SRMJEE Mock Test - 5 (Engineering) - JEE MCQ

Y = FL/Al
or
or F ∝ A or F ∝ r² or F ∝ d²
∴
Given, d₁ = d, d₂ = 2d, F₁ = 200 N
∴
or F₂ = 4 × 200 = 800 N

Since the charges are placed along the same straight line, the electric field at x = 0 will be directed along the x-axis and its magnitude is given by:

^{which is choice (1).}

K.E. of emitted electrons = radiation of energy - work function
= 6.2 eV - 4.2 eV = 2 eV = 2 x 1.6 x 10^-19 J = 3 x 10^-19 J (approx.)

Let the mass of all the liquids be m.
Let s₁, s₂, s₃ be the respective specific heats of the liquids A, B, and C.
The initial temperatures of A, B, and C are 12°C, 19°C, and 28°C, respectively.

Case 1: Mixing A and B
When A and B are mixed, the temperature of the mixture is 16°C.

We know that heat gained by A = heat lost by B,

m s₁ (16 - 12) = m s₂ (19 - 16)

4 s₁ = 3 s₂ ...(i)

Case 2: Mixing B and C
When B and C are mixed, the temperature of the mixture is 23°C.

m s₂ (23 - 19) = m s₃ (28 - 23)

4 s₂ = 5 s₃ ...(ii)

From (i) and (ii):
s₁ = (3/4) s₂ = (15/16) s₃

Case 3: Mixing A and C
When A and C are mixed, suppose the temperature of the mixture is t.

m s₁ (t - 12) = m s₃ (28 - t)

Substituting s₁ = (15/16) s₃:

(15/16) s₃ (t - 12) = s₃ (28 - t)

Canceling s₃ from both sides:

(15/16) (t - 12) = (28 - t)

Multiplying by 16:

15t - 180 = 448 - 16t

31t = 628

t = 628 / 31 = 20.3°C

Thus, the final temperature when A and C are mixed is 20.3°C.

Let gravitation field be zero at P as shown in figure.

Therefore,

=

In liquids, the object will experience an upward thrust known as buoyant force.

By Newton's Second Law,

The effective acceleration of the bob in water

where, σ and ρ are the density of water and the bob, respectively.

Since the period of oscillation of the bob in air and water are given as,

Putting, 
we obtain, 1/2 = 1 - 1/ρ
⇒   ρ = 2 g cm^-3

• Cube density: ρ = 0.5 g/cm³
• Liquid density: σ = 1 g/cm³
• Normal reaction: N = mg - Fb, where Fb = σAhg (buoyant force), and h = vt (liquid height).

So the equation becomes: N = mg - σA(vt)g.
As time (t) increases, N decreases linearly until the cube floats (Fb = mg), at which point N = 0.
Graph: The graph shows a linear decrease to zero, then it flattens out (option A).

Given the electric field equation, E = E₀ sin(kx − ωt),
Comparing with the standard equation, we get:
k = 2π/λ and ω = 2πf,
where f is the frequency and λ is the wavelength.
Now, k/ω = 1/λf = 1/c, where c is the speed of light in vacuum.
Thus, wavelength is independent of k/ω.

Correct answer: A

Phenols, on treatment with neutral FeCl₃ solution, produce purple colour. Resorcinol contains phenolic groups, hence on treatment with neutral FeCl₃ solution, it gives purple colour.

Resorcinol’s phenolic groups react with neutral FeCl_3​ to form a purple complex, and the reason explains this.

Fructose, reduced by NaBH₄​, yields sorbitol and mannitol (epimers at C₂) in equimolar amounts due to its ketone group. Mannose, glucose, and xylose (aldoses) do not produce this mixture. Answer C is correct.

The ninhydrin test is a chemical test which is used to check whether a given mixture contains amines or α-amino acids
The compound undergoes a chemical reaction with ninhydrin. Ninhydrin behaves as an oxidizing agent, hence the amino acid undergoes oxidative deamination, and liberates carbon diioxide, ammonia and an aldehyde along with hydrindantin (which is a reduced form of ninhydrin).
Now, the ammonia gas to reacts with another ninhydrin molecule to form diketohydrin (which is also known as Ruhemann’s complex). This complex is responsible for the deep blue colour.
If the mixture contains amino-acids secondary amine, a yellow coloured complex is formed.
Proline being a secondary amine gives a yellow orange colour with ninhydrin whereas all other α−amino acids give a blue-purple colour with ninhydrin.

Proline lacks a primary amino group, forming a yellow-orange product with ninhydrin, unlike glycine, lysine, and aspartic acid, which form purple.

Ptyalin is present in human saliva. The optimum pH for Ptyalin activity is 5.6 − 6.9. But normally stomach pH is 1.5 − 3.5. So activity of Ptyalin decreases in stomach.

Ptyalin is active in saliva (pH  6.8) but denatures in stomach acid, decreasing its activity.

The formula for the elevation in boiling point is:
ΔT₆ = K_b × m

where,
K_b = Molal elevation constant
m = Molality

Molality can be written as:
m = (w × 1000) / (GMM × W)

where,

w = Weight of the solute
W = Weight of the solvent
GMM = Gram molecular mass of the solute
When m = 1, which means 1 mole of solute in 1 kg of solvent, the equation simplifies to:
ΔT₆ = K_b

where,
K_b = (R × T_b²) / (1000 × L_v)

T_b = Boiling point of the solvent
L_v = Latent heat of vaporization

Molal elevation constant (K_b​) is the boiling point elevation when 1 mole of non-electrolyte is dissolved in 1000 g of solvent. Answer C is correct.

A fuel cell is an electrochemical device that combines hydrogen and oxygen to produce electricity with water and heat as by-products. 

In a hydrogen-oxygen fuel cell, the following reactions take place to create a potential difference between the two electrodes.

The net reaction is the same as burning (combustion) of hydrogen to form water.

In alkali metals, the reactivity increases down the group due to decrease in IE₁ . But in case of halogens, the reactivity decrease down the group due to decrease in their electrode potentials.

It is antipyretic i.e., a drug which is responsible for lowering the temperature of feverish organism to normal.
Antibiotics are used as drugs to treat infections because of their low toxicity for humans and animals.
Antiseptics are applied to the living tissues such as wounds, cuts, ulcers and diseased skin surfaces.

Antipyretics (e.g., paracetamol) lower body temperature in fever, unlike pyretics, antibiotics, or antiseptics.

α + β =
αβ = (-1)/1 
So, α² + β² = (α + β)² - 2αβ = (2)² - 2(-1) = 4 + 2 = 6

According to De Moivre 's theorem we get, (cosθ + i sinθ)ⁿ = cos nθ + isin nθ
Let z = √3 + i ...........(1)
r = |z| =
z =
Let z = r(cosθ + i sinθ) .........(2)
By comparing (1) and (2), we get
cos θ =
sin θ =
Therefore,
z¹⁰ = 2¹⁰
= 1024
= 1024
= 512 - 512 √3i
a = 512 and b = -512√3

Probability of hitting a target (p) = 1/5
∴ Probability of not hitting a target (q) =
Probability that none will be hit in 10 shots = (4/5)10
∴ Required probability = 

Hence, the correct answer is option 4.

Let the distance between observer and flagstaff = x

Now from above figure, we have:

Given the quadratic equation:
ax² + 2bx + c = 0

Since b² = ac, we can rewrite the equation as:
ax² + 2√(ac)x + c = 0

Factoring, we get:
(√a * x + √c)² = 0

So, x = -√c / √a , -√c / √a

Thus, aα = aβ

Now, consider the equation:
cx² + 2bx + a = 0

Rewriting using b² = ac:
cx² + 2√(ac)x + a = 0

Factoring, we get:
(√c * x + √a)² = 0

So, x = -√a / √c , -√a / √c

Thus, cγ = cδ

Therefore, aα = aβ = cγ = cδ

Given, ...(1)

Replacing x by 2/x we get,

Comparing the coefficient of x⁷,

Given:

f(x) = (x - 1)(x - 2)(x - 3) …(1)

Expanding,
f(x) = x³ - 6x² + 11x - 6

For every x in R, f(x) is also in R.
The range of every odd-degree polynomial is R.

Hence, the range of f(x) is R.

Also,
f(1) = f(2) = f(3) = 0.

We know that if a continuous function has more than one root, then the function is many-one.

Therefore, f(x) is not one-one.

For each y in R, there exists x in R such that f(x) = y.

Therefore, f(x) is onto.

Given,

ⁿC₀ - ⁿC₁ + ⁿC₂ - ⁿC₃ + ... + (-1)^r * ⁿC_r = 28

let 

From binomial expansion, we can say that

S is equal to the coefficient of x in the expansion

 In the equation (1), the right-hand side is positive.

So, r must be even. Otherwise, (−1)^r becomes negative.

⇒ n − 1 = 8

⇒ n = 9

'Cordon off something' means to close an area to people and vehicles.
In other words, police isolate the area by putting a line of people or object, to prevent people from getting into, around or in front of it.

“Cordon off” means to restrict access, synonymous with isolating an area.
Hence, this is the correct option.

The correct answer can be inferred from the given line of the passage 'Science and Humanism are equally important' this statement reflects Nehru's point of view. In the passage, the scientist and the humanist were held in perfect balance .
Thus, statement "Science and humanism are equally important"  reflects Nehru's point of view.
Hence, the option (c) is the correct answer.