Correct Answer: 702

Solution : Cost of first variety = INR 504
The cost of the second variety = INR 540
The ratio in which rice varieties are mixed = 1 : 1 : 2
Let INR $x$ be the cost of the third variety.
Cost of mixed variety = INR 612
According to the question,
$\frac{504×1 + 540×1 + x×2}{1 + 1+ 2} = 612$
$⇒\frac{1044 + 2x}{4}= 612$
$⇒x=\frac{612×4 - 1044}{2}= 702$
Hence, the correct answer is 702.

Correct Answer: 28 cm

Solution : Volume of cylinder = $\pi r^2h$
The volume of the cylinder can be written as $32y$ and $9y$
The height of the cylinder can be written as $8h$ and $9h$
Since we know that the volume of the cylinder = Area of the base × height
⇒ Volume of second cylinder = $616 \times 9h$
Let the radius of the first cylinder be r
⇒ Base area of first cylinder = $\pi r^2$
Volume of first cylinder = $\pi r^2 \times 8h$
Their ratios can be written as
$⇒\frac{ 616 \times 9h}{(\pi r^2 \times 8h)} = \frac{9}{32}$
$⇒\frac{(22r^2 \times 8)}{(616 \times 9 \times 7)} = \frac{32}{9}$
⇒ $r^2 = \frac{(616 \times 9 \times 32 \times 7)}{(9 \times 22 \times 8)}$
⇒ $r^2$ = 784
⇒ $r$ = 28
∴ The radius of the first cylinder is 28 cm.
Hence, the correct answer is 28 cm.

Correct Answer: 8,242

Solution : Simple interest (SI)= $\frac{\text{Principal × Rate × Time}}{100}$
 SI = INR 11,220
Rate = $16\frac{1}{2}$ = $\frac{33}{2}$%
Time = 8 years 3 months = $8\frac{3}{12}$ = $8\frac{1}{4}$ = $\frac{33}{4}$
According to the question,
11220 = $\frac{\text{P×33×33}}{100×2×4}$
⇒ P = $\frac{11220×800}{1089}$
= $\frac{8976000}{1089}$
= 8242.424
= 8242 Approx
Hence, the correct answer is 8,242.

Correct Answer: 21

Solution : Given:
If $\sqrt{AFI}\ :\ 13\ ::\ \sqrt{DDA}\ :\ ?$

The position values of A, F, and I are 1, 6, and 9 respectively.
On combining the place values, we get 169.
Now, $\sqrt{169}\ =\ 13$
Thus, $\sqrt{AFI}$ is coded as 13.
Similarly, follow the same pattern for $\sqrt{DDA}\ :\ ?$ –
The position values of D, D and A are 4, 4 and 1 respectively.
On combining the place values, we get 441.
Now, $\sqrt{441}\ =\ 21$

Thus, $\sqrt{DDA}$ is coded as 21. Hence, the third option is correct.

Correct Answer: $\sqrt{63}$

Solution : Given, the distance between the centres of two circles is 12 cm ($d$) and the radii are 5 cm ($r_1$) and 4 cm ($r_2$).
Length of the transverse common tangent line to the circle
= $\sqrt{d^2-(r_1+r_2)^2}$
= $\sqrt{12^2-(5+4)^2}$
= $\sqrt{144-81}$
​​​​​​= $\sqrt{63}\ \text{cm}$
Hence, the correct answer is $\sqrt{63}$.

Correct Answer: 1 : 5

Solution : 16 years ago, let my age and my grandfather's age be $x$ years and $9x$ years respectively.
According to the question,
$9x+16+8=3(x+16+8)$
⇒ $9x+24=3x+48+24$
⇒ $6x=48$
⇒ $x=8$
Required ratio 8 years ago,
= $(x+8):(9x+8)$
= (8 + 8) : (9 × 8 + 8)
= 16 : 80
= 1 : 5
Hence, the correct answer is 1 : 5.

Correct Answer: Both 1 and 2

Solution : The correct option is Both 1 and 2.

When a body is immersed in a liquid, it is subjected to two major forces. The first is the weight of the body, which pulls it downward owing to gravity. Upthrust (buoyant force) is the second force that propels the body upward. According to Archimedes' principle, this upthrust is equal to the weight of the liquid displaced by the body. If the weight of the body is less than the upthrust, it will float; otherwise, it will sink.

Correct Answer: 3

Solution : The correct option is 3.

The formation of new states and the alteration of areas, boundaries, or names of existing states in India are primarily governed by Article 3 of the Indian Constitution. Article 3 empowers the Parliament of India to make laws regarding the five matters.

(a) form a new state by the separation of territory from any state, by uniting two or more states or parts of states, or by uniting any territory with a part of any state;

(b) increase the area of any state;

(c) diminish the area of any state;

(d) alter the boundaries of any state;

(e) alter the name of any state.

Correct Answer: (4)

Solution : The fourth option is the correct choice.

''Too'' is used correctly in the sentence indicating that Viren plays both hockey and football.

Correct Answer: 11 days

Solution : Given: A and B working separately can do a piece of work in 9 and 15 days respectively. They work on alternate days, starting with A.
Let the total work = LCM of 9 and 15 = 45 units
A’s 1 day work = $\frac{45}{9}$ = 5 units
B’s 1 day work = $\frac{45}{15}$ = 3 units
If they work on alternate days, they will finish (5 + 3) = 8 units of work in 2 days,
In 10 days they will finish (8 × 5) = 40 units of work,
The remaining work = (45 – 40) = 5 units of work, which A can finish on the 11th day. 
So, the work will be completed in 11 days.
Hence, the correct answer is 11 days.