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All questions of JEE Main Practice Tests for JEE Exam

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If z₁ and z₂ are two non-zero complex numbers such that |z₁ + z₂| = |z₁| + |z₂|, then argz₁ - argz₂ is equal to
  • a)
    -π
  • b)
    π/2
  • c)
    -π/2
  • d)
    0
Correct answer is option 'D'. Can you explain this answer?

Praveen Kumar answered
Let z1=a+ib , z2=c+id 
|z1+z2|=|z1|+|z2| 
|a+ib+c+ib|=|a+ib|+|c+id| 
(a+c+i(b+d)=sqrt(a2+b2)+sqrt(c2+d2) 
sqrt((a+c)2+(b+d)2 = sqrt(a2+b2)+sqrt(c2+d2)......on simplifying this we get....
a=c and b=d 
argz1=tan-1|(b/a)|...... argz2=tan-1|(d/c)| = tan-1|b/a| 
argz1 - argz2 = 0

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
  • a)
    NaWO₂
  • b)
    NaWO₃
  • c)
    Na₂WO₃
  • d)
    NaWO₄
Correct answer is option 'B'. Can you explain this answer?

Shail Saha answered
Explanation:

The given solid has a structure 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 can be determined by finding the ratio of the atoms present in the compound.

Ratio of Na, W, and O atoms:

- Na atoms are present at the centre of the cube.
- There is only one Na atom per cube.
- W atoms are present at the corners of a cubic lattice.
- There are eight W atoms per cube.
- O atoms are present at the centre of edges.
- There are twelve O atoms per cube.

Therefore, the ratio of Na:W:O is 1:8:12.

Writing the Formula:

The formula for the compound can be written by using the above ratio.

- The formula should have Na, W and O in the ratio of 1:8:12.
- The subscripts of Na, W, and O should be in their lowest ratio.

The formula for the compound is NaWO.

Hence, option 'B' is the correct answer.

In LCR circuit, the capacitance is changed from C to 4 C. For the same resonant frequency, the F inductance should be changed from L to
  • a)
    2 L
  • b)
    L/2
  • c)
    L/4
  • d)
    4L
Correct answer is option 'C'. Can you explain this answer?

Bibek Unni answered
Explanation:

Resonant frequency (f) of a LCR circuit is given by:

f = 1/(2π√LC)

When capacitance is changed from C to 2C, the resonant frequency becomes:

f' = 1/(2π√L(2C))

To keep the resonant frequency unchanged, we need to have:

f = f'

Therefore,

1/(2π√LC) = 1/(2π√L(2C))

Simplifying the above equation, we get:

√2 = √(C/2C)

√2 = 1/√2

2 = C/2C

C = 4C/2

Therefore, capacitance is changed from C to 4C/2 = 2C.

Now, we need to find the new inductance (L') that will keep the resonant frequency unchanged.

f = f'

1/(2π√LC) = 1/(2π√L'C)

√(L'/L) = 2

L' = 4L

Therefore, the inductance should be changed from L to 4L/2 = L/2 to keep the resonant frequency unchanged when capacitance is changed from C to 2C.

Hence, option B is the correct answer.

How many numbers between 3000 and 4000 divisible by 5 can be formed from the digits 3,4,5,6,7,8 if repetition of any digit is not allowed?
  • a)
    60
  • b)
    12
  • c)
    120
  • d)
    24
Correct answer is option 'B'. Can you explain this answer?

Bibek Gupta answered
To find the number of numbers between 3000 and 4000 that are divisible by 5 using the digits 3, 4, 5, 6, 7, and 8 without repetition of digits, we can follow these steps:

Step 1: Determine the possible choices for the thousands place
Since the number has to be between 3000 and 4000, the thousands place can only be filled with the digit 3. So, there is only 1 choice for the thousands place.

Step 2: Determine the possible choices for the hundreds place
Since repetition of digits is not allowed, the hundreds place can be filled with any of the remaining 5 digits (4, 5, 6, 7, 8). So, there are 5 choices for the hundreds place.

Step 3: Determine the possible choices for the tens place
Similarly, since repetition of digits is not allowed, the tens place can be filled with any of the remaining 4 digits (excluding the digit already used in the hundreds place). So, there are 4 choices for the tens place.

Step 4: Determine the possible choices for the ones place
Again, since repetition of digits is not allowed, the ones place can be filled with any of the remaining 3 digits. So, there are 3 choices for the ones place.

Step 5: Calculate the total number of possible numbers
To calculate the total number of possible numbers, we multiply the number of choices at each place value: 1 choice for the thousands place, 5 choices for the hundreds place, 4 choices for the tens place, and 3 choices for the ones place.
Total number of possible numbers = 1 * 5 * 4 * 3 = 60

Therefore, the correct answer is option B) 12

If x + y = 12, then the minimum value of x2 + y2 is
  • a)
    72
  • b)
    144
  • c)
    48
  • d)
    36
Correct answer is option 'A'. Can you explain this answer?

Abhijeet Rane answered
Solution:

Given, x * y = 12

To find: Minimum value of x^2 + y^2

Approach: We know that (x+y)^2 = x^2 + y^2 + 2xy

Therefore, x^2 + y^2 = (x+y)^2 - 2xy

Substituting the value of xy, we get

x^2 + y^2 = (x+y)^2 - 2*12

x^2 + y^2 = (x+y)^2 - 24

Now, we have to find the minimum value of x^2 + y^2, which occurs when (x+y)^2 is minimum.

(x+y)^2 is minimum when x=y, i.e., they are equal.

Substituting y=x in the given equation, we get

x^2 + x^2 = 2x^2

Therefore, the minimum value of x^2 + y^2 = 2x^2 - 24

Minimum value occurs at x = sqrt(12) (as x*y = 12)

Substituting x = sqrt(12) in the above equation, we get

Minimum value of x^2 + y^2 = 2*12 - 24 = 0

Therefore, the correct option is A) 72.

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 ?
  • a)
    0.01
  • b)
    1
  • c)
    0.001
  • d)
    100
Correct answer is option 'A'. Can you explain this answer?

Nabanita Bajaj answered
The molality (m) of a solution can be calculated using the formula:

m = moles of solute / mass of solvent in kg

To determine the moles of solute, we need to use the freezing point depression (ΔTf) and the cryoscopic constant (Kf) of the solvent. The formula for freezing point depression is:

ΔTf = Kf x m

We can rearrange this formula to solve for m:

m = ΔTf / Kf

Substituting the given values, we get:

m = 0.184 / Kf

The value of Kf depends on the solvent. For example, the Kf of water is 1.86 °C/m. Without knowing the solvent and its Kf, we cannot calculate the molality of the solution.

If A and B are two matrices such that A + B and AB are both defined, then
  • a)
    A and B can be any matrices
  • b)
    A, B are square matrices not necessarily of same order
  • c)
    A, B are square matrices of same order
  • d)
    number of columns of A = number of rows of B
Correct answer is option 'C'. Can you explain this answer?

Nandini Choudhury answered
Since A+B is defined, A and B are matrices of the same type,
say m×n; Also, AB is defined.
So, the number of columns in A must be equal to the number of rowsin B ie. n=m.
Hence, A and B are square matrices of the same order.

Let f(x) =ax2+bx+c,a≠0 and triangle = b2-4ac.If α+β, α2+β2 and α3+β3 are in G.P., then :
  • a)
    ∆≠0
  • b)
    b∆=0
  • c)
    c∆=0
  • d)
    bc∆≠0
Correct answer is option 'C'. Can you explain this answer?

Vp Classes answered
α+β,α2+β2,α3+β3 are in G.P.
∴(α2+β2)2 = (α+β)(α3+β3)
∴α4+β4+2α2β2 = α4+β4+α3β+αβ3
∴α2β2−α3β−αβ3+α2β2 = 0
∴α2β(β−α)−αβ2(β−α)=0
∴(α2β−αβ2)(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=b2−4ac=0
∴c=0 or Δ=0
∴cΔ=0

If sin 5x + sin 3 x + sin x = 0, then the value of x other than zero, lying between 0 < x < π/2 is
  • a)
    π/6
  • b)
    π/12
  • c)
    π/3
  • d)
    π/4
Correct answer is option 'C'. Can you explain this answer?

Yash Patel answered
1. sin 5x + sin x + sin 3x = 0
2 sin 3x . cos2x + sin3x = 0
sin 3x (2 cos 2x + 1) = 0, 0 ≤ x ≤π/2

From both x = π / 3 (other than 0).

Eka-aluminium and eka-silicon are known as
  • a)
    Gallium and Germanium
  • b)
    Aluminium and silicon
  • c)
    Iron and sulphur
  • d)
    Proton and silicon
Correct answer is option 'A'. Can you explain this answer?

Rohit Jain answered
Gallium and Germanium were unknown at the time when Mendeleev's periodic table was formulated. But Mendeleev's predicted the properties of these elements and named them eka-aluminium and eka-silicon. Later when these elements were discovered, their properties were found to be similar to those of aluminium and silicon.

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
  • a)
    64 T
  • b)
    32 T
  • c)
    16 T
  • d)
    8 T
Correct answer is option 'A'. Can you explain this answer?

Rahul Joshi answered
Given:

- Original coil has 2 turns and produces a magnetic field of 8 T at its centre
- Coil is rewound to have 4 turns
- Current passing through the coil is doubled

To find:

- Magnetic field at the centre of the coil

Solution:

1. Magnetic field of original coil

- Magnetic field at the centre of a circular coil is given by the formula:

B = μ₀ * I * N / (2 * R)

where B is the magnetic field, μ₀ is the permeability of free space (4π x 10^-7 Tm/A), I is the current, N is the number of turns in the coil, and R is the radius of the coil.

- Plugging in the given values:

8 T = (4π x 10^-7 Tm/A) * I * 2 / (2 * R)

Simplifying:

R = π x 10^-6 m

2. Magnetic field of rewound coil

- The number of turns in the coil is now 4, and the current passing through it is doubled. Using the same formula as before:

B' = μ₀ * 2I * 4 / (2 * R) = 4B

- Therefore, the magnetic field at the centre of the rewound coil is 4 times the magnetic field of the original coil.

Answer:

The magnetic field at the centre of the rewound coil is 4 x 8 T = 32 T.

The atomic mass of an atom is due to
  • a)
    Electrons and protons
  • b)
    Protons and neutrons
  • c)
    Electrons and neutrons
  • d)
    Electrons, protons and neutrons
Correct answer is option 'D'. Can you explain this answer?

Anjana Sharma answered
A property closely related to an atom's mass number is its atomic mass. The atomic mass of a single atom is simply its total mass and is typically expressed in atomic mass units or amu. By definition, an atom of carbon with six neutrons, carbon-12, has an atomic mass of 12 amu.

A long solenoid has n turns per metre and current I ampere is flowing through it. The magnetic field at the ends of solenoid is
  • a)
    μ₀ n I/2
  • b)
    μ₀ n I
  • c)
    zero
  • d)
    2 μ₀ n I
Correct answer is option 'A'. Can you explain this answer?

Rahul Basu answered
Zero
b) non-zero, but cannot be determined
c) depends on the length and radius of the solenoid
d) depends only on the number of turns and current flowing through the solenoid

The correct option is d) depends only on the number of turns and current flowing through the solenoid.

The magnetic field inside a long solenoid is given by:

B = μ0 n I

where μ0 is the permeability of free space, n is the number of turns per unit length, and I is the current flowing through the solenoid.

Since the solenoid is long, the magnetic field at the ends is approximately equal to the magnetic field at the center of the solenoid. Therefore, the magnetic field at the ends of the solenoid is given by the same equation as above:

B = μ0 n I

So, the magnetic field at the ends of the solenoid depends only on the number of turns and current flowing through the solenoid, and is independent of the length and radius of the solenoid.

A force 103 newton stretches the length of a hanging wire by 1 millimetre. The force required to stretch a wire of same material and length but having four times the diameter by 1 millimeter is
  • a)
    1/16 x 103 N
  • b)
    1/4 x 103 N
  • c)
    4 x 103 N
  • d)
    16 x 103 N
Correct answer is option 'D'. Can you explain this answer?

Akshay Mukherjee answered
Understanding Wire Stretching
When a force is applied to a wire, it stretches based on its material properties and dimensions. The relationship between force, length, diameter, and stretching can be determined using the formula derived from Hooke's Law and the definition of Young's modulus.
Key Concepts
- Young's Modulus: It is a measure of the stiffness of a solid material and relates stress (force per unit area) to strain (deformation in length). The formula for Young's modulus (E) is given by:
E = (F/A) / (ΔL/L)
where F is the force applied, A is the cross-sectional area, ΔL is the change in length, and L is the original length.
- Cross-Sectional Area: The area (A) of a wire with diameter (d) is calculated as A = π(d/2)^2. If the diameter is quadrupled, the area increases by a factor of 16 (since area is proportional to the square of the diameter).
Calculating the Required Force
- Original Wire:
- Force (F1) = 103 N
- Stretch (ΔL1) = 1 mm
- New Wire:
- Diameter (d2) = 4 * d1
- Area (A2) = 16 * A1
The force required to stretch the new wire by the same amount (1 mm) can be calculated using the relationship of force and area:
- The force required (F2) for the new wire will be:
F2 = (E * A2 * ΔL) / L
Since A2 is 16 times A1, we have:
- F2 = 16 * (E * A1 * ΔL) / L = 16 * F1
Thus, F2 = 16 * 103 N = 16 x 103 N.
Conclusion
The force required to stretch the wire with four times the diameter by 1 mm is indeed 16 x 103 N, confirming that option 'D' is correct.

In a Binomial distribution, the probability of getting a success is 1/4 and standard deviation is 3. Then its mean is
  • a)
    6
  • b)
    8
  • c)
    12
  • d)
    10
Correct answer is option 'C'. Can you explain this answer?

Gaurav Kumar answered
Let n be successive independent trials and p the probability of getting a success.
 
The the mean and variance of a binomial distribution is given by :
 
Mean = np
 
Variance = np(1 - p)
 
In this case we have :
 
p = 1/4
 
Variance = (standard deviation) ²
 
Variance = 3² = 9
 
From this we can get the value of n as follows :
 
Variance = np(1 - p)
 
Doing the substitution we have
 
9 = 1/4n( 1 - 1/4)
 
9 = 1/4n(3/4)
 
9 = 3/16n
 
n = 16/3 × 9
 
n = 48
 
Mean = np
 
Mean = 48 × 1/4 = 12
 
The mean of the binomial distribution is equal to 12.

Circles x²+y²-2x-4y and x²+y²-8y-4=0Options
  • a)
    touch internally
  • b)
    touch externally
  • c)
    intersect at two points
  • d)
    do not intersect
Correct answer is option 'A'. Can you explain this answer?

Leelu Bhai answered
The simplest method is that, you can draw their graphs from the given equations of the two circles...and see from there that they will touch internally....

firstly, you make the equation in general form of circle i.e, (x - h)² + (y - k)² = (r)² by completing the square method ....you will get the following two equations:-.
(x -1)² + (y - 2)² = (√3)² and (x - 0)² + (y - 4)² = (√20)²

now draw their graphs ....and check that they will touch internally...
so your answer is option A....

The line y=mx+c touches the parabola x2=4ay if
  • a)
    c=-am
  • b)
    c=-am
  • c)
    c=-am2
  • d)
    c=a/m2
Correct answer is option 'C'. Can you explain this answer?

Anonymous answered
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

A lift of mass 1000 kg is moving with an acceleration of 1 m−s⁻2 in upward direction. Tension developed in the string, which is connected to the lift, is
  • a)
    9,800 N
  • b)
    10,000 N
  • c)
    10,800 N
  • d)
    11,000 N
Correct answer is option 'C'. Can you explain this answer?

Meera Choudhury answered
/s^2. What is the tension in the cable that is pulling the lift?

To find the tension in the cable, we need to use Newton's second law of motion, which states that the force acting on an object is equal to its mass times its acceleration:

F = m*a

where F is the force, m is the mass, and a is the acceleration.

In this case, the force we're interested in is the tension in the cable, and the mass is the mass of the lift. So we can rewrite the equation as:

T = m*a

where T is the tension in the cable, m is the mass of the lift, and a is the acceleration.

Plugging in the given values, we get:

T = 1000 kg * 1 m/s^2

T = 1000 N

Therefore, the tension in the cable that is pulling the lift is 1000 N.

Amongst the halides
(1) BCl3
(2) AlCl3
(3) GaCl3 
(4) InCl3
The order of decreasing Lewis acid character is
  • a)
    1 > 2 > 3 > 4
  • b)
    4 > 3 > 2 > 1
  • c)
    3 > 4 > 2 > 1
  • d)
    2 > 3 > 4 > 1
Correct answer is option 'A'. Can you explain this answer?

Avantika Saha answered
Lewis acid strength of group 13 halides follow the order : BCl3 > AlCl3 > GaCl3 > InCl3.
As we move down the group, the size of atom increases, and as a result, the tendency to attract electrons decreases. This leads to a decrease in Lewis acid nature down the group 

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
  • a)
    x2+y2-2x+2y-62=0
  • b)
    x2+y2-2x+2y-47=0
  • c)
    x2+y2+2x-2y-47=0
  • d)
    x2+y2+2x-2y-62=0
Correct answer is option 'B'. Can you explain this answer?

Yash Patel answered
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
⇒x2+y2−2x+2y−47=0.

 For n = 5, total number of electrons will be ___Options
  • a)
    32
  • b)
    50
  • c)
    48
  • d)
    68
Correct answer is option 'B'. Can you explain this answer?

Rajeev Choudhary answered
Explanation:

To find the total number of electrons, we need to know the electronic configuration of the element with atomic number 5.

The atomic number of an element represents the number of protons present in the nucleus of its atom. For an electrically neutral atom, the number of electrons will be equal to the number of protons.

Electronic configuration of Boron (atomic number 5) is 1s²2s²2p¹.

- The first shell (n=1) can hold a maximum of 2 electrons.
- The second shell (n=2) can hold a maximum of 8 electrons.
- The third shell (n=3) can hold a maximum of 18 electrons.
- The fourth shell (n=4) can hold a maximum of 32 electrons.

Therefore, the total number of electrons in Boron will be:

1s²2s²2p¹ = 2 + 2 + 1 = 5

However, the question asks for the total number of electrons for n=5. This means we need to consider the elements with atomic numbers ranging from 1 to 5. The electronic configurations of these elements are:

- Hydrogen (atomic number 1): 1s¹
- Helium (atomic number 2): 1s²
- Lithium (atomic number 3): 1s²2s¹
- Beryllium (atomic number 4): 1s²2s²
- Boron (atomic number 5): 1s²2s²2p¹

Adding up the total number of electrons for each of these elements, we get:

1 + 2 + 2 + 4 + 5 = 14

Therefore, for n=5, the total number of electrons will be 14.

However, the question has a typo and it should be for n=4 instead of n=5. In that case, the total number of electrons will be:

1 + 2 + 2 + 4 + 5 = 14

Adding up the maximum number of electrons that can be accommodated in the first four shells:

2 + 8 + 18 + 32 = 60

Therefore, for n=4, the total number of electrons will be 60.

Option B. 50 is not the correct answer.

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