Government exams
- Which part of the human brain maintains balance and posture of the body? Answer: B. Cerebellum Answer: (B) Cerebellum The cerebellum (hindbrain) coordinates voluntary movements and maintains posture and balance. T... 1
- Which type of mirror is used as a rear-view mirror in vehicles? Answer: A. Convex mirror Answer: (A) Convex mirror A convex mirror always forms an erect, diminished image and gives a wider field of view,... 1
- Deficiency of iodine in the diet causes which disease? Answer: C. Goitre Answer: (C) Goitre Iodine is needed to make the thyroid hormone thyroxine; its lack causes goitre (swelling of the thyroid... 1
- If \(x + \frac{1}{x} = 6\), find the value of \(x^2 + \frac{1}{x^2}\). Answer: A. 34 Answer: (A) 34 x² + 1/x² = (x + 1/x)² - 2 = 36 - 2 = 34 . 1
- If \(a + b + c = 9\) and \(ab + bc + ca = 23\), find the value of \(a^3 + b^3 + c^3 - 3abc\). Answer: D. 108 Answer: (D) 108 a³ + b³ + c³ - 3abc = (a + b + c)[(a + b + c)² - 3(ab + bc + ca)] = 9(81 - 69) = 9 × 12 = 108 . 1
- The table shows the sales (in thousand units) of a company over five years.Year20212022202320242025Sales240300270360405By what percentage did the sales increase from 2023 to 2025? Answer: A. 50% Answer: (A) 50% Increase = 405 - 270 = 135 . Percentage = 135/270 × 100 = 50% . 1
- In \(\triangle ABC\), \(\angle A = 80^\circ\). The bisectors of the exterior angles at B and C meet at O. Find \(\angle BOC\). Answer: B. 50^° Answer: (B) 50^° For the excentre formed by the external bisectors at B and C: ∠ BOC = 90^° - ∠ A/2 = 90^° - 40^° = 50^° . (... 1
- Find the total surface area of a closed cylinder of radius 14 cm and height 6 cm. (Take \(\pi = \frac{22}{7}\).) Answer: A. 1760 cm ² Answer: (A) 1760 cm ² TSA = 2π r(r + h) = 2 × 22/7 × 14 × 20 = 88 × 20 = 1760 cm ² . (528 is only the curved surface ar... 1
- In what ratio must rice costing ₹42 per kg be mixed with rice costing ₹54 per kg so that the mixture is worth ₹46 per kg? Answer: D. 2 : 1 Answer: (D) 2 : 1 Alligation: cheaper : dearer = (54 - 46) : (46 - 42) = 8 : 4 = 2 : 1 . 1
- Pipe A can fill a tank in 12 minutes and pipe B in 15 minutes, while pipe C can empty the full tank in 20 minutes. If all three are opened together on an empty tank, in how much time will the tank be filled? Answer: C. 10 minutes Answer: (C) 10 minutes Net part filled per minute = 1/12 + 1/15 - 1/20 = 5 + 4 - 3/60 = 1/10 . So the tank fills in 10... 1
- A can do a piece of work in 16 days and B can do it in 24 days. They work together for 6 days and then A leaves. In how many more days will B finish the remaining work? Answer: B. 9 days Answer: (B) 9 days In 6 days together: 6(1/16 + 1/24) = 6 × 5/48 = 5/8 . Remaining 3/8 ; B needs 3/8 × 24 = 9 days. 1
- A train 180 m long crosses a pole in 9 seconds. How long will it take to cross a platform 270 m long? Answer: B. 22.5 seconds Answer: (B) 22.5 seconds Speed = 180/9 = 20 m/s. To cross the platform it covers 180 + 270 = 450 m: 450/20 = 22.5 s. 1
- Two trains 150 m and 210 m long are running in opposite directions on parallel tracks at 45 km/h and 63 km/h. In how much time will they completely cross each other? Answer: C. 12 seconds Answer: (C) 12 seconds Relative speed (opposite directions) = 45 + 63 = 108 km/h = 108 × 5/18 = 30 m/s. Distance = 150... 1
- If \(\cos\theta = \frac{5}{13}\) and \(\theta\) is acute, find the value of \(\csc\theta + \cot\theta\). Answer: C. 3/2 Answer: (C) 3/2 With adjacent side 5 and hypotenuse 13, the opposite side is 12. cscθ = 13/12 , cotθ = 5/12 . Sum = 18/12 = 3... 1
- The average of 11 numbers is 36. The average of the first six numbers is 32 and that of the last six numbers is 40. What is the sixth number? Answer: D. 36 Answer: (D) 36 The 6th number is counted in both groups. Sixth = 6 × 32 + 6 × 40 - 11 × 36 = 192 + 240 - 396 = 36 . 1
- The average age of 30 students in a class is 14 years. When the teacher's age is included, the average becomes 15 years. What is the teacher's age? Answer: B. 45 years Answer: (B) 45 years Teacher's age = 31 × 15 - 30 × 14 = 465 - 420 = 45 years. 1
- The HCF of two numbers is 15 and their LCM is 420. If one of the numbers is 105, what is the other number? Answer: D. 60 Answer: (D) 60 Product of two numbers = HCF × LCM. Other number = 15 × 420/105 = 60 . Check: HCF(60, 105) = 15 and LCM = 420. 1
- What is the remainder when \(7^{45}\) is divided by 5? Answer: D. 2 Answer: (D) 2 7 equiv 2 ±od 5 , so we need 2⁴⁵ bmod 5 . Powers of 2 mod 5 repeat in a cycle of 4: 2, 4, 3, 1. 45 = 4 × 11 + 1 ,... 1
- What is the smallest number that must be added to 2375 so that the sum is exactly divisible by 17? Answer: C. 5 Answer: (C) 5 2375 = 17 × 139 + 12 . Remainder 12, so add 17 - 12 = 5 : 2380 = 17 × 140 . 1
- A number is first increased by 20% and then the result is decreased by 25%. What is the net percentage change in the number? Answer: C. 10% decrease Answer: (C) 10% decrease Let the number be 100. After +20%: 120. After −25%: 120 × 0.75 = 90 . Net change = 10% decr... 1
- The population of a town increased by 10% in the first year and decreased by 10% in the second year. If the population at the end of the second year is 39,600, what was it at the beginning of the first year? Answer: A. 40,000 Answer: (A) 40,000 P × 1.1 × 0.9 = 0.99P = 39600 , so P = 40000 . (A 10% rise followed by a 10% fall is a net 1% fall.) 1
- A shopkeeper marks an article 40% above its cost price and allows a discount of 20% on the marked price. What is his profit percentage? Answer: A. 12% Answer: (A) 12% Let CP = 100. MP = 140. SP = 80% of 140 = 112. Profit = 12%. (Formula: 40 - 20 - 40 × 20/100 = 12% .) 1
- By selling an article for ₹1,140, a man loses 5%. At what price should he sell it to gain 15%? Answer: C. ₹1,380 Answer: (C) ₹1,380 CP = 1140/0.95 = 1200 . SP for 15% gain = 1200 × 1.15 = 1380 . 1
- ₹7,800 is divided among A, B and C in the ratio \(\frac{1}{2} : \frac{1}{3} : \frac{1}{4}\). What is B's share? Answer: B. ₹2,400 Answer: (B) ₹2,400 Multiply by LCM 12: ratio = 6 : 4 : 3, total 13 parts. B's share = 4/13 × 7800 = 2400 . 1