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What is the remainder when \(2^{31}\) is divided by 5? Answer: D. 3 Answer: (D) 3 Powers of 2 mod 5 repeat in a cycle of 4: 2, 4, 3, 1. 31 = 4 × 7 + 3 , so 2³¹ equiv 2³ = 8 equiv 3 ±od 5 . Number system 1 answer
Which country won the FIFA World Cup 2026, beating Argentina 1–0 after extra time in the final on 19 July 2026? Answer: A. Spain Answer: (A) Spain Spain beat defending champions Argentina 1–0 after extra time at MetLife Stadium (New York New Jersey), w... Current affairs 1 answer
Find the value of \(\sqrt{1764} - \sqrt[3]{2744}\). Answer: B. 28 Answer: (B) 28 √(1764) = 42 and sqrt[3]2744 = 14 . 42 - 14 = 28 . Simplification and approximation 1 answer
If \(x - \frac{1}{x} = 3\), find the value of \(x^4 + \frac{1}{x^4}\). Answer: B. 119 Answer: (B) 119 x² + 1/x² = 3² + 2 = 11 . x⁴ + 1/x⁴ = 11² - 2 = 119 . Algebra 1 answer
If \(3x - 2y = 5\) and \(xy = 2\), find the value of \(27x^3 - 8y^3\). Answer: A. 305 Answer: (A) 305 a³ - b³ = (a - b)³ + 3ab(a - b) with a = 3x, b = 2y : ab = 6xy = 12 . 27x³ - 8y³ = 5³ + 3 × 12 × 5 = 125 + 18... Algebra 1 answer
Each exterior angle of a regular polygon is 24°. How many sides does it have? Answer: D. 15 Answer: (D) 15 Number of sides = 360^°/24^° = 15 . Geometry 1 answer
The India AI Impact Summit 2026, held in February 2026, took place in which city? Answer: B. New Delhi Answer: (B) New Delhi The summit and the India AI Impact Expo were held at Bharat Mandapam, New Delhi, in February 2026... Current affairs 1 answer
The 2026 Commonwealth Games, which ended on 2 August 2026, were held in which city? Answer: A. Glasgow Answer: (A) Glasgow The 2026 Commonwealth Games were held in Glasgow, Scotland; India finished fourth on the medal table.... Current affairs 1 answer
The Union Budget 2026-27 was presented in the Lok Sabha on 1 February 2026. Which of the following statements about it is correct? Answer: C. It was Nirmala Sitharaman's ninth consecutive Budget and was presented on a Sunday. Answer: (C) It was Nirmala Sitharaman's ninth... Current affairs 1 answer
Three bells ring at intervals of 12, 18 and 30 minutes. If they ring together at 9:00 a.m., when will they next ring together? Answer: B. 12:00 noon Answer: (B) 12:00 noon LCM(12, 18, 30) = 180 minutes = 3 hours. 9:00 a.m. + 3 h = 12:00 noon. HCF and LCM 1 answer
The price of sugar rises by 25%. By what percentage must a family reduce its consumption so that its expenditure on sugar stays the same? Answer: A. 20% Answer: (A) 20% Reduction = 25/100 + 25 × 100 = 20% . Check: 1.25 × 0.8 = 1. Percentage 1 answer
What is the area of an equilateral triangle of side 8 cm? Answer: A. 16√(3) cm² Answer: (A) 16√(3) cm² Area = √(3)/4a² = √(3)/4 × 64 = 16√(3) cm². Mensuration 1 answer
Find the surface area of a sphere of radius 21 cm. (Take \(\pi = \frac{22}{7}\).) Answer: B. 5544 cm² Answer: (B) 5544 cm² Surface area = 4π r² = 4 × 22/7 × 441 = 5544 cm². (1386 is π r² ; 38808 is the volume.) Mensuration 1 answer
A 60-litre mixture contains milk and water in the ratio 7 : 3. How much water must be added to make the ratio 7 : 5? Answer: D. 12 litres Answer: (D) 12 litres Milk = 42 L, water = 18 L. For 7 : 5 with 42 L milk, water must be 42 × 5/7 = 30 L. Water to add... Mixture and alligation 1 answer
A invests ₹15,000 for 12 months and B invests ₹20,000 for 6 months in a business. Out of a total profit of ₹10,000, what is B's share? Answer: D. ₹4,000 Answer: (D) ₹4,000 Ratio = 15000 × 12 : 20000 × 6 = 180000 : 120000 = 3 : 2. B's share = 2/5 × 10000 = ₹4,000 . Partnership 1 answer
A trader sells two articles for ₹990 each. On one he gains 10% and on the other he loses 10%. What is his overall gain or loss percentage? Answer: B. 1% loss Answer: (B) 1% loss CP of first = 990/1.1 = 900 ; CP of second = 990/0.9 = 1100 . Total CP = 2000, total SP = 1980. Loss... Profit, loss and discount 1 answer
Find the compound interest on ₹8,000 at 10% per annum for 3 years, compounded annually. Answer: C. ₹2,648 Answer: (C) ₹2,648 Amount = 8000 × (1.1)³ = 8000 × 1.331 = 10648 . CI = 10648 − 8000 = ₹2,648. (₹2,400 is the simple inter... Simple and compound interest 1 answer
Pipes A and B can fill a tank in 20 minutes and 30 minutes respectively, and pipe C can empty it in 15 minutes. If all three are opened together, in how much time will the empty tank be filled? Answer: A. 60 minutes Answer: (A) 60 minutes Net rate = 1/20 + 1/30 - 1/15 = 3 + 2 - 4/60 = 1/60 . Time = 60 minutes. Pipes and cisterns 1 answer
A boat takes 3 hours more to travel 45 km upstream than to travel 45 km downstream. If the speed of the stream is 2 km/h, what is the speed of the boat in still water? Answer: D. 8 km/h Answer: (D) 8 km/h Let the boat's speed be b. 45/b - 2 - 45/b + 2 = 3 ⇒ 180/b² - 4 = 3 ⇒ b² = 64 , b = 8 km/h. Check: upst... Boats and streams 1 answer
The present ages of A and B are in the ratio 5 : 7. After 6 years, the ratio will be 3 : 4. What is B's present age? Answer: D. 42 years Answer: (D) 42 years 5x + 6/7x + 6 = 3/4 ⇒ 20x + 24 = 21x + 18 ⇒ x = 6 . B = 7 × 6 = 42 years (A = 30). Check: 36 : 48 =... Ages 1 answer
A point is 13 cm from the centre of a circle of radius 5 cm. What is the length of the tangent drawn from the point to the circle? Answer: A. 12 cm Answer: (A) 12 cm The radius is perpendicular to the tangent: tangent = √(13² - 5²) = √(144) = 12 cm. Geometry 1 answer
In triangle ABC, I is the incentre and ∠A = 70°. Find ∠BIC. Answer: D. 125° Answer: (D) 125° ∠ BIC = 90^° + ∠ A/2 = 90^° + 35^° = 125^° . Reason: ∠ IBC + ∠ ICB = 1/2(180^° - 70^°) = 55^° , so ∠ BIC =... Geometry 1 answer
If \(\sec\theta + \tan\theta = 3\), find \(\sin\theta\). Answer: D. 4/5 Answer: (D) 4/5 Since sec²θ - tan²θ = 1 , secθ - tanθ = 1/3 . Adding: secθ = 5/3 ; subtracting: tanθ = 4/3 . sinθ = tanθ/secθ... Trigonometry 1 answer
Find the value of \(\frac{\sin 35^\circ}{\cos 55^\circ} + \frac{\cos 28^\circ}{\sin 62^\circ} - 2\cos^2 60^\circ\). Answer: A. 3/2 Answer: (A) 3/2 cos 55^° = sin 35^° and sin 62^° = cos 28^° (complementary angles), so the first two terms are 1 each. 2cos²... Trigonometry 1 answer

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