Q&A: practice questions with answers

Concept: Mode is the value with the highest frequency.

1. Frequencies: 44, 48, 58, 46, 39, 37.
2. Highest frequency $=58$.
3. It belongs to shoe size 7.

Yaad rakhein: Mode = most demanded item — just pick the largest count.

Answer: (D) 7

Concept: Read the values from the graph and simplify the ratio.

1. Friday $=12$ plants.
2. Saturday $=10$ plants.
3. $12:10=6:5$

Trick: Divide both terms by their HCF (2).

Answer: (D) $6:5$

Concept: A perfect square is the square of an integer.

1. ${14}^2=196$ ✓
2. ${14}^2=196<222<225={15}^2$; ${11}^2=121<124,141<144={12}^2$
3. So only 196 is a perfect square.

Trick: Squares never end in 2, 3, 7 or 8 — 222 is out at once.

Answer: (B) 196

Concept: $1+{\cot }^{2}A={\csc }^{2}A$ and $1+{\tan }^{2}A={\sec }^{2}A$.

1. $\frac{50(1+{\cot }^{2}A)}{25(1+{\tan }^{2}A)}=\frac{2{\csc }^{2}A}{{\sec }^{2}A}$
2. $=2\times \frac{{\cos }^{2}A}{{\sin }^{2}A}$
3. $=2{\cot }^{2}A$

Trick: Put $A={45}^{\circ }$: expression $=\frac{100}{50}=2$, and only $2{\cot }^{2}A$ gives 2.

Answer: (A) $2{\cot }^{2}A$

Concept: Let chips $=c$, biscuits $=b$; form two equations.

1. $c+b=50$ and $6c+5b=273$
2. Subtract $5\times$(first): $c=273-250=23$
3. $b=27$; difference $=27-23=4$

Trick: If all 50 were ₹5 packets: ₹250; extra ₹23 comes from ₹1 extra per chips packet → 23 chips.

Answer: (B) 4

Concept: If $\sqrt{a}=3$, then $a=9$.

1. One number $=3^2=9$
2. $9^2+y^2=145\Rightarrow y^2=145-81=64$
3. $y=8$

Trick: Check: $81+64=145$ ✓.

Answer: (C) 8

Concept: Vowels +1, consonants −1, then arrange alphabetically.

1. D I A L E C T → C J B K F B S
2. Arranged: B B C F J K S
3. From the right: S (1st), K (2nd), J (3rd).

Trick: Repeated letters (B, B) still count as separate positions.

Answer: (D) J

Concept: A probable cause directly explains how the stated effect (greenhouse-gas-driven warming) arises.

1. I: Burning fossil fuels releases most greenhouse gases → directly causes warming.
2. II: Deforestation adds about a quarter of emissions → also a cause.
3. Both explain the rise in greenhouse gases.

Yaad rakhein: Fossil-fuel burning and deforestation are the two main human sources of $\mathrm{C}{\mathrm{O}}_2$.

Answer: (B) Both I and II are probable causes.

Concept: Each letter moves forward by a fixed number of places.

1. O→U, L→R, Q→W, N→T: each $+6$.
2. LINK→ROTQ: each $+6$ ✓.
3. IFKH: I+6=O, F+6=L, K+6=Q, H+6=N → OLQN

Trick: Check only the first letter: I + 6 = O leaves options A and D; the 3rd letter K + 6 = Q picks A.

Answer: (A) OLQN

Concept: In each pair XY – MN, find the gaps between consecutive letters (wrap Z→A).

1. ZG – HQ: Z+7=G, G+1=H, H+9=Q
2. TA – BK: T+7=A, A+1=B, B+9=K; BI – JS: B+7=I, I+1=J, J+9=S
3. SW – FM: S+4=W, W+9=F — pattern $+7,+1,+9$ breaks.

Trick: Use position numbers with wrap-around: Z(26)+7 = 33 − 26 = 7 = G.

Answer: (D) SW – FM

Concept: Position from left $=$ total $-$ position from right $+1$.

1. Arihant from left $=37-14+1=24$
2. Chery is ${21}^{\text{st}}$ from left.
3. People between $=24-21-1=2$

Trick: Between two people on the same side: difference of positions $-1$.

Answer: (B) 2

Concept: Replace letters with operators and apply BODMAS.

1. D: $18\times 5+42÷6-17$
2. $=90+7-17$
3. $=80$ ✓

Trick: Option B starts with $18÷5$, a non-integer — skip such options first.

Answer: (D) 18 B 5 C 42 A 6 D 17

Concept: Replace letters with operators and apply BODMAS.

1. $22\times 5-12÷4+6$
2. $=110-3+6$
3. $=113$

Trick: Division and multiplication first, then add/subtract left to right.

Answer: (D) 113

Concept: Letters common to both words share the common digits.

1. HANKY: 5 6 4 2 8; SNAKY: 4 8 7 2 5
2. Common letters A, N, K, Y ↔ common digits 2, 4, 5, 8.
3. Left in HANKY: H ↔ 6

Trick: The unique letter of a word takes its unique digit.

Answer: (C) 6

Concept: Replace letters with operators and apply BODMAS (brackets first).

1. D: $13\times 5-2\times 6\times 3+24+(44÷2)$
2. $=65-36+24+22$
3. $=75$ ✓

Trick: Solve the bracket first in each option; only D gives an easy integer path to 75.

Answer: (D) 13 P 5 R 2 P 6 P 3 S 24 S (44 Q 2)

Concept: Find one rule that works for both pairs; test the options.

1. Rule: second $=\frac{\text{first}}{2}+10$.
2. $X=68$: $\frac{68}{2}+10=44$ ✓
3. $72$: $\frac{72}{2}+10=46=Y$ ✓

Trick: Use the option to fix the rule on one side and verify it on the other side.

Answer: (B) X = 68, Y = 46

Concept: Each letter in the cluster moves $+1$ in each step.

1. K→L→M→N→O
2. N→O→P→Q→R
3. Q→R→S→T→U

Trick: Read the series column-wise: each column is just the alphabet.

Answer: (A) ORU

Concept: Find the rule: (a, b, c) with $b=\frac{a}{3}$ and $c=\frac{b}{5}$.

1. $105÷3=35,35÷5=7$; $135÷3=45,45÷5=9$
2. $150÷3=50,50÷5=10$ ✓
3. Others fail: $90÷3=30\ne 25$; $115÷3$ not an integer; $40÷5=8\ne 12$.

Trick: Equivalently $a=15c$: $15\times 10=150$ ✓.

Answer: (A) (150, 50, 10)

Concept: The letter common to both words takes the digit common to both codes.

1. FOLD → 3, 5, 7, 9; RAIL → 2, 4, 5, 6
2. Common letter: L
3. Common digit: 5 → L = 5

Trick: Match common letter with common digit — order of digits does not matter.

Answer: (D) 5

Concept: Look for: perfect square (1, 4, 9) → even digit → odd digit.

1. Scan every even digit and check its neighbours.
2. Matches: 4 6 3, 4 8 1, 9 6 9, 9 4 5, 1 4 7
3. Total $=5$

Trick: Single-digit perfect squares are only 1, 4, 9 (0 does not appear) — check just these before each even digit.

Answer: (A) 5