All numbers except 90 are perfect squares: 6² = 36, 7² = 49, 8² = 64, 9² = 81. 90 is not a perfect square, hence the odd one.

This is a cube analogy. 3³ = 27, so 5³ = 125. Hence, the answer is 125.

(5 + 3) = 8 → 8×3 = 24 (6+4) = 10 × 4 = 40 (7+5) = 12 × 5 = 60 → Answer is 60 Correction: Answer: A. 60

These numbers are squares of consecutive integers: 2²=4, 3²=9, 4²=16, 5²=25, so the missing number is 6² = 36, followed by 7² = 49.

Apple, banana, and mango are fruits, while carrot is a root vegetable. It is the only item not belonging to the fruit category, making it the odd one out

Each letter is incremented by 1: R → S, A → B, M → N. Similarly, K → L, I → J, T → U, E → F. Thus, KITE becomes LJUF.

Using the provided codes: N=9, E=1, P=3, A=5, L=7. Arranging for PANEL → P(3), A(5), N(9), E(1), L(7) gives 91357 as the correct code.

Raj's father's only sister is his aunt. The girl is the daughter of his aunt, making her Raj’s cousin. Hence, the correct relation is cousin.

Rearranging the word TRUST to USRTT involves placing vowels in front alphabetically and consonants after them alphabetically. For FAITH, vowels (A, I) come first alphabetically, then consonants (F, H, T) follow alphabetically → AIFHT.

In this series, the first letters are moving alphabetically forward: A, B, C, D. The second letters are moving backward from Z: Z, Y, X, W. So, the correct pair following CX is DW.

Probability of complement = $ 1 - P(A) = 1 - 0.4 = 0.6 $.

Let height = $ h $. Then, $ \tan 30^\circ = \frac{h}{50} $. Since $ \tan 30^\circ = \frac{1}{\sqrt{3}} $, we get $ \frac{h}{50} = \frac{1}{\sqrt{3}} $, so $ h = \frac{50}{\sqrt{3}} = \frac{50\sqrt{3}}{3} \approx 25\sqrt{3} $ m.

$ \cos \theta = \frac{1}{2} $ at $ \theta = 60^\circ $ or $ 300^\circ $. Since $ 0 \leq \theta < 360 $, $ \theta = 60^\circ $.

Perimeter = $ 4 \times \text{side} = 48 $, so side = 12 cm. Area = $ \text{side}^2 = 12^2 = 144 $ cm².

Diagonal = $ \sqrt{\text{length}^2 + \text{width}^2} = \sqrt{12^2 + 5^2} = \sqrt{144 + 25} = \sqrt{169} = 13 $ cm.

Area of an equilateral triangle = $ \frac{\sqrt{3}}{4} \times \text{side}^2 $. For side = 6 cm, area = $ \frac{\sqrt{3}}{4} \times 36 = 9\sqrt{3} $ cm².

Area of sector = $ \frac{\theta}{360} \times \pi r^2 $. Given area = 308 cm² and $ \theta = 45^\circ $, we have $ \frac{45}{360} \times \frac{22}{7} \times r^2 = 308 $. Simplify: $ \frac{1}{8} \times \frac{22}{7} \times r^2 = 308 $. Solving, $ r^2 = 784 $, so $ r = 28 $ cm. An equilateral triangle has sides of length 6 cm. What is its area?

Given $ \frac{1}{x} + \frac{1}{y} = 1 $, we have $ \frac{x + y}{xy} = 1 $. Since $ xy = 12 $, it follows that $ x + y = 12 $. Check with roots of $ t^2 - (x+y)t + xy = 0 $: $ t^2 - 12t + 12 = 0 $. Discriminant = $ 144 - 48 = 96 $, roots are $ t = \frac{12 \pm \sqrt{96}}{2} $. However, directly, $ x + y = 12 $, but testing pairs (e.g., 3, 4) gives $ x + y = 7 $,

Solve $ 2x + 3 = 7x - 2 $. Rearrange: $ 3 + 2 = 7x - 2x $, so $ 5 = 5x $, and $ x = 1 $.

Add the equations: $ (2x + 3y) + (3x - 2y) = 12 + 5 $, giving $ 5x + y = 17 $. Subtract: $ (2x + 3y) - (3x - 2y) = 12 - 5 $, giving $ -x + 5y = 7 $. Solve the system: multiply the first by 5 ($ 25x + 5y = 85 $) and subtract the second: $ (25x + 5y) - (-x + 5y) = 85 - 7 $, so $ 26x = 78 $, and $ x = 3 $. Substitute into $ 5x + y = 17 $: $ 5(3) + y = 17 $, so $ y = 2 $. Thus, $ x + y = 3 + 2 = 4 $.

Let the greater number be $ x $, and the smaller number be $ y $. Given $ x - y = 30 $ and $ y = \frac{x}{2} + 13 $. Substitute $ y $ in the first equation: $ x - \left( \frac{x}{2} + 13 \right) = 30 $. Solving, $ \frac{x}{2} - 13 = 30 $, so $ \frac{x}{2} = 43 $, and $ x = 86 $.

Given $ x + y + z = 0 $, the expression is $ \frac{x^2}{yz} + \frac{y^2}{xz} + \frac{z^2}{xy} $. This simplifies to $ \frac{x^3 + y^3 + z^3}{xyz} $. Since $ x + y + z = 0 $, we use the identity $ x^3 + y^3 + z^3 = 3xyz $. Thus, $ \frac{3xyz}{xyz} = 3 $.

Using the alligation rule: $ (75 - 65) : (65 - 50) = 10 : 15 = 2 : 3 $. Thus, the ratio of cheaper (50/kg) to dearer (75/kg) is 3:2, or dearer to cheaper is 2:1

Let the original price be 100. After a 20% increase, price = $ 100 \times 1.2 = 120 $. After a 20% decrease, price = $ 120 \times 0.8 = 96 $. Net change = $ \frac{96 - 100}{100} \times 100 = -4\% $.

Total distance = 275 + 315 = 590 km. Time for the first part = $ \frac{275}{50} = 5.5 $ hours; second part = $ \frac{315}{70} \approx 4.5 $ hours. Total time = $ 5.5 + 4.5 = 10 $ hours. Average speed = $ \frac{590}{10} = 59 $ km/h (approximately 58.33 km/h for precision).

Simple Interest (SI) = Amount - Principal = 31,000 - 25,000 = 6,000. Using the formula $ SI = \frac{P \times R \times T}{100} $, we get $ 6,000 = \frac{25,000 \times R \times 4}{100} $. Solving, $ R = 6\% $.

Let the smaller number be $ x $. Then the larger number is $ x + 16 $. Given $ x + (x + 16) = 90 $, we solve: $ 2x + 16 = 90 $, so $ 2x = 74 $, and $ x = 37 $. Thus, the smaller number is 37.

Add the equations: (2x + 3y) + (3x - 2y) = 12 + 5. This gives 5x + y = 17. Subtract: (2x + 3y) - (3x - 2y) = 12 - 5, giving -x + 5y = 7. Solve the system: x = 3, y = 1. Thus, x + y = 4. **What is the value of x if 2x + 3 = 7ostrar