Sample JEE Main Full Mock Test
90 Questions MCQ Test TEST | Sample JEE Main Full Mock Test
The most stable measure of central tendency is
Mean is the most frequently used measure of central tendency and generally considered the best measure of it. However, there are some situations where either median or mode are preferred. Median is the preferred measure of central tendency when: There are a few extreme scores in the distribution of the data.
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.
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.
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
Volume of 8 small drops = Volume of big drop
As capacity is r, hence capacity becomes 2 times.
If the body is moving in a circle of radius r with a constant speed υ, its angular velocity is
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 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
The magnetic moment of a circular coil carrying current is
u = NiA
Area is proportional to square of length. Hence B is correct.
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
The expressions in Assertion(A) and Reason(R) are not clear. The operation between the terms is not given.
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 24th division of the Vernier scale exactly coincides with one of the main scale divisions. The diameter of the cylinder is
The natural frequency of a L-C circuit is equal to
It means that the inductive & capacitive reactances are equal.
Value of inductive reactance is given by–
X(L)=2Ï€fL
And that of capacitive reactance is given by–
X(C)=1/(2Ï€fC)
Therefore, at resonance–
2Ï€fL=1/(2Ï€fC)
f²=1/[(2πC)×(2πL)]
f²=1/(4π²LC)
f=1/[2π√(LC)] => Resonant Frequency f(R) or f(0)
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
Proton and α-particles have the same de-Broglie wavelength. What is the same for both of them ?
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
The angular velocity of the second needle in watch (in rad/s) is
The energy released in a typical nuclear fusion reaction is approximately
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 straight wire of length l and electric dipole moment p is bent to form a semicircle. The new dipole moment would be
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
Friction = (0.5)mg = 50 N
Net force in horizontal dirn = 100 N - 50 N = 50N
acceleration= 50/10 = 5 m/s2
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
When the bird flies, it pushes air down to balance its weight. So the weight of the bird and closed cage assembly remains unchanged.
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
NAND gate is
Which of the following is more effective in inducing nuclear fission
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
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
If a liquid does not wet the glass, then its angle of contact is
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.
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
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
Two identical masses of 5 kg each fall on a wheel from a height of 10 m . The wheel disturbs a mass of 22 kg water, the rise in temperature of water will be :-
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
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
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,
Dimension of CR are same as
Both light and sound waves produce diffraction. It is more difficult to observe the diffraction with light waves because
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
In Huygens wave theory, the locus of all points osculating in the same phase is called a
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.
The alcohol which does not give a stable compound on dehydration is
If you take out H2O from the Methyl Alcohol you will be left with CH2+ cation which is not stable.
Vanaspati ghee is prepared by which of the following reactions of vegetable oils?
Cinnamic acid is formed when C₆H₅CHO condenses with (CH₃CO)₂ in presence of
According to Le-Chatelier's principle, adding heat to a solid and liquid in equilibrium will cause the
A catalyst increases rate of reaction by
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
Electron affinity depends on
As the size of the atom increases, the electron affinity decreases, whereas when the nuclear charge increases the electron affinity increases.
In the diazotisation of aniline with sodium nitrite and hydrochloric acid, the excess of hydrochloric acid is used primarily to
An excess of HCl will suppress the hydrolysis of diazonium salt to phenol.
The type of isomerism present in nitropentaamminechromium (III) chloride is
On passing 0.1 faraday of electricity through fused sodium chloride, the amount of chloride liberated is (At. mass of Cl = 35.45)
In which of the following acid-base titration, pH is greater at eqivalence point?
Why are strong acids generally used as standard solutions in acid-base titrations ?
The electrolysis of aqueous NaCl produces at cathode and anode respectively
If H⁺ ion conc. of a solution is increased by 10 times, its pH will
If its concentration is increased 10 times its
pH = - log (10) = -1.
so it decreases by 1.
So, correct answer is C
When NaCl is added to the reaction mixture of an oil and caustic soda , the soap is thrown out because
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.
Increasing order of pka values (pKa = - log ka ) of H2O , C H3OH and C6H5OH is :
Option d is correct. Methanol is more acidic than water. So its pka value will be less than water. However C5H5OH wll be most acidic among all three.SO he order of pka is C6H5OH < CH3OH < H2O
The compound which can form intramolecular hydrogen bond is
Which one is a polymer compound?
Pvc is polymer compound and many other compound that made plastic are called polymer compound while pvc is present in plastic bottle.
Ionic solids with Schottky defects contain in their structure
Diamond is a
If 107 g of an aqueous solution contains 39.5 g of a solute (mol. weight = 158), then mole fraction of the solute is
Which of the following compound corresponds Vant's Hoff factor (i) to be equal to 2 in a dilute solution?
This is because, it will dissociate into Mg2+ and SO42-, i.e. two ions.
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
Ethyl bromide on treatment with alcoholic KOH gives
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?
Let the number of photons required be n
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 __
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
Which of the following is correct relation of first law of thermodynamics ?
An activated complex molecule differs from a normal molecule of the same atomicity in that it has__
Which of the following ions has zero crystal field stabilization energy in octahedral field?
An organic compound with C = 40% and H = 6.7% will have the empirical formula
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
For which one of the following values of k, the equation
2x3 + 3x2 − 12x − k = 0 has three distinct real roots?
If xh yk 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
Let A be the square of natural numbers and x, y are any two elements of A. Then
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.
If 'n' is a positive integer, then n3 + 2n is divisible by
The area enclosed between the parabola y2 = 4ax and the lines x = a, x = 9a is
Area of the curve x2+y2=2ax is
It is a circle whose equation is (x-a)2+y2=a2
with radius a. So area of such a circle is πa2
The equation of the circle passing through (0,0),(0,a),(a,0) is
If the imaginary part of [(2z+1)/(iz+1)] is -2, then the locus of z in complex plane represent.
[(1 + sinθ + icosθ)/(1 +sinθ - icosθ)]n =
(d/dx){log(secx+tanx)}=
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
Solution of the differential equation tan y sec2 x dx + tan x sec2 y dy = 0 is
If f (x) = 
, then f of f(x) =
When y = 3, which of the following is FALSE?
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
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
The line y=mx+c touches the parabola x2=4ay if
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).
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
5! - 2×4! =72
Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?
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)}
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
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
The length of the sub normal to the parabola y2=4ax at any point is equal to
The locus of x2+y2+z2=0 is
cos2α+cos2(α+120º)+cos2(α-120º)=
If 
, then the angle between the vectors a → + b → and a → − b →
is
The points with position vectors 
are collinear. The value of p is
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
If A is a singular matrix, then A adj (A)
If f(x)=x5-5x4+5x3-10 how local max and min at x=p and x=q respectively, then (p,q)=
Let α,β be the roots of x2-x+p=0 and γ,δ be the roots of x2-4x+q=0. If α,β,γ,δ are in G.P., then the integer values of p and q respectivley are :
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