188 Mathematics MCQ Questions in english हिन्दी

Share:

The probability of an event A is 0.4. What is the probability of its complement?

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

The angle of elevation of a tower from a point 50 m away is 30°. What is the height of the tower?

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.

If $ \cos \theta = \frac{1}{2} $, what is $ \theta $ (in degrees, 0 ≤ $ \theta $ < 360)?

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

The perimeter of a square is 48 cm. What is its area?

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

A rectangle has a length of 12 cm and a width of 5 cm. What is the length of its diagonal?

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

An equilateral triangle has sides of length 6 cm. What is its area?

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.

The area of a sector of a circle is 308 cm², and the central angle is 45°. What is the radius of the circle?

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?

banner ad

If $ \frac{1}{x} + \frac{1}{y} = 1 $ and $ xy = 12 $, what is the value of $ x + y $?

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 $,

What is the value of $ x $ if $ 2x + 3 = 7x - 2 $?

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

If $ 2x + 3y = 12 $ and $ 3x - 2y = 5 $, what is the value of $ x + y $?

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 $.

The difference between two numbers is 30, and the smaller number is 13 more than half of the greater number. What is the greater number?

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 $.

If $ x + y + z = 0 $, then what is the value of $ \frac{x^2}{yz} + \frac{y^2}{xz} + \frac{z^2}{xy} $?

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 $.

A shopkeeper mixes two varieties of pulses worth Rs. 50/kg and Rs. 75/kg to get a mixture worth Rs. 65/kg. In what ratio should they be mixed?

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

If the cost of apples increases by 20% and then decreases by 20%, what is the net percentage change?

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\% $.

banner ad

A car travels 275 km at 50 km/h and 315 km at 70 km/h. What is the average speed for the entire journey

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).

A sum of Rs. 25,000 amounts to Rs. 31,000 in 4 years at simple interest. What is the rate of interest?

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\% $.

The sum of two numbers is 90, and one of them exceeds the other by 16. What is the smaller number?

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.

If 2x + 3y = 12 and 3x - 2y = 5, what is the value of x + y?

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

The difference between two numbers is 30, and the smaller number is 13 more than half of the greater number. What is the greater number?

Let the greater number be x, smaller number be y. Given x - y = 30 and y = (x/2) + 13. Substitute y in the first equation: x - (x/2 + 13) = 30. Solving, x/2 = 43, so x = 86.

If x + y + z = 0, then what is the value of (x²/yz) + (y²/xz) + (z²/xy)?

Since x + y + z = 0, we can use algebraic manipulation. The expression simplifies to (x³ + y³ + z³)/(xyz). Since x + y + z = 0, x³ + y³ + z³ = 3xyz. Thus, the value is 3xyz/xyz = 3. However, rechecking the options and problem context, the correct simplification yields 0 in some cases due to cancellation (common UPSC trick).

A shopkeeper mixes two varieties of pulses worth Rs. 50/kg and Rs. 75/kg to get a mixture worth Rs. 65/kg. In what ratio should they be mixed?

Using the rule of alligation: (75 - 65) : (65 - 50) = 10 : 15 = 2 : 3. The ratio of cheaper to dearer is 3:2, so the answer is 2:1 for dearer to cheaper.

banner ad

If the cost of apples increases by 20% and then decreases by 20%, what is the net percentage change?

Let original price = 100. After 20% increase, price = 120. After 20% decrease, price = 120 × 0.8 = 96. Net change = (96 - 100)/100 × 100 = -4%.

A car travels 275 km at 50 km/h and 315 km at 70 km/h. What is the average speed for the entire journey?

Total distance = 275 + 315 = 590 km. Time for first part = 275/50 = 5.5 hours; second part = 315/70 = 4.5 hours. Total time = 5.5 + 4.5 = 10 hours. Average speed = 590/10 = 59 km/h (approx. 58.33 km/h).

Simple Interest (SI) = Amount - Principal = 31,000 - 25,000 = 6,000. SI = PRT/100, so 6,000 = (25,000 × R × 4)/100. Solving, R = 6%.

Simple Interest (SI) = Amount - Principal = 31,000 - 25,000 = 6,000. SI = PRT/100, so 6,000 = (25,000 × R × 4)/100. Solving, R = 6%.

A sum of Rs. 25,000 amounts to Rs. 31,000 in 4 years at simple interest. What is the rate of interest?

Simple Interest (SI) = Amount - Principal = 31,000 - 25,000 = 6,000. SI = PRT/100, so 6,000 = (25,000 × R × 4)/100. Solving, R = 6%.

The sum of the digits of a two-digit number is 11. If the digits are reversed, the number increases by 27. What is the original number?

Let the tens digit = x, units digit = y So the number = 10x + y

A cylinder and a cone have the same base radius and height. If the volume of the cylinder is 150 cm³, what is the volume of the cone?

Volume of a cylinder = πr²h Volume of a cone = (1/3)πr²h = (1/3) × Volume of the cylinder ⇒ (1/3) × 150 = 75 cm³

If length of arc = 5π & radius = 10, central angle =

(arc = rθ → θ rad = 5π/10 = π/2 rad = 90°)

banner ad
×
Subscribe now

for Latest Updates

Articles, Jobs, MCQ and many more!