Q&A: practice questions with answers

Concept: Reinvesting the profit makes it compound growth: $A=P{(1+\frac{r}{100})}^n$.

1. After year 1: $10,000\times 1.2=$ ₹12,000.
2. After year 2: $12,000\times 1.2=$ ₹14,400.

Trick: 20% twice = $20+20+\frac{20\times 20}{100}=44\%$ ⇒ $10,000\times 1.44=$ ₹14,400.

Answer: (C) ₹14,400

Concept: $CP=SP\times \frac{100}{100+\text{profit}\%}$. The discount is already included in SP.

1. SP = ₹180 (after discount).
2. CP = $180\times \frac{100}{150}=$ ₹120.

Trick: 50% profit ⇒ $SP=1.5\times CP\Rightarrow CP=\frac{2}{3}$ of $SP=\frac{2}{3}\times 180=120$. The 10% discount is extra data here.

Answer: (B) ₹120

Concept: Sum = average × number; new members' sum = new total − old total.

1. Rise in average = $46,500-45,000=$ ₹1,500.
2. This rise for all 12 people = $12\times 1,500=$ ₹18,000, brought in by the two newcomers above the old ₹45,000 each.
3. Newcomers' average = $45,000+\frac{18,000}{2}=$ ₹54,000.

Trick: Check by totals: $12\times 46.5k-10\times 45k=558k-450k=108k$; $\frac{108k}{2}=54k$.

Answer: (B) ₹54,000

Concept: Lateral surface area of any prism = perimeter of base × height.

1. Base perimeter = 54 cm (sides 13.5, 18, 22.5 – not needed).
2. LSA = $54\times 8=432{\text{cm}}^2$.

Trick: The 3 : 4 : 5 ratio is a distractor for LSA; it is needed only for total surface area (base area).

Answer: (D) 432 cm²

Concept: Removed value = old total − new total.

1. $12\times 85=1020$.
2. $11\times 82=902$.
3. Removed = $1020-902=118$.

Trick: Removed marks = old avg + (drop in avg × remaining) = $85+3\times 11=118$.

Answer: (B) 118

Concept: SP = $CP\times (1+\text{markup})\times (1-\text{discount})$.

1. Factor = $1.45\times 0.85=1.2325$.
2. Total CP = $14,790÷1.2325=$ ₹12,000.
3. Per charger = $12,000÷220\approx$ ₹54.5.

Trick: Net % = $45-15-\frac{45\times 15}{100}=23.25\%$, so SP = 123.25% of CP.

Answer: (A) ₹54.5

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

1. $\cot A=\frac{4}{3}\Rightarrow {\cot }^{2}A=\frac{16}{9}$.
2. ${\csc }^{2}A=1+\frac{16}{9}=\frac{25}{9}$.
3. $\csc A=\frac{5}{3}$.

Trick: 3-4-5 triangle: $\cot =\frac{\text{base}}{\text{perp}}$ = $\frac{4}{3}$, so $\csc =\frac{\text{hyp}}{\text{perp}}$ = $\frac{5}{3}$.

Answer: (C) $\frac{5}{3}$

Concept: ${\csc }^2\theta -{\cot }^2\theta =1$ for every $\theta$.

1. $3{\csc }^2{30}^{\circ }-3{\cot }^2{30}^{\circ }=3({\csc }^2{30}^{\circ }-{\cot }^2{30}^{\circ })$.
2. $=3\times 1=3$.

Trick: Verify: $\csc {30}^{\circ }=2$, $\cot {30}^{\circ }=\sqrt{3}\Rightarrow 3(4-3)=3$.

Answer: (C) 3

Concept: Sector area = $\frac{1}{2}{r}^2\theta$ ($\theta$ in radians).

1. $\frac{1}{2}\times {20}^2\times \frac{6\pi }{7}=200\times \frac{6\pi }{7}$.
2. $=\frac{1200\pi }{7}\approx 171.4\pi {\text{cm}}^2$.

Trick: $\frac{1200}{7}$: $7\times 171=1197$, remainder 3 ⇒ 171.4.

Answer: (B) 171.4π cm²

Concept: $\sec ({90}^{\circ }-\theta )=\csc \theta$.

1. $\csc \theta =y$.
2. $\sin \theta =\frac{1}{\csc \theta }=\frac{1}{y}$.

Trick: Co-function pairs: sin↔cos, tan↔cot, sec↔cosec swap when ${90}^{\circ }-\theta$ is used.

Answer: (C) $\frac{1}{y}$

Concept: Transverse (direct-cross) tangent = $\sqrt{d^2-(r_1+r_2{)}^2}$.

1. $d=12$, $r_1+r_2=11$.
2. $\sqrt{144-121}=\sqrt{23}$ cm.

Trick: Transverse uses $(r_1+r_2)$, direct uses $(r_1-r_2)$ – 'cross = sum'.

Answer: (C) $\sqrt{23}$ cm

Concept: Angles subtended by a chord in the same segment are equal.

1. C and D are on the same side of AB ⇒ same segment.
2. ∠ADB = ∠ACB = 40°.

Trick: Opposite side would give the supplement (180° − 40° = 140°) – that is the trap option.

Answer: (A) 40°

Concept: Perpendicular from centre bisects the chord: $d=\sqrt{r^2-(\text{half chord}{)}^2}$.

1. Half chord = 12.
2. $d=\sqrt{169-144}=\sqrt{25}=5$ cm.

Trick: 5-12-13 is a Pythagorean triplet – answer at sight.

Answer: (A) 5 cm

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

1. ∠PRQ = 100° ÷ 2 = 50°.

Trick: If R were on the minor arc, the angle would be 180° − 50° = 130° – not in options, confirming 50°.

Answer: (A) 50°

Concept: Radius $⟂$ tangent ⇒ ${\text{tangent}}^2=O{P}^2-r^2$.

1. Tangent = $\sqrt{{15}^2-{12}^2}=\sqrt{225-144}$.
2. $=\sqrt{81}=9$ cm.

Trick: 9-12-15 = 3 × (3-4-5) triplet – answer at sight.

Answer: (B) 9 cm

Concept: The blank is a noun explained right after the dash: 'a semiotic and performative formation' made by repetition.

1. Gender is described as produced through repeated practice, not as natural.
2. 'Praxis-field' = an area formed by practice/action – fits 'performative formation'.
3. 'Diffident' (shy) is an adjective – grammatically impossible after 'a'; 'nomos' (law/norm) and 'ontotheological mirror' do not match 'performative'.

Trick: In cloze tests, read the phrase after a dash or colon – it usually defines the missing word.

Answer: (A) praxis-field

Concept: 'Not X but ___' needs the opposite idea of 'inherent' (natural, built-in).

1. Recognition is 'distributed' through changing, political matrices – i.e. given only on certain conditions.
2. 'Conditionality' = depending on conditions ✓.
3. 'Irrevocability' (cannot be withdrawn) and 'presumption' contradict 'contingent and malleable'; 'succour' (help) is off-topic.

Trick: 'Not … but …' structure: the second word is the opposite of the first – inherent ↔ conditional.

Answer: (A) conditionality

Concept: 'Not merely to broaden … but to pursue a ___ of the foundations' asks for a deeper, freeing move.

1. The author wants to escape the very basis of recognition, not just enlarge it.
2. 'Emancipation' = setting free from control ✓.
3. 'Reiteration' (repeating) would strengthen the old base; 'interpolation' (inserting) is too mild.

Trick: 'Not merely … but …' signals a stronger step than the first – choose the most radical-positive word.

Answer: (C) emancipation

Concept: The next sentence calls it 'this dismantling', so the blank must mean removing.

1. 'Ablation' = surgical removal, cutting away ✓.
2. 'Concretization' (making solid) and 'retrieval' (getting back) keep normativity; 'immanence' (being present within) does not mean removal.

Trick: Look at the following sentence for a pronoun-summary ('this dismantling') – it names the blank's meaning.

Answer: (A) ablation

Concept: Freedom here is 'a break' and 'a refusal' – defined by what it rejects.

1. 'Apophatic' = describing something through negation (what it is not) ✓.
2. 'Recuperative' is already denied ('not recuperative'); 'regulatory' and 'valorized' imply control/approval, opposite of refusal.

Trick: 'Not A but ___' – the answer cannot be A itself, so (A) is eliminated at once.

Answer: (B) apophatic