The correct answer is option 1 i.e. 4 : 5.

Let total employees in A = 2x and B = 3x

Female in A = (2x)/3

Female in B = 2(2x)/3 = (4x)/3

Male in A = 2x - (2x)/3 = (4x)/3

Male in B = 3x - (4x)/3 = (5x)/3

The ratio of male employees (A : B) = (4x)/3 : (5x)/3 = 4:5

The correct answer is option 1 i.e. 6,750. 

Let ₹x be lent at 9%,

so ₹(9000 − x) at 7%

Total interest = 8.5% of 9000 = ₹765

According to the question,

⇒ 63000 - 7x + 9x = 76500

⇒ 2x = 13500

⇒ x = 6750

The correct answer is option 2 i.e. 25.

(303 + 9p)/(41 + p) = 8

⇒ 303 + 9p = 328 + 8p

⇒ p = 328 - 303 = 25

The correct answer is option 4 i.e. 990.

Let the other side = b

Using Pythagoras: 101² = 20² + b²

⇒ 10201 = 400 + b²

⇒ b² = 9801

⇒ b = 99 cm

Area = (1/2) × base × height

= (1/2) × 20 × 99

= 990 cm²

The correct answer is Option 4 i.e. 130.

∆MAN ≅ ∆CPT (Corresponding angles are equal)

∠M = ∠C = 75°

∠A = ∠P = 40°

∠N = ∠T = 65°

∠C = x/2 = 75 ⇒ x = 150

∠P = 6y + 16 = 40 ⇒ y = 4

So, (x – 5y) = 150 – 5(4) = 150 – 20 = 130°

The correct answer is option 2 i.e. 18°.

D - F = 25% - 20% = 5%

Central angle = (5/100) × 360° = 18°

The correct answer is Option 3 i.e. 594.

N = 2⁸ × 3⁶ × 5⁴ ×10⁵ = 2¹³ × 3⁶ × 5⁹

N = 120(2¹⁰ × 3⁵ × 5⁸)

Number of factors that are multiples of 120

⇒ (10 + 1)(5 + 1)(8 + 1)

⇒ 11 × 6 × 9 = 594

The correct answer is option 1 i.e. log_b c = 2 log_b a – 1

Explanation:

log_a b + log_a c = 2 = log_a (bc) = 2

bc = a²

b/a = a/c

log_bb – log_b a = log_b a – log_b c

1 = 2 log_b a – log_b c

log_b c = 2 log_b a – 1

The correct answer is option 3 i.e. 10 cm.

Given that

Two circles of radii 12 cm and 13 cm are concentric

The chord PQ touches the small circle at S

OP = 13 cm, OS = 12 cm

In triangle OPS,

⇒ OP² = OS² + PS²

⇒ PS² = 13² - 12² = 169 - 144 = 25 

⇒ PS = 5 cm

Hence, the chord length PQ = 2 × 5 = 10 cm

The correct answer is option 3 i.e. 324.

The length of the floor of a rectangular hall = 126 feet

The breadth of the floor of a rectangular hall = 90 feet

The side of the largest identical square tiles = HCF of length and breadth of the floor area of the hall

The side of largest identical square tiles = the HCF of (126, 90) = 18 feet

Hence, the area of square tiles = 18 × 18 = 324 feet²