201 Mathematics MCQ Questions in english

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201 Mathematics MCQ Questions in english हिन्दी

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

A. 5%

B. 6%

C. 7%

D. 8%

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\% $.

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

A. 37

B. 53

C. 45

D. 48

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.

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

A. 3

B. 4

C. 5

D. 6

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

170. 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?

A. 86

B. 76

C. 56

D. 46

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.

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

A. 0

B. 1

C. 2

D. 3

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).

168. 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?

A. 1:2

B. 2:3

C. 2:1

D. 3:2

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.

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

A. 4% decrease

B. 4% increase

C. No change

D. 2% decrease

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

166. 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?

A. 58.33 km/h

B. 60 km/h

C. 62.5 km/h

D. 65 km/h

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).

165. 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. 5%

B. 6%

C. 7%

D. 8%

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%.

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

A. 5%

B. 6%

C. 7%

D. 8%

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%.

163. 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?

A. 38

B. 42

C. 32

D. 12

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

162. 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?

A. 50 cm³

B. 75 cm³

C. 100 cm³

D. 125 cm³

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

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

A. 90°

B. 45°

C. 72°

D. 36°

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

160. If u: twice differentiation of x³ gives

A. 6x²

B. 2x

C. 4x

D. 6x

159. Equation of perpendicular bisector of AB joining (2,3) and (6,7):

A. x + y = 9

B. x – y = –1

C. x – y = 1

D. x + y = 5

x + y = 9

158. The radius of circumscribed circle about square of side 10 =

A. 5√2

B. 10√2

C. 5

D. 10

5√2

157. If a + b + c = 0, then a³ + b³ + c³ =

A. 0

B. 2abc

C. 3abc

D. -3abc

3abc

156. . Radius of circle inscribed in right triangle (6, 8, 10) is:

A. 1

B. 2

C. 3

D. 4

r = (a + b – c)/2 = (6+8–10)/2 = 2.

155. What is the area of triangle with sides (13, 14, 15)?

A. 84

B. 85

C. 869

D. 87

s = 21; area = √[21·8·7·6] = 84.

154. Sum of cubes of first n natural numbers equals 2025. n is:

A. 9

B. 10

C. 12

D. 15

n(n+1)/2) 2 =2025 → n(n+1)/2 = 45 → n(n+1) = 90 → n = 9.

153. A man spends 3/5 of his salary. If he saves ₹8000, what is his salary?

A. ₹20,000

B. ₹25,000

C. ₹30,000

D. ₹40,000

Saving = 2/5 of salary ⇒ 2/5x = 8000 ⇒ x = 8000×5/2 = ₹20,000

152. Find the value of x: 2x + 5 = 17

A. 5

B. 6

C. 7

D. 8

Explanation: 2x = 12 ⇒ x = 6

151. If the area of an equilateral triangle is 49√3 cm², find its side.

A. 7 cm

B. 10 cm

C. 12 cm

D. 14 cm

Explanatio n: Area= (√3/4)×a² ⇒ 49√3 = (√3/4)×a² ⇒ a² = 196 ⇒ a = 14 cm

150. If A:B = 2:3 and B:C = 4:5, what is A:C?

A. 8:15

B. 2:5

C. 3:5

D. 4:7

A:B = 2:3, B:C = 4:5 ⇒ LCM of B = 12 ⇒ A:C = 8:15

149. A cone has a height of 12 cm and radius 5 cm. What is its volume? (π = 3.14)

A. 314 cm³

B. 280 cm³

C. 350 cm³

D. 400 cm³

Explanation: V = (1/3)πr²h = (1/3)×3.14×25×12 = 314

148. In how many ways can the letters of the word "TALATHI" be arranged?

A. 5040

B. 2520

C. 1260

D. 10080

xplanation: Total letters = 7, but 'T' appears twice ⇒ 7!/2! = 5040/2 = 2520

147. Find the median of 4, 7, 9, 15, 21

A. 10

B. 9

C. 11

D. 12

Explanation: Middle number = 9

146. What is the angle between the hands of a clock at 3:30?

A. 75°

B. 60°

C. 45°

D. 90°

Angle = |(30×hr − (11/2)×min)| = |(30×3 − 11/2×30)| = |90 − 165| = 75°

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201 Mathematics MCQ Questions in english हिन्दी

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

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

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

170. 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?

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

168. 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?

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

166. 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?

165. 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%.

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

163. 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?

162. 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?

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

160. If u: twice differentiation of x³ gives

159. Equation of perpendicular bisector of AB joining (2,3) and (6,7):

158. The radius of circumscribed circle about square of side 10 =

157. If a + b + c = 0, then a³ + b³ + c³ =

156. . Radius of circle inscribed in right triangle (6, 8, 10) is:

155. What is the area of triangle with sides (13, 14, 15)?

154. Sum of cubes of first n natural numbers equals 2025. n is:

153. A man spends 3/5 of his salary. If he saves ₹8000, what is his salary?

152. Find the value of x: 2x + 5 = 17

151. If the area of an equilateral triangle is 49√3 cm², find its side.

150. If A:B = 2:3 and B:C = 4:5, what is A:C?

149. A cone has a height of 12 cm and radius 5 cm. What is its volume? (π = 3.14)

148. In how many ways can the letters of the word "TALATHI" be arranged?

147. Find the median of 4, 7, 9, 15, 21

146. What is the angle between the hands of a clock at 3:30?

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