Correct Answer: $3 \mathrm{~cm}$

Solution : Given: The distance between the centres of two circles of radii 2 cm and 6 cm is 5 cm
The length of the direct common tangent between two circles $ = \sqrt{d^2 - (r_1 - r_2)^2}$ where $d$ is the distance between the centres

Correct Answer: Rudimentary

Solution : The first option is the correct answer.

In the context of the sentence, advanced refers to the significant development and progress of evolutionary psychology. The antonym rudimentary fits well, indicating a basic or early stage of development, contrasting with the idea of significant advancement.

The

Correct Answer: 550 cm²

Solution : Given: The volume of a right circular cone is 1232 cm³ and its vertical height is 24 cm.
Let $r$, $h$, and $l$ be the radius, height, and slant height of the cone.
According to the question,
$\frac{1}{3}×\pi×r^2×h=1232$
Or, $\frac{1}{3}×\frac{22}{7}×r^2×24=1232$
Or, $r^2=\frac{1232×7×3}{22×24}$

Correct Answer: 23

Solution : Given:

In each row, the third number is the difference between the first two. 
Row 1: 134 – 34 = 100
Row 2: 117 – 86 = 31
Row 3: 87 – (?) = 64
⇒

Correct Answer: $100(\frac{Q-P}{Px-Qy})$

Solution : Given: $P$ is the principal, $x$ is the rate for 1st case, $Q$ is the principal and $y$ is the rate for the second case.
Let the amount be equal in $T$ years.
Simple interest = $\frac{P×R×T}{100}$
According to the question:
$P+\frac{P×x×T}{100}=Q+\frac{Q×y×T}{100}$
⇒ $\frac{PxT}{100}-\frac{QyT}{100}=Q–P$
⇒

Correct Answer: All conclusions follow

Solution : The possible Venn diagram according to statements given in the question is –

Conclusions I: Some alcohols are juices – From the diagram, it is clear that some part of the circle representing alcohol lies outside the circle representing juices. So it can

Correct Answer: Jaintia Hills

Solution : The correct answer is Jaintia Hills.

The Jaintia Hills are a portion of the Meghalaya plateau. The Meghalaya plateau is a highland area in Meghalaya, a state in northeastern India. It is a rolling tableland and the highest point of the hill range that

Correct Answer: Rs. 1,545

Solution : Given:
Principal = Rs. 12,500
Rate of Interest = 12%
Time = 1 year
Formula used:
Amount = $P(1+\frac{\frac{R}{2}}{100})^{2n}$ where n is the time in years and $R$ is rate of interest per annum when compounded half-yearly.
CI = $P(1+\frac{\frac{R}{2}}{100})^{2n} - P$
$\therefore n

Correct Answer: $\sqrt{145} \text{ cm}$

Solution : The distance between the centres of two circles with radii $r_1$ and $r_2$ (with $r_1 > r_2$), and the length of the transverse common tangent $t$,
$d = \sqrt{t^2 + (r_1 + r_2)^2}$
Substituting the given values into the equation:
$d = \sqrt{8^2

Correct Answer: Ustad Zakir Hussain

Solution : The correct option is Ustad Zakir Hussain.

The Indian tabla virtuoso and musician who won the "Best Contemporary World Music Album Grammy Award" for "Global Drum Project" is Zakir Hussain. He shared this Grammy Award with Mickey Hart, Sikiru Adepoju, and Giovanni