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This mock test of JEE Main Mock - 2 (Previous Pattern) for JEE helps you for every JEE entrance exam.
This contains 90 Multiple Choice Questions for JEE JEE Main Mock - 2 (Previous Pattern) (mcq) to study with solutions a complete question bank.
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QUESTION: 1

In a LCR circuit capacitance is changed from C to 2C. For the resonant frequency to remain unchanged, the inductance should be changed from L to

Solution:

QUESTION: 2

A transformer is employed to reduce 220 V to 11 V. The primary draws a current of 5 A and the secondary 90 A. The efficiency of the transformer is

Solution:

Primaray power = 220 *5 = 1100 w

Secondary power = 11*90 = 990 w

So , efficiency = 990w/1100w = 90 %

QUESTION: 3

Moderator used in nuclear reactor is

Solution:

Heavy water is used in certain types of nuclear reactors, where it acts as a neutron moderator to slow down neutrons so that they are more likely to react with the fissile uranium-235 than with uranium-238, which captures neutrons without fissioning.

QUESTION: 4

The unit of intensity of electric field is

Solution:

The SI unit of electric field strength is newtons per coulomb (N/C) or volts per meter (V/m). The force experienced by a very small test charge q placed in a field E in a vacuum is given by E = F/q, where F is the force experienced.

QUESTION: 5

In a hydrogen atom, when an electron jumps from second orbit to first orbit, the wavelength of spectral line emitted by hydrogen atom is

Solution:

QUESTION: 6

“If a particle of mass m is projected from the lowest point of smooth vertical circle of radius 'A' with velocity √(5ag) the pressure at its lowest point will be”

Solution:

At lowest point centrifugal force is equal to mv^{2}/a in downward direction

=> total downward force = mg + mv^{2}/a

= mg + m 5ag/a

= mg + 5 mg

= 6mg

QUESTION: 7

A particle of mass m and charge q is placed at rest in a uniform electric field E and then released. The kinetic energy attained by the particle after moving a distance y is

Solution:

By conservation of energy, the increase in kinetic energy will be the decrease in potential energy.

Thus, the kinetic energy obtained is simply: qEy

QUESTION: 8

An electron having charge e and mass m is moving in a uniform electric field E. Its acceleration will be

Solution:

QUESTION: 9

25 N force is required to raise 75 kg mass from a pulley. If rope is pulled 12 m, then the load is lifted to 3 m, the efficiency of pulley system will be

Solution:

Efficiency = output/input = (75x3) / (25x12)

=75/100 =75%

QUESTION: 10

Two wires of same length are shaped into a square and a circle. If they carry same current, ratio of the magnetic moments is

Solution:

Let magnetic moment of square wire be μ_{1} = I_{1}A_{1}

Let magnetic moment of circle wire be μ_{2}= I_{2}A_{2}

If the wires carry same current then the ratio of their magnetic moments will be

QUESTION: 11

In a capillary tube, water rises by 1.2 mm. The height of water that will rise in another capillary tube having half the radius of the first, is

Solution:

QUESTION: 12

Three forces start acting simultaneously on a particle moving with velocity v → . These forces are represented in magnitude and direction by the three sides of a triangle *ABC* (as shown). The particle will now move with velocity

Solution:

According to triangle law of vector addition, if three vectors are represented by three sides of a triangle taken in same order, then their resultant will be zero. Here, three forces acting on the particle are represented by the three sides of a triangle taken in one order, thus the resultant is zero. So, in presence of zero external force, the particle's velocity remains unchanged.

QUESTION: 13

Four bodies P, Q, R and S are projected with equal velocities having angles of projection 15º, 30º, 45º and 60º with the horizontal respectively. The body having shortest range is

Solution:

When the angle of projection is very far from 45° then range will be minimum.

QUESTION: 14

An electric current of 5 A is same as

Solution:

Hence 5A of current is same as 5 C/sec

QUESTION: 15

The nucleus of _{56}Ba^{141} contains ---- neutrons

Solution:

Given ,

=> atomic mass=141

=>atomic number=56

So, neutrons=atomic mass-atomic number

=141-56

=85

QUESTION: 16

Assertion : The work done during a round trip is always zero.

Reason : No force is required to move a body in its round trip.

Solution:

In a round trip work done is zero only when the force is conservative in nature. Force is always required to move a body in a conservative or non-conservative field

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)__: Study of Fraunhofer lines in the spectrum of sun led to the discovery of hydrogen.

__Reason(R)__:Fraunhofer lines are dark lines in the continuous solar spectrum.

Solution:

In 1868 Lockyer observed a line among the Fraunhofer lines which could not be traced in the spectrum of any element on earth. So it was assumed that there was some new element in the sun's chromsphere. It was named helium. In 1895 Ramsay found this gas on earth. Thus, the study of Fraunhofer lines led to the discovery of new elements.

QUESTION: 18

A body A of mass M while falling vertically downwards under gravity breaks into two parts, a part B of mass M/3 and body C of mass 2M/3. The centre of mass of the bodies B and C taken together

Solution:

No horizontal external force is acting

∴ a_{cm} = 0

since v_{cm} = 0

∴ Δx_{cm} = 0

QUESTION: 19

A Carnot engine used first an ideal monoatomic gas and then an ideal diatomic gas. If the source and sink temperature are 411ºC and 69ºC respectively and the engine extracts 1000 J of heat in each cycle, then area enclosed by the P-V diagram is

Solution:

QUESTION: 20

The Martians use force (F), acceleration (A) and time (T) as their fundamental physical quantities. The dimensions of length on Martians system are

Solution:

Acceleration

QUESTION: 21

Wave optics is based on wave theory of light put forward by Huygen and modified later by

Solution:

The Huygens–Fresnel principle (named after Dutch physicist Christiaan Huygens and French physicist Augustin-Jean Fresnel) is a method of analysis applied to problems of wave propagation both in the far-field limit and in near-field diffraction.

It states that every point on a wavefront is itself the source of spherical wavelets. The sum of these spherical wavelets forms the wavefront.

QUESTION: 22

Doppler's effects in sound and light are

Solution:

An apparent change in the frequency of waves, as of sound or light, occurring when the source and observer are in motion relative to each other, with the frequency increasing when the source and observer approach each other anddecreasing when they move apart.

QUESTION: 23

The ray of light

Solution:

A perpendicular drawn to the surface of a wavefront at any point in the direction of propagation of light is called as wave normal. The direction of propagation of a wave front is given by a ray of light. Therefore, a wave normal represents a ray of light.

QUESTION: 24

The phase difference between two points separated by 0.8 m in a wave of frequency 120 Hz is 90º. Then the velocity of wave will be

Solution:

Here, path difference Δx=0.8m Frequency n =120 Hz Phase difference is ϕ=0.5π The phase difference is given by

Hence, the wave velocity is given by v = nλ (where λ is the wavelength of wave) =120 × 2.3 = 384m/s

QUESTION: 25

Which of the following is not a statement?

Solution:

QUESTION: 26

When the electron in a hydrogen atom of mass *M* undergoes transition from an orbit of higher quantum number *n _{2}* to an orbit of lower quantum number

Solution:

The wave number of the photon emitted because of the electron transition is

ν' = 1/λ = R(1/(n_{1})^{2} – 1/(n_{2})^{2}) where λ is the wave length of the photon and R is Rydberg’s constant.

The momentum of the photon is p = h/λ = hR(1/(n_{1})^{2} – 1/(n_{2})^{2}) where h is Planck’s constant.

When the photon is emitted with this momentum, the atom recoils (like a gun firing a bullet) with an equal and opposite momentum. Therefore, the recoil velocity of the atom is given by

v = p/M = (hR/M)(1/(n_{1})^{2} – 1/(n_{2})^{2}).

QUESTION: 27

A 5.0 μ F capacitor is charged to a potential difference of 800 V and discharged through a conductor. The energy given to the conductor during the discharge is

Solution:

QUESTION: 28

A stone of mass 1 kg tied to a light inextensible string of length L = 10/3 m is whirling in a circular path of radius L in a vertical plane. If the ratio of the maximum tension in the string to the minimum tension in the string is 4 and if g is taken to be 10 m/sec^{2}, the speed of the stone at the highest point of the circle is

Solution:

The ratio of maximum (T_{2) }to the minimum tension is

Now, the difference between the two tensions should be 6 mg.

Hence, we have

Now, the tension at the top of the circle is

QUESTION: 29

If six identical cells each having an *e.m.f* of 6*V* are connected in parallel, the *E.M.F* of the combination is

Solution:

In parallel combination E_{eq}=E=6V

QUESTION: 30

There are 20 divisions in 4 cm of the main scale. The vernier scale has 10 divisions. The least count of the instrument is

Solution:

QUESTION: 31

A charged particle of mass m and charge q is released from rest in a uniform electric field E. Neglecting the effect of gravity, kinetic energy of the charged particle after 't' seconds is

Solution:

F= qE

a = qE/m -------(1)

start from rest so u= 0

v= u+ at

v= at

from 1

v= qEt/m

kinetic energy= 1/2 mv²

KE= q²E²t²/2m

QUESTION: 32

The wavelength associated with a golf ball weighing 200g and moving with a speed of 5 m/h is of the order __

Solution:

QUESTION: 33

Rutherford's experiment, which established nuclear model of atom, used a beam of

Solution:

alpha particles are helium atoms stripped off their two electrons.

QUESTION: 34

The enthalpy change (∆H) for neutralisation of 1 M HCl by caustic soda in dilute solutions at 298 K is

Solution:

It's actually factual.The enthalpy of neutralisation for strong acid and strong base per mole is 57.1KJ i.e 0.0571J/mole

QUESTION: 35

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

Solution:

QUESTION: 36

The CFSE (Crystal Field Stabilisation Energy) for a high spin octahedral complex having d^{1} configuration is __

Solution:

CFSE = [− 0.4p + 0.6q]Δ_{0}

= [− 4p + 6q]Dq

p = electrons in e_{g} orbitals

q = electrons in t_{2g} orbitals

For d_{1} (high spin) configuration t 2 g 1 e g 0

CFSE = [- 0.4 X+ 0.6 X 0]Δ_{0}

=[−0.40 + 0]Δ_{0} = − 0.4 Δ

= 4Dq.

(Configuration of d^{1} in high spin or low spin is same).

QUESTION: 37

Duma's method involves the determination of content of nitrogen in the organic compound in the form of

Solution:

Dumas' method involves the determination of nitrogen content in the organic compound in the form of nitrogen . Organic compound is oxidized with cupric oxide in an atmosphere of carbon dioxide which gives free nitrogen along-with carbon dioxide and water.

QUESTION: 38

Ethanal reacts with alkali to give 3-hydroxybutanal. the reaction is

Solution:

Aldol reaction is an important organic reaction of aldehydes and ketones. This reaction is shown by aldehydes and Ketones having alpha-hydrogen atom in the compound. Such a-hydrogen atom containing aldehydes and ketones will undergo self condensation in presence dilute alkalies like dil.NaOH (dilute Sodium hydroxide), dil.Ba(OH)2(dilute Barium hydroxide) forming alpha, β-hydroxyaldehyde (an aldol) or β-hydroxyketone (a Ketol) .The Aldol or the Ketol thus formed in the reaction upon heating eliminates a molecule of water (i.e. it undergoes dehydration) forming alpha, β-unsaturated Aldehydes or Ketones respectively. This reaction now is called Aldol condensation reaction.

QUESTION: 39

Methanol is manufactured by passing compressed water gas with excess of hydrogen over

Solution:

QUESTION: 40

Pick out the correct statement __

Solution:

QUESTION: 41

For the reaction system : 2NO(g) + O₂(g) → 2NO₂(g) volume is suddenly reduced to half its value by increasing the pressure on it. If the reaction is of first order with respect to O₂ and second order with respect to NO, the rate of reaction will

Solution:

**Rate 1 = k[NO] ^{2} [O_{2}]**

When

Rate 2 = k[2NO]

QUESTION: 42

The ∆H value for reaction C + 1/2 O₂ → CO and CO + 1/2O₂ → CO₂ are 100 and 200 kJ respectively. The heat of reaction for C + O₂ → CO₂ will be

Solution:

QUESTION: 43

The hypothetical complex Diaquatriammine-chloro-cobalt(III) chloride can be represented as

Solution:

Chlorodiaquatriamminecobalt(Ill) chloride can be represented as [CoCl(NH_{3})_{3}(H_{2}O)_{2}]Cl_{2}.

QUESTION: 44

Which of the following is isoelectronic with carbon atom?

Solution:

Isoelectronic species: a group of ions, atoms, or molecules that have the same number of electrons. Thus, carbon and N^{+} are isoelectronic with 6 electrons.

Electronic configuration of C and N^{+}:

QUESTION: 45

Compound A has a molecular formula C₇H₇NO on treatment with Br₂/KOH, A gives an amine B which respond to carbylamine test. B on diazotisation and coupling with phenol give an azo dye. A can be

Solution:

QUESTION: 46

The electrochemical equivalent of metal is *x* gram-coulomb^{-1}. The equivalent weight of metal is

Solution:

QUESTION: 47

Which is the best description of the behaviour of bromine in the reaction: H₂O + Br₂ → HOBr + HBr?

Solution:

QUESTION: 48

Identify the indicator used to titrate Na₂CO₃ solution with HCl

Solution:

I would pick either phenophthalein or methyl-orange. Phenophthalein will change for the first protonation:

Na2CO3 + HCl = NaHCO3 + NaCl

Methyl-orange will change for the second protonation:

NaHCO3 + HCl = H2CO3 + NaCl

H2CO3 = H2O + CO2

Either titration will tell you the amount of Na2CO3 you have.

Combining both indicators is possible but since Methyl-orange is yellow on the basic side, it may obscure the transition of the phenophthalein (purple to colorless). If you were to use both, it would be best to add the methyl orange indicator after the first equivalence point when the phenophthalein has gone colorless. You would also have to remember to divide the concentration you get using two equivalents of acid by 2 to get the concentration of Na2CO3.

QUESTION: 49

It is found that 0.1 m solution of four sodium salts NaA,NaB and NaD have the following pH values :

Which one of the corresponding acids is strongest ?

Solution:

Salts of strong acids and strong base have pH = 7

QUESTION: 50

Which one of the following salt's aqueous solution is likely to have pH < 7 ?

Solution:

Bcause NH_{4}Cl is formed by strong acid HCl and weak base NH_{4}OH

QUESTION: 51

The pH value of a 10 M solution of HCI is

Solution:

Ph = -log[H⁺] = -log10

ph= -1

which is less than 0

QUESTION: 52

Which of the following reagents is useful in separating benzoic acid from phenol?

Solution:

Benzoic acid dissolves in a aqueous solution of NaHCO_{3}, while phenol being less acidic than H_{2}CO_{3} do not react.

QUESTION: 53

When CH_{3}Cl undergoes homolytic bond-fission:

Solution:

QUESTION: 54

The catalyst used for the polymerization of olefins is

Solution:

A Ziegler–Natta catalyst, named after Karl Ziegler and Giulio Natta, is a catalyst used in the synthesis of polymers of 1-alkenes (alpha-olefins).

QUESTION: 55

The reaction/method that does not give an alkane is

Solution:

Dehydrohalogenation of alkyl halide gives alkenes but not alkane

QUESTION: 56

Example of unit cell with crystallographic dimensions a≠b≠c,α=γ=90º,β≠90º is

Solution:

QUESTION: 57

Xenon crystallises in the face-centered cubic lattice and the edge length of the unit cell is 620 pm. The distance between two neighbour atoms is

Solution:

QUESTION: 58

Acetic acid dissolved in benzene shows a molecular mass of

Solution:
Acetic acid dimerizes in benzene, Its molar mass would be 2 x 60gmol−1, i.e 120gmol−1

QUESTION: 59

What is the molality of a solution of a certain solute in a solvent if there is a freezing point depression of 0.184ºC and the freezing point constant is 18.4 ?

Solution:
Given: ∆Tf=0.184•c and Kf = 18.4

WKT

∆Tf=Kf m

m = ∆Tf/Kf

m=0.184/18.4

m=0.01

WKT

∆Tf=Kf m

m = ∆Tf/Kf

m=0.184/18.4

m=0.01

QUESTION: 60

Acetylene when passed through 20% H₂SO₄ at 80ºC gives acetaldehyde. The catalyst required for this conversion is

Solution:

Preparation of aldehyde from acetylene : Acetylene when passed through 20% H2SO4 solution at 600C in presence of 2% HgSO4 isoxidised to produce acetaldehyde.

QUESTION: 61

Which of the following is not a function of proteins?

Solution:

Protein are the building block of the body.

**Collagen** is found as strong non-elastic white fibres in tendons, cartilage and bone.

**Elastin** is found as yellow elastic fibres in ligaments and joint capsules.

**Keratin** is found as a horny impermeable protein in skin, hair, feathers, nails and hooves.

**Lipoproteins** of cell membranes, viral coat proteins, fibroin are found as spider silk and cocoon silk, sclerotin found in insect exoskeletons, and mucoproteins found in lubricating joint (synovial) fluid.

QUESTION: 62

When 5^{99} is divided by 13 then the remainder is

Solution:

QUESTION: 63

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

Solution:

QUESTION: 64

Area enclosed between the curve y^{2} (2a - x) = x^{2 }and the line x = 2a above x-axis is

Solution:

QUESTION: 65

The equation of the diameter of the circle x^{2} + y^{2} - 6x + 2y = 0 which passes thro' the origin is

Solution:

Since the line passes through origin the equation of line is Y=mX,it also passes through the center (3,-1),Y= -1/3(X)

X+3Y=0

QUESTION: 66

If the lines *3x - 4y - 7 = 0* and *2x - 3y - 5 = 0* are two diameters of a circle of area 49 π square units, the equation of the circle is

Solution:

Point of intersection of 3x − 4y − 7 = 0 and 2x − 3y − 5 = 0 is (1 , − 1), which is the centre of the circle and radius = 7.

∴ Equation is (x−1)^{2}+(y+1)^{2}=49

⇒x^{2}+y^{2}−2x+2y−47=0.

QUESTION: 67

If z₁ and z₂ are two non-zero complex numbers such that |z₁ + z₂| = |z₁| + |z₂|, then argz₁ - argz₂ is equal to

Solution:

Let z_{1}=a+ib , z_{2}=c+id

|z_{1}+z_{2}|=|z_{1}|+|z_{2}|

|a+ib+c+ib|=|a+ib|+|c+id|

(a+c+i(b+d)=sqrt(a^{2}+b^{2})+sqrt(c^{2}+d^{2})

sqrt((a+c)^{2}+(b+d)^{2} = sqrt(a^{2}+b^{2})+sqrt(c^{2}+d^{2})......on simplifying this we get....

a=c and b=d

argz_{1}=tan^{-1}|(b/a)|...... argz_{2}=tan^{-1}|(d/c)| = tan^{-1}|b/a|

argz_{1} - argz_{2} = 0

QUESTION: 68

If (1 + i√3)/[(1 + i√3)^{n}] is an integer ,then n is equal to

Solution:

Presuming the question actually means

[ ( 1 + √3i ) / [( 1 - √3i ) ⁿ]

i.e. the whole thing raised to the power of n, not just the denominator.

Let w = ( 1 + √3i ) / ( 1 - √3i )

Multiplying numerator and denominator by ( 1 + √3i ) gives

w = ( 1 + √3i )² / [ ( 1 - √3i ) ( 1 + √3i ) ]

= ( 1 - 3 + 2√3i ) / ( 1 + 3 )

= ( -2 + 2√3i ) / 4

= ( -1 + √3i) / 2.

So w is a primitive cubed root of unity. (*) ... see note below

So wⁿ is an integer

<=> wⁿ = 1

<=> n is a multiple of 3.

QUESTION: 69

The solution of the differential equation cos x sin y dx + sin x cos y dy =0 is

Solution:

QUESTION: 70

The interval in which y=x^{2}e^{x} is increasing with respect to x, is

Solution:

We have,

y=X^{2}e^{-x}

^{}

The points x = 0 and x = 2 divide the real line into three disjoint intervals

∴ f is strictly increasing on (0, 2).

Hence, f is strictly increasing in interval (0, 2).

The correct answer is D.

QUESTION: 71

If f(x) = 1 + αx, α ≠ 0 is the inverse of itself, then the value of α is

Solution:

**Toolbox:**

- If f(g(x))=x then g is inverse of x and f is inverse of g

Given f is inverse of itself.

⇒f(f(x)) = x

⇒1+α(1+αx) = x

⇒1+α+(α)^{2}x = x

Equating the like terms on either side, we get

1+α=0and(α)^{2}=1

⇒ α = −1.

QUESTION: 72

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 points , (1,3) and (82,30) are collinear.

Reason(R): Three points P_{1},P_{2},P_{3} are collinear , if ∆ = 0 or x_{1} (y_{2}-y_{3}) + x_{2} (y_{3}-y_{1}) + x_{3} (y_{1}-y_{2}) = 0 or = 0

Solution:

QUESTION: 73

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): If x^{2} + x + 1, 2x + 1 and x^{2} - 1 represent lengths of the sides of a triangle , then x > 1.

Reason(R): If a,b,c be the lengths of sides of ∆, then a + b > c, b + c < a, c + a > b.

Solution:

QUESTION: 74

The number of solutions of 2x + y = 4, x - 2 y = 2, 3x + 5y = 6 is

Solution:

QUESTION: 75

The line y=mx+c touches the parabola x^{2}=4ay if

Solution:

Y= mx + c; x²= 4ay

Subst y in the equation of parabola

x²= 4a(mx + c)

x²-4amx-4ac = 0

Since the line touches the parabola at one point The above quadratic will have one root

b²-4ac = 0

b²= 4ac

16a²m² = 4(1)(-4ac)

16a²m²= -16ac

c=-am²

QUESTION: 76

If ^{n}P_{r}=840, ^{n}C_{r}=35, then n=

Solution:

QUESTION: 77

If the integers m and n are chosen at random between 1 and 100, then the probability that a number of the form 7^{m} + 7^{n} is divisible by 5 equals

Solution:

We know 7^{k}, k∈ N, has 1, 3, 9, 7 at the unit's place for

k = 4p, 4p - 1, 4p - 2, 4p - 3 respectively, where p = 1, 2, 3.....

7^{m} + 7^{n} will be divisible by 5 if 7^{m} has 3 or 7 in the unit's place

and 7^{n} has 7 or 3 in the unit's place or 7^{m} has 1 or 9 is the unit's place and 7^{n } has

9 or 1 in the unit's place

∴ For any choice of m, n the digit in the unit's place of 7^{m} + 7^{n} is 2, 4, 6, 0 or 8

It is divisible by 5 only when this digit is 0

∴ the required probability = 1/5

QUESTION: 78

Mean of 100 observations is 45. It was later found that two observations 19 and 31 were incorrectly recorded as 91 and 13. The correct mean is

Solution:

QUESTION: 79

The equation of a line passing through the intersection of lines 3x-2y-1=0 and x-4y+3=0 and point (π,0) is

Solution:

QUESTION: 80

The slope of the tangent of the curve x=t^{2}+3t-8, y=2t^{2}-2t-5 at the point (2,-1) is

Solution:

QUESTION: 81

The equation of the sphere with centre (3, 6, -4) and touching the plane

2x - 2y - z - 10 = 0 is

Solution:

As the required sphere touches the plane

2x - 2y - z - 10 = 0 .....(1)

∴ Radius of the required sphere = ⊥ from the center (3, 6, -4) of the required sphere to the plane (1)

∴ The required equation of the sphere is given by

(x - 3)^{2} + (y - 6)^{2} + (z + 4)^{2} = 16 (Central form)

⇒ x^{2} + 9 - 6x + y^{2} + 36 - 12y + z^{2} + 16 + 8z = 16

⇒ x^{2} + y^{2} + z^{2} - 6x - 12y + 8z + 45 = 0

QUESTION: 82

If for real values of x, cos θ = x+1/x, then

Solution:

QUESTION: 83

The moment of the couple formed by the forces 5 î + k̂ and -5 î - k̂ acting at the points (9, -1, 2) and (3, -2, 1) respectively is

Solution:

QUESTION: 84

A force F → = 2 î + ĵ − k̂ acts at a point A whose position vector is 2 î − ĵ. If point of application of F → moves from A to the point B with position vector 2 î + ĵ , then work done by F → is

Solution:
W=F.ds ds=2i+j-(2i-j) ds =2j F=2i +j-k W=(2i+j-k).(2j)=2(0)+1(2)+(-1)(0)=2

QUESTION: 85

Solution:
As the given function is odd function. So by property six (see in ncert) the answer is zero

QUESTION: 86

Lim_{x→-1} [1 + x + x² + ……….+ x^{10}] is

Solution:

Given, Lim_{x→-1} [1 + x + x² + ……….+ x^{10}]

= 1 + (-1) + (-1)² + ……….+ (-1)^{10}

= 1 – 1 + 1 – ……. + 1 = 1

QUESTION: 87

A square tank of capacity 250 cubic m has to be dug out. The cost of land is Rs 50 per sq.m. The cost of digging increases with the depth and for the whole tank is 400 (depth)^{2} rupees. The dimensions of the tank for the least total cost are

Solution:

Let x side of square base.

Volume of tank = 250 cubic metres.

Let C be total cost.

square tank is of side 10 metres and height 2.5 metres.

QUESTION: 88

The g^{-1}({0}) for the function g(x)= ⌊x⌋ is ___________

Solution:

g({0}) for the function g(x) is {x | 0 ≤ x ≤ 1}. Put g(x) = y and find the value of x in terms of y such that ⌊x⌋ = y.

QUESTION: 89

. Then *a* and *b* are respectively

Solution:

QUESTION: 90

Let f(x) = ax^{2}+bx+c,a ≠ 0 and triangle = b^{2}-4ac.If α+β, α^{2}+β^{2} and α^{3}+β^{3} are in G.P., then :

Solution:

α+β,α^{2}+β^{2},α^{3}+β^{3} are in G.P.

∴(α^{2}+β^{2})^{2 }= (α+β)(α^{3}+β^{3})

∴α^{4}+β^{4}+2α^{2}β^{2} = α4+β^{4}+α^{3}β+αβ^{3}

∴α^{2}β^{2}−α^{3}β−αβ^{3}+α^{2}β^{2 }= 0

∴α^{2}β(β−α)−αβ^{2}(β−α)=0

∴(α^{2}β−αβ^{2})(β−α)=0

∴αβ(α−β)(β−α)=0

∴αβ(α−β)^{2}=0

∴α=0 or β=0 or α−β=0

Case (1) α=0 or β=0,

⟹x=0 is a solution of given equation

∴a(0)^{2}+b(0)+c=0

∴c=0

Case (2) α−β=0

⟹α=β

So, the equation has equal roots.

∴Δ=b^{2}−4ac=0

∴c=0 or Δ=0

∴cΔ=0

### NTA 101 JEE MAIN MOCK TESTS

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- JEE Main Mock - 2 (Previous Pattern)
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