SRMJEE Mock Test - 8 (Engineering) - JEE MCQ

Magnetic field around the straight current carrying wire is given by:

B ∝ 1/r

For destructive interference, 2μtcosi = nλ
For normal incidence, i = 0
And for minimum thickness, n = 1

According to the principle of calorimetry:

ML_f + msΔT = (msΔT)_Water + (msΔT)_Flask

Step 1: First Addition of Ice
When 50 g of ice melts, the heat balance equation is:

50L_f + 50 × 1 × (40 - 0) = 200 × 1 × (70 - 40) + W × (70 - 40)

50L_f + 2000 = (200 + W) × 30

50L_f = 6000 + 30W → (Equation 1)

Step 2: Second Addition of Ice
After melting, the system contains (200 + 50) g = 250 g of water at 40°C. Now, 80 g of ice is added and melts, lowering the temperature to 10°C.

80L_f + 80 × 1 × (10 - 0) = 250 × 1 × (40 - 10) + W × (40 - 10)

80L_f + 800 = (250 + W) × 30

80L_f = 7500 + 30W → (Equation 2)

Step 3: Solving for L_f
Subtracting Equation 1 from Equation 2:

(80Lf - 50L_f) = (7500 + 30W) - (6000 + 30W)

30L_f = 1500

L_f = 1500 ÷ 30 = 90 cal/g

Step 4: Solving for W
Substituting L_f = 90 in Equation 1:

50 × 90 = 6000 + 30W

4500 = 6000 + 30W

30W = 4500 - 6000

30W = -1500

W = 50 g

Final Answer
The latent heat of fusion of ice is 90 cal/g, and the mass of the flask is 50 g.

Angular moment is the measure of amount of rotational inertia an object has.

It is a vector quantity and the unit for Angular momentum is kg m² s⁻¹kg.

Angular Impulse is the change in Angular momentum. It is also a vector quantity with the same unit as that of angular momentum

Just after the string becomes taut due to the impulse of the tension, that is, ∫Tdt=J⏐↓ say, the linear momentum changes from 0.

The angular impulse of the tension about C = JR, which changes the angular momentum from 0 to I_Cω.

Where,

This gives 

The velocity of P is 

Where v_PC = ωR and v_C= v

This gives v_P = ωR + v

The substituting w and v, we have 

Since the string is inextensible, v_P = v₀

This gives 

Hence 

As we know that
(Rate)₁ = k[A]^x
(Rate)₂ = k[4A]^x

According to the question, the rate is doubled when concentration is increased by 4 times.
Therefore, 2 = (4)^x
(2) = (2)^2x
x = 1/2
Thus, the order of the reaction is half.

For a 1^st order chemical reaction,


Arrhenius equation:

[A = Pre-exponential factor]
In a 1^st order reaction, the unit of the pre-exponential factor is reciprocal second.
Because the pre-exponential factor depends on the frequency of collisions, it is related to collision theory and transition state theory.

If atom or group of higher priority are on opposite direction at the double bond of each carbon atom then the configuration is known as E and if they are in same direction then the configuration is known as Z configuration.

PhS^- is a strong nucleophile and dimethyl formamide (DMF) is a highly polar aprotic solvent. Condition indicates that nucleophilic substitution (S_N2) takes place at 2° benzylic place, stereochemically, it involves inversion of configuration.

Let A be an invertible symmetric matrix.
We have AA^–1 = A^–1A = I_n
⇒ (AA^–1)' = (A^–1A)' = (I_n)'
⇒ (A^–1)' A' = A'(A^–1)' = I_n
⇒ (A^–1)' A = A(A^–1)' = I_n
(A^–1)' = A^–1 [inverse of a matrix is unique]

Given that,
sin A + cos B = a ...(i)
and sin B + cos A = b ...(ii)
On squaring and adding Eqs. (i) and (ii), we get

⇒ 2sin (A + B) + 2 = a² + b²
⇒ 

The equation of the ellipse can be assumed as:

x²/a² + y²/b² = 1

Now, the points P, Q, and R can be written as:

P (a cos 2α, b sin 2α), Q (a cos 2β, b sin 2β), and R (a cos 2γ, b sin 2γ).

The equation of the chord PR is:

x a cos(α + γ) + y b sin(α + γ) = cos(α - γ)

Let us assume that the chord PR passes through the focus (-ae, 0).

⇒ -e = cos(α - γ) cos(α + γ) …(i)

The equation of the chord PQ is:

x a cos(α + β) + y b sin(α + β) = cos(α - β)

PQ passes through the focus (ae, 0).

∴ e = cos(α - β) cos(α + β) …(ii)

Now, from (i) and (ii), we get:

Applying componendo and dividendo, we get

Let h be the height of the cone and α be the semi-vertical angle. Then,

h = 20 cm, α = 30°, and dα/dt = 2 deg/sec

We have to find dr/dt.

From trigonometry, the relation between r and α is:

tan α = r / 20
⇒ r = 20 tan α

Differentiating with respect to t, we get:

dr/dt = 20 sec² α × dα/dt

Substituting α = 30°:

dr/dt = 20 (sec 30°)² × 2

Since sec 30° = 2/√3,

dr/dt = 20 × (4/3) × 2

⇒ dr/dt = 160/3 cm/sec

log₂₀₀₄(log₂₀₀₃(log₂₀₀₂(log₂₀₀₁x)))  is defined if
log₂₀₀₃(log₂₀₀₂(log₂₀₀₁x)) > 0

Therefore, c = (2001)²⁰⁰²

m  is constant for last two sigma so ⁿC_m will come outside and replace ^mC_p and ^pC_k by applying formula 

(Multiply and divide by (m − k)!

Consider 

= 

Adding and subtracting 2^m.

Given,

Expanding with respect to R₁

⇒ x³ + y³ + z³ − 3xyz = 0
⇒ (x + y + z)(x² + y² + z² − xy − yz − zx) = 0
⇒ (x + y + z){x² + y² + z² + xy(ω + ω²) + yz(ω + ω²) + xz(ω + ω²)} = 0
⇒ (x + y + z)(x + yω + zω²)(x + yω² + zω) = 0
⇒ The determinant vanishes, i.e., the value of the determinant is zero if x = y = z or x + yω + zω² = 0.

Let the age of Guri and Shuri five years ago be x and y, respectively.
According to the question,
x + y = 36
x = 36 - y ... (i)
Also,x - y = 4
Putting the value of x as given in (i) we get,
36 - y - y = 4
36 - 2y = 4
-2y = 4 - 36
-2y = -32
2y = 32
y = 32 ÷ 2
y = 16
Therefore, the age of Shuri, 5 years ago = 16 years
Putting y = 16 in the equation x - y = 4,
x - 16 = 4
x = 4 + 16
x = 20
Hence, age of Guri, 5 years ago = 20 years
Present age of Guri = 20 + 5 = 25 years
Present age of Shuri = 16 + 5 = 21 years
Age of Guri and Shuri, 7 years from now, will be 32 years and 28 years, respectively.
Required ratio = 32 : 28
= 8 : 7

Given equations: 15p – 45q = 24 and 6p – 18q = 48/5
We will compare these equations with a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0.
15/6 = =
5/2 = 5/2 = 5/2
This implies

So, the given pair of equations has infinite solutions.

Area of circle = πr²

Given, area of the circle = 745.3 sq. cm

πr² = 745.36 sq cm

Circumference of a circle = 2πr

= 96.8 cm.

Thus, option D is the correct answer.

We assume that;

AB is the tower and CD is the platform.
Then,

Thus, the required distance = 40√3 m

Let the ten’s digit be T.

Then, the unit digit = 2T, and the hundred’s digit = (2T) ÷ 1.5.

According to the question:

T + 2T + [2T ÷ 1.5] = 13
1.5T + 3T + 2T/1.5 = 13
(1.5T + 3T + 2T) = 13 × 1.5
1.5T + 3T + 2T = 19.5
6.5T = 19.5
T = 19.5 ÷ 6.5
T = 3

So, the unit digit = 6, the ten’s digit = 3, and the hundred’s digit = 4.

Therefore, the number is 436.

Height of platform = 5 m
Relative height of tower from the platform = 40 m
Elevation of tower = 30°
Distance of platform from tower D
tan30° = height/base

D = 40√3 m

If you do something on the spur of the moment, you do it suddenly, without planning it beforehand.
For example: They admitted they had taken a vehicle on the spur of the moment.
It wasn't a spur-of-the-moment decision.
Hence, this is the correct answer.

It can be inferred from the given lines of the passage, "But a point to note here is that modern retailers themselves push their own private brands in these very categories and can emerge as a big threat for the consumer goods and foods companies. For instance, the private label Clean Mate of Big Bazaar is hugely popular and sells more than a brand like Harpic in its own stores". So, there is a certain amount of conflict and competition that will play out over the next few years which the FMCG companies will have to watch out for", said KPMG's executive director (retail)".
Therefore, option A is correct according to the passage.

The minister suggested the king to make a declaration that whoever has he dog who used to live at the royal elephant's shed will be penalized. 
Hence, it is the correct option.

The elephant was actually missing the dog.The minister diagnosed that the elephant was feeling lonely due to the loss of his dear friend. 
Hence, it is the correct option.