Correct Answer: (3)

Solution : The correct answer is the third option, "which allowed them to sit for the exams".

It maintains the intended meaning that the college authority, i.e., the officials forming an organisation having power and control, permitted the students to take the exams and would be

Correct Answer: He started with the element having the lowest atomic mass (hydrogen) and ended with thorium which was the 56th element

Solution : The correct option is He started with the element having the lowest atomic mass (hydrogen) and ended with thorium, which was the 56th element.

Newlands' law

Correct Answer: EHJ

Solution : Let's check the options –
First option: EHJ; E + 3 = H; H + 2 = J
Second option: JML; J + 3 = M; M – 1 = L
Third option: PSR; P + 3 = S; S – 1 = R
Fourth

Correct Answer: 6 years , or till they attain 65 years of age 

Solution : The correct option is 6 years , or till they attain 65 years of age .

The term of office for a member of the Union Public Service Commission (UPSC) in India is six years

Correct Answer: Coulomb

Solution : The correct option is Coulomb.

One coulomb is defined as the amount of electric charge transported by a constant current of one ampere in one second. In other words, 1 C = 1 A·s (ampere-second).

C= Coloumb

A= Ampere has a fixed numerical value.

s=

Correct Answer: Small Intestine

Solution : The correct option is the Small intestine.

Villi are tiny, finger-like extensions that line the small intestine's walls. They are composed of specialised cells and are surrounded by even smaller projections known as microvilli. The surface area of the intestinal lining is considerably

Correct Answer: $60^{\circ}$

Solution : $7\cos^{2}\theta +3\sin^{2}\theta = 4$
$⇒7\cos^{2}\theta +3(1-\cos^{2}\theta) = 4$ ........[we know that $\sin^{2}\theta + \cos^{2}\theta=1$]
$⇒4\cos^{2}\theta +3 = 4$
$⇒\cos^{2}\theta = \frac{1}{4}$
$⇒\cos^{2}\theta - \frac{1}{4}$ = 0
$⇒(\cos\theta + \frac{1}{2})(\cos\theta - \frac{1}{2})$ = 0
$⇒\cos\theta =\frac{1}{2}\ \text{or,} -\frac{1}{2}$
$⇒\cos\theta =\cos 60^{\circ}\ \text{or,}\cos 120^{\circ}$
Since $\theta$ is

Correct Answer: Implementation

Solution : To complete the sentence correctly, we need a word that conveys that these projects have reached the final stage where conclusions or solutions are being determined. The word "resolution" fits here. In the context of projects, it refers to reaching a final decision or finding

Correct Answer: 8 cm

Solution :
Let O be the centre of the concentric circle of radii 5 cm and 3 cm, respectively. Let PQ be a chord of the larger circle that touches the smaller circle at point M.
OM $\perp$ PQ
In $\triangle \mathrm{OMP}$,
$\mathrm{OP^2=OM^2+PM^2}$
⇒ $\mathrm{5^2=3^2+PM^2}$
⇒

Correct Answer: 4.8 cm

Solution : Given: $\triangle BAC\sim \triangle PQR$.
The area of $\triangle BAC$ and $\triangle PQR$ is 25 cm² and 36 cm² respectively.
BA = 4 cm
A similar triangle's area is proportional to the squares of the respective sides.
Let PQ be $x$ cm.