Q&A: practice questions with answers

Concept: $\text{Discount}=\text{Marked price}\times \frac{\text{rate}}{100}$.

1. 20% of ₹3000 = $3000\times \frac{20}{100}$.
2. = ₹600.

Trick: 10% of 3000 = 300 → 20% = 600.

Answer: (C) Rs. 600

Concept: Take CP = 100; apply mark-up, then discounts one after another.

1. MP = $100+200=300$.
2. After 40% off: $300\times 0.6=180$.
3. After 10% off: $180\times 0.9=162$ → profit 62%.

Trick: Multiply factors: $3\times 0.6\times 0.9=1.62$ → 62% profit.

Answer: (C) 62%

Concept: B's rate = combined rate − A's rate.

1. $\frac{1}{B}=\frac{1}{20}-\frac{1}{25}$.
2. $=\frac{5-4}{100}=\frac{1}{100}$.
3. B alone = 100 days.

Trick: For x and y days: other alone = $\frac{xy}{y-x}=\frac{20\times 25}{5}=100$.

Answer: (C) 100 days

Concept: Angle at centre = 2 × angle at the circumference (same arc).

1. Central angle of arc AB = 200°.
2. Angle at a point on the remaining circle = 200° ÷ 2 = 100°.

Trick: Just halve the central angle — don't subtract from 360° first.

Answer: (C) 100°

Concept: Compare centre distance d with r₁ + r₂.

1. r₁ + r₂ = 6 + 3 = 9; d = 10.
2. d > r₁ + r₂ → circles are separate.
3. Separate circles: 2 direct + 2 transverse = 4 tangents.

Trick: d > sum → 4; d = sum → 3; cutting → 2; internal touch → 1; one inside other → 0.

Answer: (A) 4

Concept: CSA of hemisphere = $2\pi r^2$.

1. $2\times \frac{22}{7}\times 14\times 14$.
2. $=44\times 28=1232{\text{cm}}^2$.

Trick: With $r=14$, $\pi r^2=616$ — so $2\pi r^2=1232$ directly.

Answer: (D) $1232{\mathrm{cm}}^2$

Concept: $\text{Exterior angle}={180}^{\circ }-\text{interior}$; $n={360}^{\circ }÷\text{exterior}$.

1. Exterior = ${180}^{\circ }-{144}^{\circ }={36}^{\circ }$.
2. $n=360÷36=10$.

Trick: Interior 144° ↔ decagon; 135° ↔ octagon; 120° ↔ hexagon.

Answer: (B) 10

Concept: At the same time, $\frac{\text{height}}{\text{shadow}}$ is constant.

1. Ratio = 4 : 3.
2. Shadow 18 m = $3\times 6$ → height = $4\times 6=24$ m.

Trick: Shadow became 6 times, so height is also 6 times.

Answer: (B) 24 m

Concept: $\text{Discount}\%=\frac{\text{MP}-\text{SP}}{\text{MP}}\times 100$.

1. Discount = $18000-12000=$ ₹6000.
2. $\frac{6000}{18000}=\frac{1}{3}=33.33\%$.

Trick: $\frac{1}{3}=33.33\%$ — when the fraction is exact, pick the exact decimal, not the rounded value.

Answer: (B) $33.33\%$

Concept: SP from profit; then $\text{MP}\times (100-d)\%=\text{SP}$.

1. SP = $1200\times 1.2=$ ₹1440.
2. $\text{MP}\times 0.78=1440$.
3. MP = $1440÷0.78\approx$ ₹1846.15.

Trick: $\text{MP}=\text{CP}\times \frac{100+p}{100-d}=1200\times \frac{120}{78}\approx 1846.15$.

Answer: (A) 1846.15

Concept: Distance = $\text{revolutions}\times \text{circumference}$ ($2\pi r$).

1. 2.75 km = 275000 cm.
2. Circumference = $275000÷875\approx 314.29$ cm.
3. r = $314.29÷(2\times 3.1416)\approx 50.02$ cm.

Trick: Circumference ≈ 314 → r ≈ $\frac{314}{6.28}\approx 50$ → pick 50.02.

Answer: (A) 50.02 cm

Concept: $(a+b{)}^2=2(a^2+b^2)-(a-b{)}^2$.

1. $a^2+b^2={13}^2=169$.
2. $(a+b{)}^2=2\times 169-7^2=338-49=289$.
3. $a+b=17$.

Trick: Triplet 5-12-13: difference 7 ✓, so sum = 17 instantly.

Answer: (A) 17 cm

Concept: Expand $(A-B{)}^2$ and use ${\sin }^{2}x+{\cos }^{2}x=1$.

1. ${\sin }^{2}x+{\cos }^{2}x-2\sin x\cos x$.
2. $=1-2\sin x\cos x$.

Trick: Test $x={45}^{\circ }$: LHS = 0; option A gives 1 ✗, option D gives $1-2\times \frac{1}{2}=0$ ✓.

Answer: (D) $1-2\sin x\cos x$

Concept: $\text{Angle at centre}=2\times \text{angle at the circumference}$.

1. Camera on the circle sees 60°.
2. Angle at centre = $2\times {60}^{\circ }={120}^{\circ }$.

Trick: Inside-the-circle angle (centre) is always double the edge angle for the same chord's arc.

Answer: (D) 120°

Concept: B's one-day work = (A + B)'s − A's.

1. $\frac{1}{20}-\frac{1}{30}=\frac{3-2}{60}=\frac{1}{60}$.
2. B alone = 60 days.

Trick: $\frac{xy}{y-x}=\frac{20\times 30}{10}=60$.

Answer: (D) 60 days

Concept: The Mughal Empire began with Babur's victory at Panipat.

1. Babur defeated Ibrahim Lodi at the First Battle of Panipat in 1526.
2. This ended the Lodi dynasty (last Delhi Sultanate dynasty).
3. 1556 = Second Battle of Panipat (Akbar vs Hemu); 1530 = Babur's death.

Trick: Panipat battles: 1526, 1556, 1761 — gaps of 30 and 205 years.

Answer: (B) 1526

Concept: Shanti Tigga is India's first woman jawan.

1. She joined the Territorial Army's railway engineer regiment in 2011 as a sapper.
2. She topped her batch in physical tests, beating male recruits.
3. Punita Arora was an officer (first woman Lt General), not a jawan.

Trick: Jawan = other ranks; officers (Lt Gen etc.) are a different category — eliminate officer names.

Answer: (B) Shanti Tigga

Concept: Pankaj Advani is India's leading cue-sports player.

1. He plays billiards and snooker and has won many world titles.
2. He received the Khel Ratna (now Major Dhyan Chand Khel Ratna) in 2006.

Trick: Other cue-sport names: Geet Sethi, Michael Ferreira, Aditya Mehta.

Answer: (B) Billiards and Snooker

Concept: Swavalambini is the 2025 women entrepreneurship programme of the Skill Development Ministry.

1. Launched by MoS (IC) Jayant Chaudhary in 2025, with NITI Aayog as partner.
2. Targets women students in higher education institutions, beginning in the North-East.
3. It offers awareness, training, mentoring and funding linkage.

Trick: Swa-valamb = self-reliance → 'Swavalambini' = self-reliant woman.

Answer: (D) Swavalambini

Concept: NMNF (Cabinet approval, Nov 2024) targets 1 crore farmers.

1. Goal: chemical-free natural farming for 1 crore farmers.
2. Area target ≈ 7.5 lakh hectare; budget ≈ ₹2,481 crore.
3. Implemented by the Ministry of Agriculture & Farmers' Welfare.

Trick: Link the numbers: 1 crore farmers, 7.5 lakh ha.

Answer: (A) 1