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This mock test of JEE Main Mock Test 7 for JEE helps you for every JEE entrance exam.
This contains 90 Multiple Choice Questions for JEE JEE Main Mock Test 7 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

The frequency for which a 5 μF capacitor has a reactance of 1/1000 ohm is given by

Solution:
Given:C=5uf Xc=1/1000. Xc=1/wc=1/1000 ,, wc=10002Ï€f=1000/5u =200*10^6= F=100/Ï€ M Hz

QUESTION: 2

If the instantaneous current in a circuit is given by: I = 2cos(ω t + φ)A, then r.m.s. value of the current is

Solution:

QUESTION: 3

Solution:
Because these electrons are losing energy.

QUESTION: 4

In which of the following systems will the radius of the first orbit (n = 1) be minimum

Solution:

QUESTION: 5

To see first 20 lines of Balmer series distinctly, minimum resolving power of instrument should be

Solution:

QUESTION: 6

A ball weighing 10 g hits a hard surface vertically with a speed of 5 ms⁻^{1} and rebounds with the same speed. The ball remains in contact with the surface for 0.01 s. The average force exerted by the surface on the ball is

Solution:

Since, F=P/T

where, P= change in momentum and T = total time

F= ( mv1 - mv2 )/T

F= { 0.01[5-(-5)]}/0.01

F=10 N

QUESTION: 7

A dipole of dipole moment p̅ is placed in uniform electric field E̅, then torque acting on it is given by

Solution:
Torque=pÃ—E.

It is due to the reason that torque is a vector quantity .therefore we use a cross product to measure the torque acting on the body

It is due to the reason that torque is a vector quantity .therefore we use a cross product to measure the torque acting on the body

QUESTION: 8

In a certain 0.1m^{3} of space, electric potential is found to be 5*V* throughout. The electric field in this region is

Solution:
Consider there is sphere of volume 0.1m3 now since it is in space it is a hollow sphere so electric field inside it will be zero now this was the easy method u can also do it by taking a sphere and deriving values.

QUESTION: 9

A ball of mass 0.25 kg attached to the end of a string of length 1.96 m is moving in a horizontal circle. The string will break if the tension is more than 25 N. What is the maximum speed with which the ball can be moved?

Solution:

Given,

Length of String, l = 1.96m

Mass of Ball, m = 0.25 Kg

Maximum Tension of String, T_{max} = 25 N

Let the speed of the balls is v m/s

In the horizontal circular motion of the ball tension in the string is balanced by the centrifugal force (mv^{2}/l) and hence the maximum tension in the string will be for the maximum speed of the ball (since m and l are fixed)

Therefore,

Therefore, maximum speed of the ball will be 14 m/s

QUESTION: 10

A ball of mass m strikes elastically a wall at an angle of 30º with velocity ν. The change in momentum is

Solution:

QUESTION: 11

A current passing through a circular coil of two produces a magnetic field of 8 T at its centre. The coil is then rewound, so as to have four turns and current is passed through it is doubled. Now magnetic field at the centre of the coil will be

Solution:

QUESTION: 12

The following figure shows a logic gate circuit with two inputs A and B and the output C. The voltage waveforms of A, B and C are as shown below.

The logic circuit gate is

Solution:

QUESTION: 13

Sixty four spherical rain drops of equal size are falling vertically through air with a terminal velocity 1.5 m-s⁻^{1} If these drops coalesce to form a big spherical drop, then terminal velocity of big drop is

Solution:
There is a general formula for calculating the velocity of big drop which is formed by the number of smaller drops The terminal velocity of bigger drop be v' The terminal velocity of smaller drop be v The total no.of smaller drop is 64(n) v'=vÃ—n^2/3 v'=1.5Ã—(64)^2/3 v'=24m/s

QUESTION: 14

An aeroplane is flying horizontally with a velocity of 600 km/h and at a height of 1960 m. When it is vertically at a point A on the ground, a bomb is released from it. The bomb strikes the ground at point B. The distance AB is

Solution:

First resolve the motion is 2 components 1st horizontal and 2nd vertical .

1st vertical component :-

As there is no velocity in the vertical direction so in Italy velocity there will be zero but the gravitational force is acting in that direction so the accleration in the vertical direction will be g(10)m/s^2

Apply equation of motion here and u will get the time i.e about 19.79sec .

Then we have no acceleration in the horizontal direction so simply

Velocity[horizontal] =distance /time

Hence distance will be 3.3km approx

QUESTION: 15

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): When charges are shared between two bodies, there occurs loss of energy.

Reason(R): In case of sharing of charges, conservation of energy fails.

Solution:

QUESTION: 16

Number of particles emitted in the reaction is

Solution:
The mass number differs by 4 so 1 Alpha, and atomic number differs by 1 so one electron.

QUESTION: 17

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): For refraction in a plane surface v can be used for the light moving from μ_{1} to μ_{2}.

Reason(R): for light getting into a medium of index μ_{2} from μ_{1}.

Solution:

QUESTION: 18

For a gas, if the ratio of specific heats at constant pressure and volume is Î³, then the value of degree of freedom is

Solution:

QUESTION: 19

The moment of inertia of a uniform disc about an axis passing through its centre and perpendicular to its plane is 1kg - m^{2}. It is rotating with an angular velocity 100 radians/second. Another identical disc is gently placed on it so that their centres coincide. Now these two discs together continue to rotate about the same axis. Then the loss in kinetic energy in kilo joules is

Solution:

QUESTION: 20

Faraday is the unit of

Solution:

QUESTION: 21

The penetration of light into the region of geometrical shadow is called

Solution:

QUESTION: 22

Huygen's wave theory of light can not explain

Solution:

QUESTION: 23

A metal wire of linear mass density 9.8 g/m is stretched with a tension of 10 kg wt between two rigid supports 1 metre apart. The wire passes at its middle point between the poles of a permanent magnet and it vibrates in resonance when carrying an alternating current of frequency n. The frequency n of alternating source is

Solution:

The wire vibrates because of the magnetic force on it. When the alternating current completes one cycle, the wire completes one oscillation and hence the frequency of oscillation of the wir is the same as the frequency of the alternating current (n). Therefore we have

n = (1/2L)âˆš(T/m) where L is the length of the segment of the wire betweenetween the supports, T is the tension and â€˜mâ€™ is the linear density (mass per unit length) of the wire. Substituting for L, T and m we have

n = (1/2)âˆš[(10X9.8)/(9.8X10â€“3 )] = 50 Hz.

QUESTION: 24

When a star moves away from earth, the spectrum of the star shifts towards higher wavelength side. This is due to

Solution:

QUESTION: 25

Which of the following will give maximum ions in solution ?

Solution:
A) has 2 ions :- K+& (I3)- ,
b) & d) have 3 ions ,
While FeCl3 has 4 ions :- 1Fe+Â³ and 3 Cl-
So (c) has maximum number of ions

QUESTION: 26

According to the Bohr model, electrons of quantum number *n* = 4 in excited hydrogen atoms can undergo transitions to lower energy states in different ways and give rise to photons of discrete frequencies. How many discrete frequencies are possible in this case?

Solution:

QUESTION: 27

A parallel plate capacitor with air between the plates has a capacitance of 9 pF. The separation between its plates is 'd' . The space between the plates is now filled with two dielectrics. One of the dielectrics has dielectric constant K_{1} = 3 and thickness d 3 while the other one has dielectric constant K_{2} = 6 and thickness. 2d 3 Capacitance of the capacitor is now

Solution:

QUESTION: 28

The angular speed of an engine wheel making 90 revolutions per minute is

Solution:
Angular speed=2Ï€ Ã— n =2Ï€Ã—(1.5rps)=3 rad/s

QUESTION: 29

The resistivity of a wire depends on its

Solution:

QUESTION: 30

An electron moves in a circular orbit with a uniform velocity v. It produces a magentic field B at the centre of the circle. The radius of the circle is proportional to

Solution:

QUESTION: 31

Two identical conducting spheres, each of radius *R*, carry charges *+Q* and -*Q/2* respectively. When the distance between their centres is *d(d > 2R)*, the attractive force between them is *F*. The spheres are now brought into contact and then separated to the initial distance *d*. The force between the spheres is now

Solution:

QUESTION: 32

3 moles of ethanol react with one mole of phosphorus tribromide to form 3 moles of bromoethane and one mole of *X*. Which of the following is *X*?

Solution:

QUESTION: 33

When formaldehyde and KOH are heated we get,

Solution:

When formaldehyde and potassium hydroxide are heated,we get methyl alcohol and formic acid, it is cannizarroo reaction. The Cannizzaro reaction, named after its discoverer StanislaoCannizzaro, is a chemical reaction that involves the base-induced disproportionation of an aldehyde. HENCE, CORRECT OPTION IS (C).

QUESTION: 34

Oils are converted into fats by

Solution:

QUESTION: 35

An equilibrium mixture for the reaction

2A_{2}B_{(g)} ⇌ 2A_{2(g)} + B_{2(g)} had 0.5, 0.1 and 0.4 moles of A_{2}B, and A_{2} and B_{2} in a two litre vessel respectively the equilibrium constant (K) is__

Solution:

QUESTION: 36

In a reaction : A → B, the rate of reaction, increases two times, on increasing the concentration of reactants four times. Then, order of reaction is

Solution:

QUESTION: 37

Calculate the difference between the Δ E AND Δ H for the following reaction at 2º C (in *K.cal*)

Solution:

R = 2 cals/deg-mole

T = 27 º C = 27 + 273 = 300 º A

Δ n = No of moles of gaseous products - No of moles of gaseous reactants = 2-3=-1

Δ H = Δ E + Δ n R T

Δ H − Δ E = Δ n R T = − 1 x2 x300 = − 600 cals = − 0.6 K . c a l .

QUESTION: 38

Which pair of elements of atomic numbers given below will have similar chemical properties?

Solution:

In the periodic table, the elements belong to the same group have similar chemical properties. Atomic number-3 (i.e. Li ) and atomic number-11 (i.e. Na ) belong to the same group (i.e. alkali metals), thus they have similar chemical properties.

QUESTION: 39

The art of electroplating was given by

Solution:

QUESTION: 40

Which of the following is orgno-metalic compound?

Solution:

QUESTION: 41

Which of the following compound gives dye test ?

Solution:

QUESTION: 42

The electrode potentials of half-cell reactions are: Zn → Zn^{2}⁺ + 2e⁻ ; E = -0.76 V and Fe → Fe^{2⁺} + 2e⁻ ; E=0.41 V. The e.m.f. of the cell Fe^{2}⁺ + Zn → Zn^{2}⁺ + Fe is

Solution:
Emf = Ereduction of fe - Ereduction of Zn = - 0.41V - 0.76V = -1. 17 V

QUESTION: 43

When HCl gas is passed through a saturated solution of common salt, pure NaCl is precipiated because

Solution:

The increase in [Cl^-] brings in an increase in [ Na^+][Cl^-] which will lead for backward reaction because,

The increase in [Cl^-] brings in an increase in [ Na^+][Cl^-] which will lead for backward reaction because,

QUESTION: 44

Which of the following will act as Lewis base, nucleophilic reagent as well as ligand in complex compound ?

Solution:

QUESTION: 45

Sodium carbonate cannot be used in place of ammonium carbonate for the identification of the fifth group radicals . This is because the

Solution:

QUESTION: 46

Alcoholic beverages are made of

Solution:

QUESTION: 47

Nylon thread are made of

Solution:

QUESTION: 48

Which effect is not reversible?

Solution:
The inductive effect is an experimentally observed effect of the transmission of unequal sharing of the bonding electron through a chain of atoms in a molecule, leading to a permanent dipole in a bond. In short, alkyl groups tend to donate electrons, leading to the inductive effect.

QUESTION: 49

Which of the following isomers will have the highest octane number ?

Solution:

QUESTION: 50

A solid has a structure in which in which 'W' atoms are located at the corners of a cubic lattice, 'O' atoms at the centre of edges and 'Na' atoms at the centre of the cube. The formula for the compound is

Solution:

QUESTION: 51

Body-centred cubic has coordination number of

Solution:

QUESTION: 52

The lowering in vapour pressure, caused by the addition of 100 g of surcose (molecular weight = 342) in 1000 g of water, if the vapour pressure of pure water at 25ºC is 23.8 mm of Hg, is

Solution:

QUESTION: 53

A 0.6% solution of urea (molecular weight = 60) would be isotonic with

Solution:

QUESTION: 54

Propan-1-ol can be prepared from propene by

Solution:

QUESTION: 55

For a d electron,the orbital angular momentum is :

Solution:

QUESTION: 56

Which shell would be the first to have a g sub-shell?

Solution:

For g subshell, l = 4. Minimum n should be 5.

QUESTION: 57

Given : C + 2S→CS₂ ; ∆H = 117 KJ

C + O₂→CO₂; ∆H = -393 KJ

S + O₂→ ; ∆H = -297 KJ

The heat of combustion of CS₂ to form CO₂ and SO₂ is

Solution:

QUESTION: 58

The equation for an overall reaction is M+ 2N → X + Y; therefore, the rate equation for this reaction is__

Solution:

No concentrations of reactants and products are given at different intervals of time.

QUESTION: 59

The oxidation number of the central metal ion in Wilkinson's catalyst is__

Solution:

Wilkinson's catalyst is [(Ph_{3}P)_{3}RhCl]

QUESTION: 60

The Beilstein test for organic compounds is used to detect

Solution:

QUESTION: 61

The number of real solution of the equation x^{2} - 3∣x∣ 2 = 0 is :

Solution:

QUESTION: 62

If *'n'* is a positive integer, then *n*^{3} + 2*n* is divisible by

Solution:

Basis Step: If n=0, then n^3+2n=0^3+ 2*0=0. So it is divisible by 3.

Induction: Assume that for an arbitrary natural number n, n^3+2n is divisible by 3.

Induction Hypothesis: To prove this for n+1, first try to express (n+1)^3+2(n+1) in terms of n^3+2n and use the induction hypothesis. Got it

(n+1)^3+2(n+1)=(n^3+3n^2+3n+1)+(2n+2){Just some simplifying}

=(n^3+2n)+(3n^2+3n+3){simplifying and regrouping}

=(n^3+2n)+3(n^2+n+1){factored out the 3}

which is divisible by 3, because (n^3+2n) is divisible by 3 by the induction hypothesis.

QUESTION: 63

the area of the ellipse x^{2}/a^{2} + y^{2}/b^{2} = 1 is

Solution:

QUESTION: 64

The locus of the points from which the lengths of the tangents to the two circles *x ^{2} + y^{2} + 4x + 3 = 0, x^{2} + y^{2} - 6x + 5 = 0* are in the ratio 2:3 is a circle with centre

Solution:
The length of a tangent from any point (x1,y1) to a circle S=0 is âˆšS1.Let the point be (x,y).Thus According to Questionâˆšx^2+y^2+4x+3/âˆšx^2+y^2-6x+5 =2/3On solving further we get,x^2+y^2+12x+7/5=0The center of this circle is (-6,0)

QUESTION: 65

The equation of the circle described on the common chord of the circles x^{2} + y^{2-}8x + y -15 = 0 and x^{2}+ y^{2 }- 4x + 4y - 42 = 0 as diameter is

Solution:

QUESTION: 66

The locus represented by |z - 1| = |z + i| is

Solution:

QUESTION: 67

If and α is constant then the locus of *z* is

Solution:

QUESTION: 68

The solution of the differential equation *cos(x + y)dy = dx* is

Solution:

QUESTION: 69

If y = √(sin x + y), then dy/dx =

Solution:

QUESTION: 70

Let f : Z → Z be defined as f x = x^{2} , x ∈ Z. The function f is

Solution:

QUESTION: 71

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):The determinants are not identically equal.

Reason(R): If two rows (or columns) of a determinant are identical, then value of the determinant is zero.

Solution:

QUESTION: 72

Ajay runs a mile in 8 minutes. At this rate how long will it take him to run a 26-mile marathon?

Which of the following problems can be solved using the same arithmetic operations that are used to solve the problem above?

Solution:

Ajay runs one mile in 8 minutes, so you’d have to multiply 8 by 26 to get the minutes it would take him to run the 26 miles at the same rate. The arithmetic operation used to solve this problem is multiplication.

In choice A, you’d have to divide the 220 minutes by 26 to get the time for one mile. For choice B, the total number of books would have to be divided by the number of shelves to get the books per shelf. Finally, in choice D, to find the number of baskets you’d have to divide the 500 grams by 60. But to figure out choice C, the weight of one box of crackers, 200 grams, would have to be multiplied by 100 to find the weight of all the boxes. Only in choice C would you have to multiply, as in the questions

QUESTION: 73

The system of equations x+y+z=6, x+2y+3z=10. x+2y+λz=12 is inconsistent, if

Solution:

QUESTION: 74

In the following question, a Statement-1 is given followed by a corresponding Statement-2 just below it. Read the statements carefully and mark the correct answer-

Statement-1:

The curve is symmetric with respect to the line x = 1.

Statement-2:

A parabola is symmetric about its axis.

Solution:

QUESTION: 75

Axis of the parabola x^{2} − 3 y − 6 x + 6 = 0 is

Solution:

QUESTION: 76

A polygon has 44 diagonals. The number of its sides is

Solution:

QUESTION: 77

A pair of dice is thrown and the numbers appearing have sum greater than or equal to 10. The probability of getting 10 is

Solution:

QUESTION: 78

The plane XOZ divides the join of (1, -1, 5) and (2, 3, 4) in the ratio λ : 1, then λ is

Solution:

QUESTION: 79

Which of the following is not a measure of central tendency?

Solution:

QUESTION: 80

The equation of line passing through (c,d) and parallel to ax+by+c=0 is

Solution:

QUESTION: 81

Angle of intersection of the curves y=4-x^{2 }and y=x^{2} is

Solution:

QUESTION: 82

The one root of the equation cos x-x+(1/2)=0 lies in the interval

Solution:

QUESTION: 83

The unit normal vector to the line joining i-j and 2i+3j towards origin is

Solution:

QUESTION: 84

The projection of a along b is

Solution:
The projection of a along b is (a.b/lbl)according to projection formula

QUESTION: 85

If f^{'}(2) = 4 and f^{'} (1) = 2 then

Solution:

QUESTION: 86

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):

Reason:

Solution:

QUESTION: 87

∫

Solution:

QUESTION: 88

If A is a non-singular, then adj A is

Solution:
Show that if A is singular, then adj A is also singular. I had been going to use the fact that if a matrix is singular, its determinant is 0, and the theorem that says that det(adj A) = [det(A)]^(n-1), but then realized that the theorem was only true if A was non-singular.

QUESTION: 89

If *x + y* = 12, then the minimum value of *x ^{2} + y^{2}* is

Solution:

QUESTION: 90

Consider an infinite series with first term 'a' and common ration 'r'. If it sum is 4 and the second term is 3/4, then

Solution:

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