Correct Answer: 36

Solution : Given:
$4^{10}\times7^{3}\times16^{2}\times11\times10^{2}$
Rewrite this equation with the prime factors.
$(2^{2})^{10}\times7^{3}\times(2^{4})^{2}\times11\times2^{2}\times5^{2}$
= $2^{20+8+2}\times7^{3}\times11^{1}\times5^{2}$
= $2^{30}\times7^{3}\times11^{1}\times5^{2}$
Total number of prime factors = 30 + 3 + 1 + 2 = 36
Hence, the correct answer is 36.

Correct Answer: 28°

Solution : Given: Three angles of a triangle are (2y + 40°), (5y – 60°), and (3y – 80°).
We know that the sum of all three angles of a triangle is 180°.
Then, (2y + 40°) + (5y – 60°) + (3y – 80°) = 180°

Correct Answer: 3

Solution : Given that:
$p^3 + 3p^2 + 3p = 7$
Adding unity to both sides,
$p^3 + 3p^2 + 3p + 1 = 7 + 1$
⇒ $(p+1)^3 = (2)^3$
⇒ $p+1=2$
⇒ $p = 1$
$\therefore p^2 + 2p = 1 + 2 \times 1

Correct Answer:

Solution : As per the mirror image properties, closer things appear closer to the mirror in the reflection.
Here, according to the information provided, the mirror is placed on the right side of the figure (on line MN). So, the left side of the reflected image will appear

Correct Answer: 5 units

Solution : Equation of a circle with centre (0,0): $x^2+y^2=r^2$ where $r$ is the radius of the circle.
The radius of the circle $x^2+y^2=25$
⇒ $r=\sqrt{25}$ = 5 units
Hence, the correct answer is 5 units.

Correct Answer: 18th December

Solution : The correct option is 18th December.

Every year on 18th December, Minorities Rights Day is observed in India to promote the rights of minority populations. This day also emphasises improving understanding of and educating the public on matters about minorities and their protection.

Correct Answer: Both I and II

Solution : The correct answer is Both I and II.

In a perfectly competitive market, there are many sellers, and there is easy entry and exit of firms and homogeneous products. In a competitive market, no single consumer or producer has the

Correct Answer: 7500

Solution : Given:
20 : 1200 :: 28 : 2352 :: 50 : ?

Find the square of the first number and then multiply by 3 to obtain the second number.
Like, (20 : 1200)→(20)² × 3 = 400 × 3 = 1200
And, (28 :

Correct Answer: 7

Solution : Given:
a – b = 3
a³ – b³ = 117
We know,
a³ – b³ = (a – b)³ + 3ab(a – b)
⇒ 117 = 27 + 3ab(3)
⇒ 9ab = 117 – 27
⇒ 9ab = 90

Correct Answer: 25

Solution : Given:
8, 11, 22, ?, 50, 53

Add 3, and multiply 2 alternately to the numbers to obtain the next number of the series.
8 + 3 = 11; 11 × 2 = 22; 22 + 3 = 25; 25 × 2 = 50; 50