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Sample JEE Main Full Mock Test

90 Questions MCQ Test TEST | Sample JEE Main Full Mock Test

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This mock test of Sample JEE Main Full Mock Test for JEE helps you for every JEE entrance exam. This contains 90 Multiple Choice Questions for JEE Sample JEE Main Full Mock Test (mcq) to study with solutions a complete question bank. The solved questions answers in this Sample JEE Main Full Mock Test quiz give you a good mix of easy questions and tough questions. JEE students definitely take this Sample JEE Main Full Mock Test exercise for a better result in the exam. You can find other Sample JEE Main Full Mock Test extra questions, long questions & short questions for JEE on EduRev as well by searching above.

QUESTION: 1

The transition from the state n = 3 to n=1 in a hydrogen-like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition from.

A.
2 → 1
B.
3 → 2
C.
4 → 2
D.
4 →3

Solution:

Infrared radiation is found in Paschen, Brackett and pfund series nd it is obtained when electron transition occurs from high energy level to minimum third level.

QUESTION: 2

Eight drops of mercury of equal radii possessing equal charges combine to form a big drop. Then the capacitance of bigger drop compared to each individual small drop is

A.
8 times
B.
4 times
C.
2 times
D.
32 times

Solution:

Volume of 8 small drops = Volume of big dropAs capacity is r, hence capacity becomes 2 times.

QUESTION: 3

If the body is moving in a circle of radius r with a constant speed υ, its angular velocity is

A.
v²/r
B.
vr
C.
v/r
D.
r/v

Solution: In circular motion, angular velocity (w)= v( linear velocity) / radius if circle (r)

QUESTION: 4

To convert a 800 mV range milli voltmeter of resistance 40 Ω into a galvanometer of 100 mA range, the resistance to be connected as shunt is

A.
10 Ω
B.
20 Ω
C.
30 Ω
D.
40 Ω

Solution:

QUESTION: 5

A point charge q is placed at the centre of a skeleton cube made of thin non-conducting wire. The electric flux passing through one face of the cube is

A.
q ∕ 6 ε₀
B.
q ∕ 24 ε₀
C.
q ∕ 8 ε₀
D.
q ∕ 8 π ε

Solution: Because total flux coming out from a closed body is q/ě. So flux through 1 face is 1/6th of it.

QUESTION: 6

The magnetic moment of a circular coil carrying current is

A.
directly propotional to the length of the wire in the coil
B.
directly propotional to the square of the length of the wire in the coil
C.
inversely propotional to the length of the wire in th ecoil
D.
inversely propotional to the square of the length of the wire in the coil

Solution:

QUESTION: 7

In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-
Assertion(A): a + i b c + i d = p where p > 0 , then a² + b² c² + d² = p² c
Reason(R) : cos θ + i sin θ n = cos n θ + i sin n θ

A.
Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
B.
Both Assertion and Reason are true and Reason is not the correct explanation of Assertion.
C.
Assertion is true but Reason is false.
D.
Assertion is false but Reason is true.

Solution:

The expressions in Assertion(A) and Reason(R) are not clear. The operation between the terms is not given.

QUESTION: 8

The diameter of a cylinder is measured using a Vernier callipers with no zero error. It is found that the zero of the Vernier scale lies between 5.10 cm and 5.15 cm of the main scale. The Vernier scale has 50 divisions equivalent to 2.45 cm. The 24^th division of the Vernier scale exactly coincides with one of the main scale divisions. The diameter of the cylinder is

A.
5.112 cm
B.
5.124 cm
C.
5.136 cm
D.
5.148 cm

Solution:

QUESTION: 9

The natural frequency of a L-C circuit is equal to

A.
1/2π √C
B.
1/2π√LC
C.
1/2π √L/C
D.
1/2π √C/L

Solution: At resonance, X(L)=X(C)
It means that the inductive & capacitive reactances are equal.

Value of inductive reactance is given by–
X(L)=2πfL
And that of capacitive reactance is given by–
X(C)=1/(2πfC)

Therefore, at resonance–

2πfL=1/(2πfC)

f²=1/[(2πC)×(2πL)]

f²=1/(4π²LC)

f=1/[2π√(LC)] => Resonant Frequency f(R) or f(0)

QUESTION: 10

A coil of inductance 40 henry is connected in series with a resistance of 8 ohm and the combination is joined to the terminals of a 2 volt battery. The time constant of the circuit is

A.
40 seconds
B.
20 seconds
C.
8 seconds
D.
5 seconds

Solution:

Time constant in in RL circuit is t = L/R

L = 40 henry

R = 8 ohm

t = L/R = 40/8 = 5 second

It is the time in which the current in RL circuit grows to 63.2 % of its peak value.

QUESTION: 11

Proton and α-particles have the same de-Broglie wavelength. What is the same for both of them ?

A.
Time period
B.
Energy
C.
Frequency
D.
Momentum

Solution: De brogile wavelength has formula lambda =h/MV. h is Planck's constant. If they have same de brogile wavelength then they have same m.v as h is constant.

QUESTION: 12

After an interval of one day, 1/16th of the initial amount of a radioactive material remains in a sample. It's half life will be

A.
2 hour
B.
3 hour
C.
6 hour
D.
12 hour

Solution: If 1/16 of the initial material is left after a day or 24 hours means it has gone through 4 half lives. So the answer will be 24/4 = 6 hours.

QUESTION: 13

The angular velocity of the second needle in watch (in rad/s) is

A.
π/30
B.
2π
C.
π
D.
60/π

Solution:

The seconds hand of a clock completes one rotation in 1 minute i.e 60 seconds.

Angular speed=angle swept by the radius vector/time taken

Angle swept for one complete rotation is 2π radians

Therefore, 2π/60=π/302π/60=π/30

QUESTION: 14

The energy released in a typical nuclear fusion reaction is approximately

A.
25 Me V
B.
200 Me V
C.
800 Me V
D.
1050 Me V

Solution:

QUESTION: 15

Two infinite plane parallel sheets, separated by a distance d have equal and opposite uniform charge densities σ. Electric field at a point between the sheets is

A.
Depends upon location of the point
B.
σ/2∈₀
C.
σ/∈₀
D.
Zero

Solution:

QUESTION: 16

A straight wire of length l and electric dipole moment p is bent to form a semicircle. The new dipole moment would be

A.
p/2
B.
2p/π
C.
p/2π
D.
2p

Solution:

QUESTION: 17

A block of mass 10 kg is placed on rough horizontal surface whose coefficient of friction is 0.5. If a horizontal force of 100 N is applied on it, then acceleration of block will be

A.
10 m/s²
B.
5 m/s²
C.
15 m/s²
D.
0.5 m/s²

Solution:

Friction = (0.5)mg = 50 N
Net force in horizontal dirn = 100 N - 50 N = 50N
acceleration= 50/10 = 5 m/s²

QUESTION: 18

A bird weighs 2 kg and is inside a closed cage of 1 kg. If it starts flying, then what is the weight of the bird and cage assembly

A.
1.5 kg
B.
2.5 kg
C.
3 kg
D.
4 kg

Solution:

When the bird flies, it pushes air down to balance its weight. So the weight of the bird and closed cage assembly remains unchanged.

QUESTION: 19

A particle of mass M and charge Q moving with velocity V → describes a circular path of radius R when subjected to a uniform transverse magnetic field of induction B. The work done by the field when the particle completes one full circle is

A.
B.
zero
C.
B Q . 2 π R
D.
B Q v . 2 π R

Solution:

When particle describes circular path in a magnetic field, its velocity is always perpendicular to the magnetic force?

Hence, work done W = 0 (everywhere)

QUESTION: 20

NAND gate is

A.
a basic gate
B.
not a universal gate
C.
a basic universal gate
D.
a universal gate

Solution:

QUESTION: 21

Which of the following is more effective in inducing nuclear fission

A.
Fast neutron
B.
Fast proton
C.
Slow proton
D.
Slow neutron

Solution:

QUESTION: 22

The kinetic energy k of a particle moving along a circle of radius R depends on the distance covered s as K = as² where a is a constant. The force acting on the particle is

A.
2a s²/R
B.
2as (1 + s²/R²)^1∕2
C.
2as
D.
2a R²/s

Solution:

Given K.E = 1/2 mv² = as²

= mv² = 2as²

now differenciating with respect to t

2mv = dv/dt = 4as ds/dt = 4asv

mat = 2 as

Hence Ft = 2 as here (Ft = tangential force) .... 1>

centripetal force = Fc = mac = mv^2/R = 2 mas^2/ mR = 2as^2/R .... 2>

now net force of particle is = √Ft^2 + F^2 c = √(2as)^2 + (2as^2/R)^2

= 2 as(√1 + s^2/R^2or 2as(1 + s^2/R^2) raise to power 1/2

QUESTION: 23

If a liquid does not wet the glass, then its angle of contact is

A.
zero
B.
acute
C.
obtuse
D.
right angle

Solution:

If a liquid does not wet the sides of containing vessel, then the value of angle of contact is obtuse i.e. greater than 90degree .e.g. mercury.

QUESTION: 24

A 1 kg stationary bomb exploded in three parts having mass ratio 1:1:3 . Parts having same mass are moving in perpendicular direction with velocity 30m/s, then the velocity of bigger part will be

A.
10 √2 m/s
B.
10/√2 m/s
C.
15 √s m/s
D.
15/s m/s

Solution:

Conservation of momentum
1×0=1 ×30i +1×30j +3v
3v= -(30i +30j)
v = -(10i +10j)
v ( magnitude)= √(10)²+(10)²
=10√2 m/s

QUESTION: 25

Of two masses of 5 kg each falling from height of 10m, by which 2 kg water is stirred. The rise in temperature of water will be

A.
2.6ºC
B.
1.2ºC
C.
0.32ºC
D.
0.12ºC

Solution:

W = J Q

2m * g* h = J * m' * Cp * Delta T

2 *5*10*10 = 4.2 *(2* 1000* delta T)

Delta T = 0.12°c

QUESTION: 26

A parallel monochromatic beam of light is incident normally on a narrow slit. A diffraction pattern is formed on a screen placed perpendicular to the direction of the incident beam. At the first minimum of the diffraction pattern, the phase difference between the rays coming from the two edges of slit is

A.
Zero
B.
π
C.
π/3
D.
2π

Solution:

The phase difference between the wavelets from the top and bottom edge of the slit=2π/λd sinθ
where d=width of slit
The first minimum of diffraction patterns occurs at,

QUESTION: 27

Dimension of CR are same as

A.
Frequency
B.
Energy
C.
Time period
D.
Current

Solution:

QUESTION: 28

Both light and sound waves produce diffraction. It is more difficult to observe the diffraction with light waves because

A.
Light wave do not require medium
B.
Wavelength of light waves is far smaller
C.
Light waves are transverse
D.
Speed of light is far greater

Solution: WAVELENGTH AND DIFFRACTION. The reason for the difference—that is, why sound diffraction is more pronounced than light diffraction—is that sound waves are much, much larger than light waves. Sound travels by longitudinal waves, or waves in which the movement of vibration is in the same direction as the wave itself.

QUESTION: 29

The velocities of sound at the same temperature in two monoatomic gases of densities ρ₁ and ρ₂ are ν₁ and ν₂ respectively. If ρ₁/ρ₂= 4, then the value of ν₁/ν₂ is

A.
1/4
B.
2
C.
1/2
D.
4

Solution:

QUESTION: 30

In Huygens wave theory, the locus of all points osculating in the same phase is called a

A.
ray
B.
vibrator
C.
wavefront
D.
half period zone

Solution:

Huygen, a Dutch mathematician, in 1678, gave a theory regarding nature of light. The theory is popularly known as Huygen’s wave theory. According to this theory, light is a sort of disturbance. The particles of the medium, vibrate in a direction, at right angle to the direction of propagation of disturbance. The process is called wave motion.

Straight wave front

Huygens's principle applied to a straight wave front. Each point on the wave front emits a semicircular wavelet that moves a distance s=vt. The new wavefront is a line tangent to the wavelets.

QUESTION: 31

The alcohol which does not give a stable compound on dehydration is

A.
Ethyl alcohol
B.
Methyl alcohol
C.
n-Propyl alcohol
D.
n-Butyl alcohol

Solution:

If you take out H₂O from the Methyl Alcohol you will be left with CH²⁺ cation which is not stable.

QUESTION: 32

Vanaspati ghee is prepared by which of the following reactions of vegetable oils?

A.
oxidation
B.
distillation
C.
hydrogenation
D.
dehydrogenation

Solution: Vanaspati ghee is made by hydrogenation of vegetable oils that is why it is considered harmful while vegetable oils are safe.

QUESTION: 33

Cinnamic acid is formed when C₆H₅CHO condenses with (CH₃CO)₂ in presence of

A.
Conc. H₂SO₄
B.
Sodium acetate
C.
Sodium metal
D.
None of these

Solution:

QUESTION: 34

According to Le-Chatelier's principle, adding heat to a solid and liquid in equilibrium will cause the

A.
temperature to increase
B.
temperature to decrease
C.
amount of liquid to decrease
D.
amount of solid to decrease

Solution:

When we add heat to the equilibrium between solid and liquid, then the equilibrium shifts towards liquid and hence, the amount of solid decrease and amount of liquid increase.

QUESTION: 35

A catalyst increases rate of reaction by

A.
decreasing enthalpy
B.
decreasing internal energy
C.
decreasing activation energy
D.
increasing activation energy

Solution: A catalyst increases the rate of reaction by decreasing the energy of activation (Ea). a catalyst provides a new reaction path for the reaction. Because a catalyst forms an unstable intermediate with the reactants and it decomposes to give products and the catalyst is regenerated.

QUESTION: 36

C + O₂ → C O₂ , Δ H = − 94 K . c a l s , → C O₂ , Δ H = − 67.7 K . cal .

On the basis of above data, the heat of formation of CO is

A.
− 26.3 K.cal
B.
+26.3 K.cal
C.
+52.6 K.cal
D.
+13.2 K.cal

Solution: Add equations 1 and (-2) and you'll see there's the formation of CO. So ∆H of formation of CO=(-94)-(-67.7)= -26.3 Kcal.

QUESTION: 37

Electron affinity depends on

A.
Atomic size
B.
Nuclear charge
C.
Atomic number
D.
Atomic size and nuclear charge both

Solution:

As the size of the atom increases, the electron affinity decreases, whereas when the nuclear charge increases the electron affinity increases.

QUESTION: 38

In the diazotisation of aniline with sodium nitrite and hydrochloric acid, the excess of hydrochloric acid is used primarily to

A.
Suppress the concentration of free aniline
B.
Suppress the hydrolysis to phenol
C.
Ensure a stochiometric amount of nitrous acid
D.
Neutralise the base liberated

Solution:

An excess of HCl will suppress the hydrolysis of diazonium salt to phenol.

QUESTION: 39

The type of isomerism present in nitropentaamminechromium (III) chloride is

A.
Optical
B.
Linkage
C.
Ionization
D.
Polymerization

Solution: Nitropentamine chromium (III) chloride exhibits linkage isomerism as -NO2 is an ambidendate ligand.

QUESTION: 40

On passing 0.1 faraday of electricity through fused sodium chloride, the amount of chloride liberated is (At. mass of Cl = 35.45)

A.
35.45 g
B.
70.9 g
C.
3.545 g
D.
17.77 g

Solution: On passing 0.1F of electricity in NaCl, the amt of chloride liberated = 35.45*0.1 = 3.545

QUESTION: 41

In which of the following acid-base titration, pH is greater at eqivalence point?

A.
acetic acid versus ammonia
B.
hydrochloric acid versus ammonia
C.
acetic acid versus sodium hydroxide
D.
hydrochloric acid versus sodium hydroxide

Solution:

QUESTION: 42

Why are strong acids generally used as standard solutions in acid-base titrations ?

A.
The pH at the equivalent point will always be 7
B.
They can be used to titrate both strong and weak bases
C.
Strong acids from more stable solutions than weak acids
D.
The salts of strong acid do not hydrolysis

Solution:

QUESTION: 43

The electrolysis of aqueous NaCl produces at cathode and anode respectively

A.
H₂ and Cl₂
B.
Na and O₂
C.
H₂ and O₂
D.
Na and Cl₂

Solution: Electrolysis of aqueous sodium chloride: Electrolysis of aqueous NaCl results in hydrogen and chloride gas. At the anode (A), chloride (Cl-) is oxidized to chlorine. The ion-selective membrane (B) allows the counterion Na+ to freely flow across, but prevents anions such as hydroxide (OH-) and chloride from diffusing across. At the cathode (C), water is reduced to hydroxide and hydrogen gas. The net process is the electrolysis of an aqueous solution of NaCl into industrially useful products sodium hydroxide (NaOH) and chlorine gas.

QUESTION: 44

If H⁺ ion conc. of a solution is increased by 10 times, its pH will

A.
increase by one
B.
remain unchanged
C.
decrease by one
D.
increase by 10

Solution: Concept: pH = -log (H+)

If its concentration is increased 10 times its
pH = - log (10) = -1.
so it decreases by 1.

So, correct answer is C

QUESTION: 45

When NaCl is added to the reaction mixture of an oil and caustic soda , the soap is thrown out because

A.
NaCl is an ionic compound
B.
Soap is insoluble in the presence of chloride ions
C.
the solubility product of NaCl decreases in the presence of soap
D.
the solubility of the soap is exceeded due to the increased concentration of Na⁺ ions

Solution:

Formation of soap involves reaction with ester and NaOH when NaCl has added it results in the increase in repulsion between the ions namely NA⁺ which shifts the reaction in the formation of soap.

QUESTION: 46

The compound which can form intramolecular hydrogen bond is

A.
m-Hydroxybenzaldehyde
B.
Benzaldehyde
C.
Salicyladehyde
D.
p-Hydroxybenzaldehyde

Solution:

QUESTION: 47

Increasing order of pk_a values (pK_a = - log k_a) of H₂O , C H₃OH and C₆H₅OH is :

A.
H₂O < CH₃OH < C₆H₅OH
B.
CH₃O H < H₂O < C₆H₅OH
C.
C₆H₅OH < CH₃OH < H₂O
D.
C₆H₅OH < H₂O < CH₃OH

Solution:

Option d is correct. Methanol is more acidic than water. So its pk_a value will be less than water. However C₅H₅OH wll be most acidic among all three.SO he order of pk_a is C₆H₅OH < CH₃OH < H₂O

QUESTION: 48

Which one is a polymer compound?

A.
SO₂
B.
CO₂
C.
CH₄
D.
PVC

Solution:

Pvc is polymer compound and many other compound that made plastic are called polymer compound while pvc is present in plastic bottle.

QUESTION: 49

Ionic solids with Schottky defects contain in their structure

A.
equal number of cation and anion vacancies
B.
interstitial anions and anion vacancies
C.
cation vacancies only
D.
cation vacancies and interstitial cations

Solution:

QUESTION: 50

Diamond is a

A.
Ionic crystal
B.
Covalent crystal
C.
Metallic crystal
D.
Molecular crystal

Solution:

QUESTION: 51

If 107 g of an aqueous solution contains 39.5 g of a solute (mol. weight = 158), then mole fraction of the solute is

A.
2.25%
B.
4.25%
C.
6.25%
D.
8.25%

Solution: First find no. of moles of solute that is 0.25(39.5/158)then moles of solvent that is 107-39.5/18 = 3.75 mole reaction of solute = no of moles of solute/total moles 0.25/4 into 100 = 6.25

QUESTION: 52

Which of the following compound corresponds Vant's Hoff factor (i) to be equal to 2 in a dilute solution?

A.
MgSO₄
B.
K₂SO₄
C.
NaHSO₄
D.
C₆H₁₂O₆

Solution:

This is because, it will dissociate into Mg²⁺ and SO4^2-, i.e. two ions.

QUESTION: 53

One mole of 1, 2-Dibromopropane on treatment with X moles of NaNH₂ followed by treatment with ethyl bromide gave a pentyne. The value of X is

A.
one
B.
two
C.
three
D.
four

Solution:

QUESTION: 54

Ethyl bromide on treatment with alcoholic KOH gives

A.
Ethylene
B.
Ethanol
C.
Acetic acid
D.
Ethane

Solution:

QUESTION: 55

If the energy of an electron in the second energy level of hydrogen atom is -E, its value in the third energy level will be __

A.
− 2E/4
B.
− 9E/4
C.
− 4E /9
D.
− 4E x 9

Solution:

According to question :
− E = -13.6 x Z² /n²
o r − 13.6 = − E x 4 (i)
Energy for third energy level:
E₃ = − 13.6 x Z² 3²
E₃ x 9 = − 13.6 i i
By (i) and (ii)
− E x 4 = E ₃ x 9
or E₃ = − 4E /9

QUESTION: 56

Suppose 10^-17 J of energy is needed by the interior of human eye of to see an object. How many photons of green light (λ = 500 nm) are needed to generate this minimum amount of energy?

A.
14
B.
28
C.
39
D.
42

Solution:

Let the number of photons required be n

QUESTION: 57

Which of the following is correct relation of first law of thermodynamics ?

A.
∆U = q+W
B.
∆U = q-W
C.
∆U =∆q =nRT
D.
All the above

Solution:

QUESTION: 58

An activated complex molecule differs from a normal molecule of the same atomicity in that it has__

A.
One vibrational degree of freedom more
B.
It has one translational degree of freedom more
C.
It has one rotational degree of freedom more
D.
It has one rotational degree of freedom less

Solution:

QUESTION: 59

Which of the following ions has zero crystal field stabilization energy in octahedral field?

A.
Cr³⁺ (High spin)
B.
Co²⁺ (Low spin)
C.
Fe³⁺ (Low spin)
D.
Fe³⁺ (High spin)

Solution:

QUESTION: 60

An organic compound with C = 40% and H = 6.7% will have the empirical formula

A.
CH₄
B.
CH₂O
C.
C₃H₆O₃
D.
C₂H₄o₂

Solution:

C is 40% and H is 6.7% so O is 53.3%
now calculate % / at. weight
c= 40/12
H=6.7/1
O=53.3/16
now get the simplest ratio as CH₂O

QUESTION: 61

For which one of the following values of k, the equation
2x³ + 3x² − 12x − k = 0 has three distinct real roots?

A.
16
B.
20
C.
26
D.
31

Solution:

QUESTION: 62

If x^h y^k is an integrating factor of the differential equation
y(1 + xy) dx + x(1 − xy) dy = 0,
then the ordered pair (h, k) is equal to

A.
(−2, −2)
B.
(−2, −1)
C.
(−1, −2)
D.
(−1, −1)

Solution:

QUESTION: 63

Let A be the square of natural numbers and x, y are any two elements of A. Then

A.
x − y ∈ A
B.
x y ∈ A
C.
x + y ∈ A
D.
none

Solution:

Because as x is a squared quantity and y is also a squared quantity so xy will also be perfect square of a number but in case of x+y and x-y it may be perfect square or not.

QUESTION: 64

If 'n' is a positive integer, then n³ + 2n is divisible by

A.
15
B.
3
C.
2
D.
6

Solution:

QUESTION: 65

The area enclosed between the parabola y² = 4ax and the lines x = a, x = 9a is

A.
8a²
B.
8a²/3
C.
208a² /3
D.
a²

Solution:

QUESTION: 66

Area of the curve x²+y²=2ax is

A.
πa²
B.
2πa²
C.
4πa²
D.
πa²/2

Solution:

It is a circle whose equation is (x-a)²+y²=a²

with radius a. So area of such a circle is πa²

QUESTION: 67

The equation of the circle passing through (0,0),(0,a),(a,0) is

A.
x²+y²+ax+ay=0
B.
x²+y²-ax-ay=0
C.
x²+y²+2ax+2ay=0
D.
None

Solution:

The general equation of circle is x^2+y^2+2gx+2fy+c=0 where center is (-g,-f)

Given the point (0,0 ) Equation of the circle through that point is c=0

Given the point (a,0).Equation of the circle through that point is a^2+2ga+c=0

⇒a^2+2ag=0

a(a+2g)=0→g=−a2⇒g=−a/2

Given the point (0,a) Equation of the circle through that point is a^2+2fa+c=0

⇒a^2+2fa=0→a(a+2f)=0→a=-2f

f=-a/2

the equation will be

x^2+y^2+2(-a/2)x+2(-a/2)y+0=0

x^2+y^2-ax-ay=0

x^2+y^2-a(x+y)=0

QUESTION: 68

If the imaginary part of [(2z+1)/(iz+1)] is -2, then the locus of z in complex plane represent.

A.
a circle
B.
a straight line
C.
parabola
D.
an ellipse

Solution:

QUESTION: 69

[(1 + sinθ + icosθ)/(1 +sinθ - icosθ)]ⁿ =

A.
cos [(nπ/2) - (nθ)] + i sin [(nπ/2) -(nθ)]
B.
cos[(nπ/2) +(nθ)] + i sin [(nπ/2) + (nθ)]
C.
sin [(nπ/2) - (nθ)] + i cos [(nπ/2) - (nθ)]
D.
cos nθ + i sin nθ

Solution:

QUESTION: 70

(d/dx){log(secx+tanx)}=

A.
cos x
B.
sec x
C.
tan x
D.
cot x

Solution:

d/dx {log Sec x + tan x}
= 1 Sec x + tan x Sec x . tan x + sec 2x
= Sec x Sec x + tan x Sec x + tan x
= Sec x

QUESTION: 71

Solution of the differential equation tan y sec² x dx + tan x sec² y dy = 0 is

A.
tan x . tan y = k
B.
tan x - tan y = K
C.
tan x/tan y = K
D.
none

Solution:

QUESTION: 72

If f (x) = , then f of f(x) =

A.
B.
C.
D.
None of these

Solution:

QUESTION: 73

When y = 3, which of the following is FALSE?

A.
y is prime and y is odd
B.
y is odd and 3y is odd
C.
y is not prime and y is odd
D.
y is odd and 2y is even

Solution:

QUESTION: 74

If A is a non-zero column matrix of order m x1 and B is a non-zero row matrix of order 1 x n, then rank of AB is equal to

A.
m
B.
n
C.
1
D.
none of these

Solution:

Let
be two non-zero column and row matrices respectively

Since A, B are non-zero matrices. .% matrix AB will be a non-zero matrix. The matrix AB will have at least one non-zero element obtained by multiplying corresponding non-zero elements of A and B. All the two rowed minors of AB clearly vanish. Since AB is non-zero matrix,
∴ rank of AB = 1

QUESTION: 75

The line y=mx+c touches the parabola x²=4ay if

A.
c=-am
B.
c=-a/m
C.
c=-am²
D.
c=a/m²

Solution:

Concept: Straight line. x²=4ay.............(1)
y=mx+c....,........(2)
From (1) and (2) we get x² = 4a(mx+c)
=> x²−4amx−4ac=0
=16a²m²+16ac(b² -4ac). =16a(am² + c ).
Line 2 will touch the parabola. if D=0. i.e if C=−am²
Hence, correct answer is (C).

QUESTION: 76

Number of ways in which 6 persons can be seated around a table so that two particular persons are never seated together is equal to

A.
480
B.
72
C.
120
D.
240

Solution:

5! - 2×4! =72

QUESTION: 77

Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?

A.
1/2
B.
3/4
C.
3/8
D.
5/16

Solution:

In a simultaneous throw of two dice, we have n(S) = (6 x 6) = 36.
Then, E = ((1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3, 4), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

QUESTION: 78

The most stable measure of central tendency is

A.
mean
B.
median
C.
mode
D.
none of these

Solution:

Mean is considered as most stable central tendency because it uses all the observation in any given distribution.

QUESTION: 79

The equation of a line passing through (-4,3) and this point divides the portion of line between axes in the ratio 5:3 internally, is

A.
9x+20y+96=0
B.
20x+9y+96=0
C.
9x-20y+96=0
D.
20x-9y-96=0

Solution:

Let the line through the point P(-A, 3) meets axis at A(h, 0) and 0(0, k)
Now according to the question AP : BP =5:3

QUESTION: 80

The length of the sub normal to the parabola y²=4ax at any point is equal to

A.
√2a
B.
2√2a
C.
a/√2
D.
2a

Solution: The length of the subnormal is always constant and is equal to the semi-latus rectum i.e. 2a …Hence D is the correct.

QUESTION: 81

The locus of x²+y²+z²=0 is

A.
(0,0,0)
B.
a sphere
C.
a circle
D.
none of these

Solution:

QUESTION: 82

cos²α+cos²(α+120º)+cos²(α-120º)=

A.
3/2
B.
1
C.
1/2
D.
0

Solution:

QUESTION: 83

If , then the angle between the vectors a → + b → and a → − b →

A.
30º
B.
60º
C.
90º
D.
0º

Solution:

QUESTION: 84

The points with position vectors are collinear. The value of p is

A.
7
B.
-37
C.
-7
D.
37

Solution:

QUESTION: 85

In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-
Assertion(A): At x = 0, the curve y = 11 + x² has the greatest slope.
Reason(R) : dy/dx = 0 and d² + yd x² < 0 at x = 0

A.
Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
B.
Both Assertion and Reason are true and Reason is not the correct explanation of Assertion.
C.
Assertion is true but Reason is false.
D.
Assertion is false but Reason is true.