Q&A: practice questions with answers

Concept: Successive % change: $a+b+\frac{ab}{100}$.

1. +40% and −20%: $40-20-\frac{40\times 20}{100}=12\%$.
2. Check: CP 100 → MP 140 → SP $140\times 0.8=112$ → profit 12%.

Trick: $1.4\times 0.8=1.12$ → 12% profit.

Answer: (C) 12%

Concept: SI is the same every year.

1. Interest per year = $4800÷2$ = ₹2400 = 12% of P → P = ₹20,000.
2. 6-year SI = $2400\times 6$ = ₹14,400.
3. Amount = $20,000+14,400$ = ₹34,400.

Trick: Find yearly interest first; SI simply multiplies by years.

Answer: (C) ₹34,400

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

1. $81=47+2ab$.
2. $2ab=34$ → $ab=17$.

Trick: $ab=\frac{(a+b{)}^2-(a^2+b^2)}{2}=\frac{81-47}{2}$.

Answer: (A) 17

Concept: Use bounds and the unit digit.

1. ${90}^2=8100<9604<10000={100}^2$ → root in the 90s.
2. Ends in 4 → root ends in 2 or 8.
3. ${95}^2=9025<9604$ → root $>95$ → 98 (${98}^2=9604$).

Trick: Compare with ${95}^2$ (ends in 25) to choose between …2 and …8.

Answer: (B) 98

Concept: Milk stays fixed when only water is added.

1. 1 part = $\frac{99}{11}=9$ L → milk 45 L, water 54 L.
2. New ratio 3 : 4 → 3 parts = 45 → 1 part = 15 → water = 60 L.
3. Water added = $60-54=6$ L.

Trick: Make milk the same in both ratios (5 : 6 → 15 : 18, 3 : 4 → 15 : 20) → water +2 parts of 3 L = 6 L.

Answer: (C) 6 litres

Concept: Volume remains constant; $\text{number}={\left(\frac{R}{r}\right)}^3$ for spheres.

1. $\frac{R}{r}=\frac{15}{3}=5$.
2. Number of spheres = $5^3=125$.

Trick: Same shape → ratio of radii cubed.

Answer: (C) 125

Concept: Hemisphere volume = $\frac{2}{3}\pi r^3$; $\text{time}=\frac{\text{volume}}{\text{rate}}$.

1. $V=\frac{2}{3}\pi \times 216=144\pi {\text{m}}^3=1,44,000\pi \text{L}$.
2. Time = $1,44,000\pi ÷1440\pi =100$ minutes.

Trick: π cancels – just do $144000÷1440=100$.

Answer: (B) 100 minutes

Concept: Pure recurring decimal = $\frac{\text{repeating block}}{\text{as many 9s as digits}}$.

1. Repeating block = 56 (2 digits).
2. $0.5656\dots =\frac{56}{99}$ (no common factor).

Trick: $0.\overline{ab}=\frac{ab}{99}$.

Answer: (A) $\frac{56}{99}$

Concept: Two equal largest circles lie along a diameter, so each diameter = half the sheet's diameter.

1. $2\times (2r)=2R$ → $r=\frac{R}{2}$.
2. Circumference is proportional to radius → plate = $\frac{424}{2}=212$ cm.

Trick: Half the radius → half the circumference.

Answer: (D) 212 cm

Concept: Read the term as $(\sqrt{8}{)}^n$; write everything as powers of 2 and equate exponents.

1. $512=2^9$, $\sqrt{8}=2^{3/2}$, ${64}^4=2^{24}$.
2. $9+\frac{3n}{2}=24$ → $\frac{3n}{2}=15$ → $n=10$.

Trick: Check: $(\sqrt{8}{)}^{10}=8^5=2^{15}$ and $2^9\times 2^{15}=2^{24}$ ✓.

Answer: (B) 10

Concept: y − y₁ = m(x − x₁).

1. y − 5 = −6(x − 4).
2. y = −6x + 24 + 5 = −6x + 29.

Trick: Slope −6 → only option with −6x is D; check (4, 5): −24 + 29 = 5 ✓.

Answer: (D) $y=-6x+29$

Concept: Read the data as $x+y=\sqrt{19}$, $x-y=1$ (with $x+y=19$ no option fits); use squares.

1. $(x+y{)}^2=19$, $(x-y{)}^2=1$.
2. Add: $2(x^2+y^2)=20$ → $x^2+y^2=10$.
3. Subtract: $4xy=18$ → $xy=\frac{9}{2}$.
4. $\frac{x^2+y^2}{xy}=10÷\frac{9}{2}=\frac{20}{9}$.

Trick: $x^2+y^2=\frac{S^2+D^2}{2}$ and $xy=\frac{S^2-D^2}{4}$.

Answer: (C) $\frac{20}{9}$

Concept: Use $(1-\sin x)(1+\sin x)={\cos }^{2}x$ as the common denominator.

1. Numerator = $(1+\cos x)(1+\sin x)+(1-\cos x)(1-\sin x)$.
2. $=2+2\sin x\cos x$ (sinx, cosx terms cancel).
3. Result = $\frac{2(1+\cos x\sin x)}{{\cos }^{2}x}$.

Trick: Put $x=0$: value = $\frac{2}{1}+\frac{0}{1}=2$; only B gives $\frac{2(1+0)}{1}=2$.

Answer: (B) $\frac{2(1+\cos (x\left)\sin \right(x\left)\right)}{{\cos }^2\left(x\right)}$

Concept: $\cot \theta =\frac{\text{base}}{\text{perpendicular}}$.

1. Base = 15, perpendicular = 8 (k = 1).
2. Hypotenuse = $\sqrt{225+64}=\sqrt{289}=17$.

Yaad rakhein: 8-15-17 is a Pythagorean triplet.

Answer: (A) 17

Concept: $\sin A=\frac{\text{perpendicular}}{\text{hypotenuse}}$; get base by Pythagoras.

1. Perpendicular 5, hypotenuse 13 → base = $\sqrt{169-25}=12$.
2. $\cos A=\frac{12}{13}$, $\tan A=\frac{5}{12}$.

Trick: cos can never exceed 1 → options with $\frac{13}{12}$ are out instantly.

Answer: (A) $\frac{12}{13}$ and $\frac{5}{12}$

Concept: 28 February marks C.V. Raman's 1928 discovery.

1. On 28 Feb 1928 Raman announced the Raman Effect – light scattered by molecules changes its wavelength.
2. He received the Physics Nobel in 1930 for it.
3. Photoelectric effect (Einstein) and relativity are not his work.

Yaad rakhein: First Asian to win a science Nobel – C.V. Raman (1930).

Answer: (B) Raman Effect

Concept: Defence current affairs, 2025.

1. Indian Navy officer Lt. Cdr. Yashasvi Solanki became the first woman Aide-de-Camp to the President (2025).
2. An ADC is a personal staff officer assisting a high dignitary.

Yaad rakhein: The President is the Supreme Commander of the armed forces (Article 53).

Answer: (B) Lt. Commander Yashasvi Solanki

Concept: YUVA = Young, Upcoming and Versatile Authors.

1. Ministry of Education scheme to mentor writers below 30 years.
2. Third edition launched in March 2025; implemented by National Book Trust (NBT).

Trick: Expand the acronym – 'Authors' in YUVA points straight to option B.

Answer: (B) Mentoring and empowering young authors

Concept: ONOS = single national licence for research journals.

1. From 1 Jan 2025, government higher-education and R&D institutions get free access to scholarly journals.
2. Coordinated by INFLIBNET (under UGC).

Yaad rakhein: ONOS removes the need for each institution to buy separate journal subscriptions.

Answer: (B) Academic journals and educational resources

Concept: Supreme Court's State of the Judiciary Report 2023.

1. Roughly 36.3% of judges now serving in district courts are women.
2. Their share is much lower in the High Courts.

Yaad rakhein: The report was released by the Centre for Research and Planning, Supreme Court of India.

Answer: (C) 36.3%