. Which of the following is a polyamide:
1) Nylon 2) Orlon 3) Teflon 4) Terylene
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Sri Chaitanya IIT Academy, India JEE-MAIN_ONLINE P5_Prepared by CBSE BOARD28. Which of the following is a non-reducing sugar?
1) Sucrose 2) Lactose 3) Fructose 4) Maltose
29. Aspirin can be prepared by the reaction of:
1) Salocylic acid with Acetic anhydride in presence of 2 4 H SO
2) Salocylic acid with methanol in presence of 2 4 H SO
3) Salicylic acid with acetic anhydride in presence of 2 4 H SO
4) Cinnamic acid with acetic anhydride in presence of 2 4 H SO
30. Beilstein test is used for the estimation of which one of following
elements?
1) N 2) Cl 3) S 4) C and H
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Sri Chaitanya IIT Academy, India JEE-MAIN_ONLINE P5_Prepared by CBSE BOARDMATHEMATICS
1. If P(s) denotes the set of all subsets of a given set S, then the number of
one – to – one functions from the set 1,2,3S to the set P(S) is :
1) 8 2) 24 3) 320 4) 336
2. Let Z and W be complex numbers such that Z W , and arg Z denote
the principal argument of Z.
Statement 1: If arg arg Z W , then Z W
Statement 2: Z W implies arg arg Z W .
1. Statement 1 is true, Statement 2 is true; Statement 2 is a correct
explanation for Statement 1.
2. Statement 1 is true, Statement 2 is true; Statement 2 is not a correct
explanation for Statement 1.
3. Statement 1 is true, Statement 2 is false
4. Statement 1 is false, Statement 2 is true
3. Let , , p q r R and r>p>0. If the quadratic equation 2 0 px qx r has
tow complex roots and , then is :
1) equal to 1.
2) equal to 23) less than 2 but not equal to 1
4) greater than 2
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Sri Chaitanya IIT Academy, India JEE-MAIN_ONLINE P5_Prepared by CBSE BOARD4. If a,b,c are non zero complex numbers satisfying 2 2 2 0 a b c and
2 2
2 2 2 2 2
2 2
b c ab ac
ab c a bc ka b c
ac bc a b
, then k is equal to:
1) 1 2) 2 3) 3 4) 4
5. If T A denotes the transpose of the matrix
0 0
0
a
A b c
d e f
, where a, b, c, d
e and f are integers such that 0 abd , then the number of such matrices
for which1 T
A A is :
1) 3 2! 2) 32 3) 23 4) 2 3!
6. The number of arrangements that can be formed from the letters a,b, c,
d, e, f, taken 3 at a time without repetition and each arrangement
containing at least one vowel, is:
1) 24 2) 72 3) 96 4) 128
7. If 2 m n C , then the value of 2
n C is given by:
1) 1 4 m C 2)1
4 m C 3)2
42 m C 4) 1 43
m C
8. Suppose and 0 are such that sec , sec and sec are
in A.P. if cos cos 2 k
for some k, then k is equal to:
1) 12
2) 1 3) 2 4) 2
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Sri Chaitanya IIT Academy, India JEE-MAIN_ONLINE P5_Prepared by CBSE BOARD
9. The sum of the series4 10 28
1 ______3 9 27
upto n terms is :
1) 11 13 3.2 n
n 2) 11 12 2.3 n
n
3) 17 1 16 6 3.2 n
n 4) 15 7 13 6 2.3 n
n
10. Let : 1, 3 f R be a function satisfying 6 x
f x x x
, for all
2 x and 2 1 f , where R is the set of all real numbers and [x] denotes
the largest integer less than or equal to x.
Statement 1 :2
lim x
f x exists
Statement 2: f is continuous at x = 2.
1) Statement 1 is true, Statement 2 is true; Statement 2 is a correct
explanation for Statement 1
2) Statement 1 is true, Statement 2 is true; Statement 2 is not a correctexplanation for Statement 1
3) Statement 1 is true, Statement 2 is false
4) Statement 1 is false, Statement 2 is true
11. If 10 8 6 3 23 7 5 21 3 7 f x x x x x x , then 301 1
lim3
f f
is :
1)553
2)533
3)533
4)553
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Sri Chaitanya IIT Academy, India JEE-MAIN_ONLINE P5_Prepared by CBSE BOARD12. Consider a quadratic equation 2 0 ax bx c , where 2 3 6 0 a b c
and let2 2
3 2 x x
g x a b cx .
Statement 1: The quadratic equation has at least one root in the internal
(0, 1).
Statement 2: The Rolle’s Theorem is applicable to function g(x) on the
interval [0, 1].
1) Statement 1 is true, Statement 2 is true; Statement 2 is a correct
explanation for Statement 1
2) Statement 1 is true, Statement 2 is true; Statement 2 is not a correctexplanation for Statement 1
3) Statement 1 is true, Statement 2 is false
4) Statement 1 is false, Statement 2 is true
13. The weight W of a certain stock of fish is given by W n , where n is thesize of stock and w is the average weight of a fish. If n and w change with
time t as2
2 3 n t and2
2w t t , then the rate of change of W withrespect to t at 1 t is:1) 1 2) 5 3) 8 4) 13
14. The general solution of the differential equation 22 dy
y x dx x
, is :
1)3
2
5 x
y cx 2)3
2
5 x
y cx
3)2
3
4 x
y cx 4)2
3
4 x
y cx
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Sri Chaitanya IIT Academy, India JEE-MAIN_ONLINE P5_Prepared by CBSE BOARD
15. If2 2
22
sinsec
1 x x
f x xdx x
and 0 0 f , then f(1) equals:
1) 14
2)4
3) tan14
4) tan1 1
16. the value of the integral0.9
0[ 2[ ] x x dx , where [.] denotes the greatest
integer function, is:
1) 0 2) 0.9 3) 1.8 4) –0.9
17. The area of the region bounded by the curve 3 y x , and the lines, 8 y
and 0 x is :1) 8 2) 10 3) 12 4) 16
18. A value of 1 12
tan sin cos3
is :
1) 2 2) 3 3) 6 4) 4
19. If 0 a b c
, 3, 5 a b and 7 c , then the angle between a and b
is :
1)6
2)4
3)3
4)2
20. If ˆ ˆ ˆ ˆ ˆ ˆ2 3 , 2 3 a i j k b i j k
and ˆ ˆ ˆ2 1 c ri j r k are three
vectors such that c is parallel to the plane of a and b
, then r is equal to:1) –1 2) 0 3) 0 4) 2
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Sri Chaitanya IIT Academy, India JEE-MAIN_ONLINE P5_Prepared by CBSE BOARD21. Let p and q be two statements. Amongst the following, the statement that
is equivalent to p q is :
1) ~ P q 2) ~ p q 3) ~ p q 4) ~ p q
22. statement 1 : The shortest distance between the lines2 1 2 x y z and
1 1 14 2 4
x y z is 2
Statement 2 : The shortest distance between two parallel lines is the
perpendicular distance from any point on one of the lines to the other
line.1) Statement 1 is true, Statement 2 is true; Statement 2 is a correct
explanation for Statement 1.
2) Statement 1 is true, Statement 2 is true; Statement 2 is not a correct
explanation for Statement 1.
3) Statement 1 is true, Statement 2 is false4) Statement 1 is false, Statement 2 is true
23. If the three planes 5,2 5 3 2 0 x x ay z and 3 3 0 bx y z contain
a common line, then (a, b) is equal to :
1)8 1
,15 5
2)8 1
,15 5
3)1 8
,5 15
4)1 8
,5 15
24. If six students, including two particular students A and B stand in a row,
then the probability that A and B are separated with one student in
between them is:
1) 1/5 2) 2/15 3) 4/15 4) 8/15
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Sri Chaitanya IIT Academy, India JEE-MAIN_ONLINE P5_Prepared by CBSE BOARD25. The median of 100 observations grouped in classes of equal width is 25. If
the median class interval is 20 – 30 and the number of observations less
than 20 is 45, then the frequency of median class is:
1) 10 2) 12 3) 15 4) 20
26. If the foci of the ellipse2 2
2 116 x y
b coinside with the foci of the hyperbola
2 2
1144 81 25 x y , then 2 b is equal to:
1) 10 2) 9 3) 8 4) 7
27. The equation of the normal to the parabola, v at 4 x is :
1) 2 0 x y 2) 2 0 x y 3) 2 x y 4) 6 x y
28. If the line 1 y mx meets the circle 2 2 3 0 x y x in two points
equidistant from and on opposite sides of x-axis, then:
1) 2 3 0 m 2) 2 3 0 m 3) 3 2 0 m 4) 3 2 0 m
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Sri Chaitanya IIT Academy, India JEE-MAIN_ONLINE P5_Prepared by CBSE BOARD29. Let L be the line 2 y x , in the two dimensional plane.
Statement 1: The image of the point (0, 1) in L is the point4 3
,5 5
Statement 2: the points (0,1) and 4 3,5 5 lie on opposite sides of the line L
and are at equal distance from it.
1) Statement 1 is true, Statement 2 is true; Statement 2 is a correct
explanation for Statement 1.
2) Statement 1 is true, Statement 2 is true; Statement 2 is not a correct
explanation for Statement 1.
3) Statement 1 is true, Statement 2 is false
4) Statement 1 is false, Statement 2 is true
30. If three distinct points A, B, C are given in the 2-dimensional coordinate
plane such that the ratio of the distance of each one of them from the
point (1, 0) to the distance from (–1, 0) is equal to12
, then the
circumcentre of the triangle ABC is at the point:
1) 0,0 2)1
,03
3) 3, 0 4)5
,03