Q&A: practice questions with answers

Concept: Article 85(2)(b) empowers the President to dissolve the Lok Sabha.

1. Under Article 74 the President acts on the aid and advice of the Council of Ministers headed by the Prime Minister.
2. So premature dissolution happens on the PM's recommendation – not on a court order or at the President's own will.

Yaad rakhein: Dissolve Lok Sabha → Art. 85 + PM's advice (Art. 74).

Answer: (C) On the recommendation of the Prime Minister

Concept: The Drain of Wealth theory explained how Britain transferred India's wealth without equivalent return.

1. Dadabhai Naoroji put it forward in 'Poverty and Un-British Rule in India' (1901).
2. R.C. Dutt also supported it, but Naoroji is its chief proponent.

Yaad rakhein: Drain theory → Dadabhai Naoroji, 'Grand Old Man of India'.

Answer: (A) Dadabhai Naoroji

Concept: In Windows, Delete sends a file to the Recycle Bin, from where it can be restored.

1. Shift + Delete bypasses the Recycle Bin and deletes the file permanently (after confirmation).
2. Pressing Delete alone only moves it to the Recycle Bin; Open and Rename do not delete.

Yaad rakhein: Shift = 'skip the bin'.

Answer: (B) Press Shift + Delete

Concept: The 8th Delhi Legislative Assembly election (70 seats) was held in February 2025; BJP won 48 seats.

1. Statement 2 ✓: BJP's Parvesh Verma defeated Arvind Kejriwal in New Delhi and was sworn in as Deputy Chief Minister (Rekha Gupta became CM).
2. Statement 3 ✓: AAP won 22 seats.
3. Statement 1 ✗: the largest victory margin was of AAP's Aaley Mohammad Iqbal (Matia Mahal). Statement 4 ✗: Congress again won 0 seats.

Yaad rakhein: Delhi 2025: BJP 48, AAP 22, INC 0.

Answer: (A) Only 2 and 3

Concept: The Palk Strait lies between Tamil Nadu (India) and the Jaffna peninsula of Sri Lanka.

1. It connects the Bay of Bengal (Palk Bay) with the Gulf of Mannar; Adam's Bridge (Ram Setu) lies to its south.
2. Maldives is separated from India by the Eight Degree Channel, not by Palk Strait.

Yaad rakhein: Palk Strait → India–Sri Lanka; 8° Channel → Minicoy–Maldives; 10° Channel → Andaman–Nicobar.

Answer: (B) Sri Lanka

Concept: The Satyajit Ray Lifetime Achievement Award honours outstanding contribution to cinema.

1. In January 2025 it was conferred on filmmaker-actor Aparna Sen.
2. She is known for films such as '36 Chowringhee Lane' and 'Mr. and Mrs. Iyer'.

Yaad rakhein: Aparna Sen → '36 Chowringhee Lane' → Satyajit Ray award 2025.

Answer: (B) Aparna Sen

Concept: $\text{SP}=\text{MP}\times (1-\text{discount})$ and $\text{CP}=\frac{\text{SP}}{1+\text{gain}}$.

1. $\text{SP}=5180\times 0.69=3574.2$
2. $\text{CP}=\frac{3574.2}{1.05}=3404$

Trick: Directly: $\text{CP}=5180\times \frac{69}{105}=3404$ ; check $3404\times 105=357420$ ✓.

Answer: (C) ₹3,404

Concept: Net filling rate = filling rate − leaking rate.

1. Tap fills $\frac{1}{6}$ per hour; hole empties $\frac{1}{15}$ per hour.
2. Net $=\frac{1}{6}-\frac{1}{15}=\frac{5-2}{30}=\frac{1}{10}$ per hour.
3. Time $=10$ hours.

Trick: Shortcut: $\frac{ab}{b-a}=\frac{6\times 15}{15-6}=\frac{90}{9}=10$.

Answer: (C) 10 hours

Concept: Downstream $=u+v$, upstream $=u-v$, so still-water speed $u=\frac{\text{down}+\text{up}}{2}$.

1. $u=\frac{37+27}{2}=\frac{64}{2}=32\text{km/h}$
2. (Stream speed $=\frac{37-27}{2}=5\text{km/h}$.)

Trick: Still water = average of the two speeds; stream = half the difference.

Answer: (C) 32 km/hr

Concept: Use $(a\pm b{)}^2=a^2\pm 2ab+b^2$; the cross terms cancel.

1. $(3z-9y{)}^2=9z^2-54yz+81y^2$
2. $(9z+3y{)}^2=81z^2+54yz+9y^2$
3. Sum $=90z^2+90y^2$; subtract $81z^2$ → $9z^2+90y^2$.

Trick: $(a-b{)}^2+(c+d{)}^2$ with $ab=cd$ cancels the $yz$ terms – just add squares.

Answer: (B) $9z^2+90y^2$

Concept: Consecutive integers are $x$ and $x+1$.

1. $x(x+1)=247$
2. $x^2+x-247=0$
3. Only the form of the equation is asked, so this is the required equation.

Trick: Product = $c$ moves across as $-c$; the $+x$ comes from $x\times 1$.

Answer: (C) $x^2+x-247=0$

Concept: $\text{Mode}=l+\frac{f_1-f_0}{2f_1-f_0-f_2}\times h$

1. Mode 165 lies at the end of class 160–165 (highest known frequency 37): $l=160,f_1=37,f_0=25,f_2=x,h=5$.
2. $165=160+\frac{12}{74-25-x}\times 5$ → $5=\frac{60}{49-x}$
3. $49-x=12$ → $x=37$.

Trick: Mode at the upper boundary means $f_1-f_0=2f_1-f_0-f_2$, i.e. $f_2=f_1$ → $x=37$ instantly.

Answer: (A) 37

Concept: Find profit on one bag, then divide the target profit by it.

1. CP per bag $=\frac{41622}{42}=991$
2. SP per bag $=\frac{37345}{35}=1067$
3. Profit per bag $=76$; bags $=\frac{3952}{76}=52$.

Trick: Always reduce to 'per unit' first – then target ÷ unit profit.

Answer: (A) 52

Concept: Income = Expenditure + Savings.

1. Expenditure $=50\%$ of income, so savings $=50\%$ too.
2. Hence expenditure = savings = ₹7,056.

Trick: Equal percentages ⇒ equal amounts – no calculation needed.

Answer: (A) 7,056

Concept: Centroid $G=(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})$.

1. x-coordinate: $\frac{0+(-2)+p}{3}=3$
2. $p-2=9$ → $p=11$
3. (y check: $\frac{4+0+2}{3}=2$ ✓)

Trick: Sum of x's $=3\times 3=9$; already have $-2$, so $p=11$.

Answer: (D) 11

Concept: Let a pen cost $a$ and a pencil $b$; form two equations.

1. $15a+6b=291$
2. $9(a-9)+3(b+2)=75$ → $9a+3b=150$ → $18a+6b=300$
3. Subtract: $3a=9$ → $a=3$, $b=\frac{291-45}{6}=41$
4. $12a+3b=36+123=159$

Trick: Double the second equation to match the $6b$ term and subtract.

Answer: (D) ₹159

Concept: Net rate = filling − emptying.

1. Net $=\frac{1}{9}-\frac{1}{90}=\frac{10-1}{90}=\frac{1}{10}$ per hour.
2. One tank: 10 hours; twice the volume: $2\times 10=20$ hours.

Trick: Don't stop at 10 – the question asks for double the volume.

Answer: (D) 20

Concept: Third proportional of $a$ and $b$ is $\frac{b^2}{a}$.

1. $\frac{(12xy{)}^2}{2x^2}=\frac{144x^2{y}^2}{2x^2}$
2. $=72y^2$

Trick: $a:b=b:c$ ⇒ $c=\frac{b^2}{a}$.

Answer: (D) $72y^2$

Concept: If bisectors of $\angle R$ and $\angle S$ meet at T, then $\angle STR=\frac{\angle P+\angle Q}{2}$.

1. $\angle STR={180}^{\circ }-\frac{R+S}{2}=\frac{{360}^{\circ }-(R+S)}{2}=\frac{P+Q}{2}$
2. $P+Q=2\times {32.5}^{\circ }={65}^{\circ }$
3. $P:Q=4:9$ → 13 parts $={65}^{\circ }$ → 1 part $=5^{\circ }$
4. $Q-P=5\times 5^{\circ }={25}^{\circ }$

Trick: Angle between bisectors of two adjacent angles = half the sum of the other two angles.

Answer: (C) 25°

Concept: Dividend = Divisor × Quotient + Remainder.

1. $L-S=2134$ and $L=2S+147$ → $S+147=2134$ → $S=1987$, $L=4121$.
2. HCF(4121, 4225): $4225-4121=104$; $4121=104\times 39+65$.
3. $104\to 65\to 39\to 26\to 13$ (Euclid) → HCF $=13$.

Trick: $4225=13\times 325$ and $4121=13\times 317$ – test the options as divisors.

Answer: (D) 13