VITEEE PCME Mock Test - 5 - JEE MCQ

Since the diagonals of a rhombus bisect each other,
∴ and
^So,

The general term of given expression (x² + cx)⁵ can be written as, 

Then for the coefficient of x,

∴10−3r=1
⇒ 3r = 9
⇒ r = 3 
The coefficient of 

So, 

Let A = {1, 2, 3}, B = {1, 3, 5}. A relation R: A → B is defined by R = {(1, 3), (1, 5), (2, 1)}.

Then, R⁻¹ (the inverse of R) is defined by:

R⁻¹ = {(3, 1), (5, 1), (1, 2)}

So, the correct answer is:

C. {(1, 2), (5, 1), (3, 1)}

Hence sum = 2π

Power gain = (Current gain)²

For virtual image, magnification m = 5 . Focal length f = −0.4 m = −40cm.

u + 40 = 8 ⇒u = −32cm

Distance: ∣u∣ = 32 cm

Given, a block of weight W rests on a rough horizontal plane, with the angle of friction θ,
Let N be the normal force and f be the limiting friction acting on the block, then the angle of friction is defined as,

tanθ = f/N = μ; where μ is the coefficient of friction.
So, the minimum force required to move the block should be equal to the frictional force applied on the block, i.e.,
F_min = μN = μW = W tanθ.

Let x be the equivalent resistance of the entire network between A and B. Hence, we have

R_AB = 1 + the resistance of the parallel combination of 1 Ω and x Ω


⇒ x + x² = 1 + x + x
⇒ x² − x − 1 = 0
⇒ 

From acting on block are shown in adjoining figure
As the block does not move, hence
Fcos60° = f = μN = μ(Mg + Fsin60°)


On simplification, we get F = 20N

Breaking force does not depend upon length.

Breaking force = breaking stress × area of cross-section

For a given material, breaking stress is constant.

∴ F₂ / F₁ = A₂ / A₁ = π(6r)² / πr² = 36

Or F₂ = 36F₁ = 36F

As the given condition is of balanced Wheatstone bridge, current can not flow through bridge arm whether switch is open or close. So, current in galvanometer will remain the same (zero) and would be independent of the position of switch.

In a balanced Wheatstone bridge:

Galvanometer current is zero.

Weight of the rod has to be balanced by the magnetic force such that tension in the strings become zero.
Let a current i is allowed to flow in the rod, such that,
magnetic force on the rod = Bil
where B is the magnetic field and ll is the length of the rod.
Now, weight of the rod = mg
Thus for no tension in the wire,
Bil = mg

= 5 A

The Celsius and Fahrenheit scales are related by the following equation:

C/5 = (F - 32)/9

where C is the temperature in degrees Celsius and F is in Fahrenheit.

Given: F = 140°F

Substituting the value:

(140 - 32)/9 = C/5

(140 - 32) = 108

108/9 = 12

C = 12 × 5 = 60°C

So, the temperature on the Celsius scale is 60°C.

Half-life of a radioactive element is given by,
T_h = 0.693 / λ
Where λ is called decay constant.
Mean-life of a radioactive element is given by T_m = 1/λ
Clearly, T_h < T_m

According to Nernst equation,

The Hinsberg reaction is an excellent test for distinguishing primary, secondary and tertiary amines. In this test, the amine is shaken well with Hinsberg reagent in the presence of an aqueous alkali (either KOH or NaOH). A reagent containing an aqueous sodium hydroxide solution and benzenesulphonyl chloride is added to a substrate to form sulphonamides.
RNH₂ (Primary amine) + C₆H₅SO₂Cl (Hinsberg reagent) → R-NH-SO₂-C₆H₅ R-N-Na⁺-SO₂C₆H₅ (Soluble)
R₂NH (Secondary amine) + C₆H₅SO₂Cl (Hinsberg reagent) → R₂NSO₂C₆H₅ (precipitate) No reaction (Insoluble)
R₃N (Tertiary amine) + C₆H₅SO₂Cl (Hinsberg reagent) → No reaction

Step 1: Acidic Hydrolysis of Diethylmalonate
Diethylmalonate has the structure:

 
When diethylmalonate undergoes acidic hydrolysis, the ester groups (–COOEt) are broken down by the acid, resulting in the formation of malonic acid:

Step 2: Heating the Malonic Acid
After hydrolysis, heating malonic acid leads to its decarboxylation (removal of a carbon dioxide molecule), which results in the formation of acetic acid (ethanoic acid):

Final Answer: After acidic hydrolysis followed by heating, the carboxylic acid formed is ethanoic acid (also known as acetic acid).

Thus, the correct answer is: D: Ethanoic acid

Both N^3- and O^2- are isoelectronic with each other, means they have the exact same electronic configuration. But O^2- has one more proton than N^3-; hence, the ionic radius of N^3- is larger than O^2-. Hence, statement P is correct.
In general, moving left to right across a period, atomic radius usually decreases, but in this case, both Cr (125 pm) and Co (125 pm) have exceptionally equal atomic radius. Thus, statement Q is false.
Technetium is the chemical element with atomic number 43 and symbol Tc. It is the lowest atomic number element without any stable isotope; every form of it is radioactive. Nearly all technetium is produced synthetically and only minute amounts are found in nature. Naturally occurring technetium occurs as a spontaneous fission product in uranium ore or by neutron capture in molybdenum ores. Thus, statement R is false.

After losing H^⊕  ions anion should be more stable and stability of anion is proportional to −M effect.
-M effect of 
Order of stability:

Thus order of acidity: A > B > C > D

The size of lanthanide ions decreases as we move through the lanthanides from lanthanum to lutetium. This steady decrease in the ionic radii of M⁺³ cations in the lanthanide series is called lanthanide contraction. Due to the lanthanide contraction, the atomic and ionic radius of the next and the before, on the lanthanide elements with the same group, are about the same, i.e., the atomic radius of Zr(group-4, period-5) and Hf (group-4, period-6) are almost the same.

Energy of electron in 2^nd orbit of Li⁺²
= 
Energy required = 0 − (−30.6) = 30.6 eV

We know that the activation energy of a chemical reaction
is given by the formula, 

The formula is obtained from the Arrhenius equation, where k₁ is the rate constant at the temperature T₁, k₂ is the rate constant at the temperature T₂ and E_a is the activation energy.
Therefore, the activation energy of a chemical reaction is determined by evaluating the rate constant at two different temperatures.

Here, Statement II is a simple continuation of Statement I. It further extends sentence I, and can be connected by using ‘for instance’. The correct formation of the sentence will be:
Studies on nonlinear dependence on applied voltage can be expanded to more complex quantum transport experiments, for instance, those on artificial atoms are called quantum dots.

In the first sentence, an adverb is required, which qualifies the verb. Replace ‘right’ with ‘rightly’.
Sentence B has an error (incorrect use of "criteria" instead of "criterion").
Hence, option C is the correct answer.

The correct answer is 'for'
A Preposition is a word or set of words that indicates location (in,near,beside) or some other relationship between a noun or pronoun or other parts of a sentence. The preposition 'for' usually tell us about the use of something, a reason or purpose.
So, in the given sentence, the subject left home for a purpose (for a walk). Hence, the correct answer is 'for'.