RRB NTPC Graduate CBT 1 2024 PYQs

Concept: Monthly saving = Income − Expenditure.

1. Monthly saving $=10000-(6000+3000)=1000$ (₹).
2. In the birthday month the saving is spent, so savings occur in only $12-1=11$ months.
3. Yearly saving $=11\times 1000=11000$ (₹).

Trick: Just subtract one month’s saving from 12 months’ saving: $12000-1000$.

Answer: (D) 11,000

Concept: Divide each option by 41 (or use multiples of 41).

1. $41\times 195=7995$ ✓ (since $41\times 200=8200$ and $8200-205=7995$).
2. $7431=41\times 181+10$; $8537=41\times 208+9$; $7889=41\times 192+17$ – not divisible.

Trick: Use a near round multiple: $41\times 200=8200$, then subtract multiples of 41 ($205=41\times 5$).

Answer: (A) 7995

Concept: Let length $=l$, breadth $=b$; form two equations from the area changes.

1. $(l+5)(b-7)=lb+8\Rightarrow -7l+5b=43$.
2. $(l-5)(b+8)=lb+33\Rightarrow 8l-5b=73$.
3. Adding: $l=116$; then $5b=43+812=855\Rightarrow b=171$.
4. Perimeter $=2(116+171)=574\text{m}$.

Trick: The $5b$ terms have opposite signs – just add the equations.

Answer: (D) 574

Concept: $\text{Average speed}=\frac{\text{Total distance}}{\text{Total time}}$.

1. Times: $\frac{370}{37}=10$ h, $\frac{390}{5}=78$ h, $\frac{720}{8}=90$ h; total $=178$ h.
2. Total distance $=370+390+720=1480\text{km}$.
3. Average speed $=\frac{1480}{178}=\frac{740}{89}=8\frac{28}{89}\text{km/h}$.

Trick: Never average the speeds; always total distance ÷ total time.

Answer: (D) $8\frac{28}{89}$

Concept: $\tan \theta =\frac{\text{Height}}{\text{Base}}$.

1. Height $=250\sqrt{3}\text{m}$, base $=250\text{m}$.
2. $\tan \theta =\frac{250\sqrt{3}}{250}=\sqrt{3}$.
3. $\tan {60}^{\circ }=\sqrt{3}\Rightarrow \theta ={60}^{\circ }$.

Trick: Height $=\sqrt{3}\times$ base → ${60}^{\circ }$; base $=\sqrt{3}\times$ height → ${30}^{\circ }$.

Answer: (B) ${60}^{\circ }$

Concept: Let cost price $=C$. Gain at ₹3,437 is 75% more than loss at ₹3,338.

1. $3437-C=\frac{175}{100}(C-3338)$.
2. $4(3437-C)=7(C-3338)\Rightarrow 13748+23366=11C\Rightarrow C=\frac{37114}{11}=3374$ (₹).
3. For 50% gain: $\text{SP}=3374\times \frac{150}{100}=5061$ (₹).

Trick: 75% more means ratio gain : loss $=7:4$, so CP divides 3338 and 3437 in $4:7$: $3338+\frac{4}{11}\times 99=3374$.

Answer: (A) 5,061

Concept: Complete the square in $x^2$ and use $a^2-b^2=(a+b)(a-b)$.

1. $x^4-10x^2+22=(x^2-5{)}^2-25+22=(x^2-5{)}^2-3$.
2. $=(x^2-5{)}^2-(\sqrt{3}{)}^2$.
3. $=(x^2-5+\sqrt{3})(x^2-5-\sqrt{3})$.

Trick: Check: the constants multiply to $25-3=22$ and add to $-10$ ✓.

Answer: (D) $(x^2-5+\sqrt{3})(x^2-5-\sqrt{3})$

Concept: Work done = rate × time; an emptying pipe has negative rate.

1. In 6 minutes A fills $\frac{6}{18}=\frac{1}{3}$ of the tank; remaining $=\frac{2}{3}$.
2. Net rate of A and B $=\frac{1}{18}-\frac{1}{27}=\frac{3-2}{54}=\frac{1}{54}$ per minute.
3. Time $=\frac{2}{3}÷\frac{1}{54}=36$ minutes.

Trick: LCM method: tank $=54$ units; A $=+3$, B $=-2$, net $+1$/min; after 6 min, $54-18=36$ units → 36 min.

Answer: (A) 36

Concept: Successive percentages multiply.

1. $2\%\text{ of }50\%\text{ of }N=\frac{2}{100}\times \frac{50}{100}\times N=\frac{N}{100}$.
2. $\frac{N}{100}$ is $1\%$ of $N$.

Trick: $2\times 50=100$, and $\frac{100}{100}=1\%$.

Answer: (C) 1%

Concept: Mode = the observation that occurs most often.

1. Frequencies: 1 → 2, 3 → 7, 4 → 1, 5 → 1, 7 → 2, 8 → 2.
2. 3 occurs most often (7 times).

Trick: Tally just the repeated values; no calculation needed.

Answer: (C) 3

Concept: Empirical formula: $\text{Mode}=3\text{Median}-2\text{Mean}$.

1. $89.7=3(32)-2\text{Mean}=96-2\text{Mean}$.
2. $2\text{Mean}=96-89.7=6.3$.
3. $\text{Mean}=3.15$.

Trick: Remember “3 Median − 2 Mean” – the coefficients 3 and 2 go with median and mean.

Answer: (D) 3.15

Concept: In a right triangle, $(\text{hyp}{)}^2=a^2+b^2$; the largest side $x$ is the hypotenuse, and $\text{Area}=\frac{1}{2}ab$.

1. $(x-13{)}^2+(x-26{)}^2=x^2\Rightarrow x^2-78x+845=0$
2. $(x-65)(x-13)=0\Rightarrow x=65$ ($x=13$ makes sides negative/zero).
3. Legs: $65-13=52$ and $65-26=39$.
4. $\text{Area}=\frac{1}{2}\times 52\times 39=1014{\text{cm}}^2$

Trick: $39:52:65=3:4:5$ (×13) — spot the 3-4-5 triple directly.

Answer: (B) 1014

Concept: $(1+\sin \theta )(1-\sin \theta )={\cos }^2\theta$ and $(1+\cos \theta )(1-\cos \theta )={\sin }^2\theta$.

1. Expression $=\frac{{\cos }^2\theta }{{\sin }^2\theta ·\cot \theta }$
2. $={\cot }^2\theta \times \frac{1}{\cot \theta }=\cot \theta$
3. $\tan \theta =\frac{7}{8}\Rightarrow \cot \theta =\frac{8}{7}$

Trick: The whole expression collapses to $\cot \theta$ — just invert $\tan \theta$.

Answer: (A) $\frac{8}{7}$

Concept: Translate the words into an equation and solve.

1. Let the number be $x$: $3x-24=258$
2. $3x=282$
3. $x=94$

Trick: Check: $3\times 94=282$, $282-24=258$ ✔

Answer: (A) 94

Concept: Area of rectangle $=l\times b$; area of circle $=\pi r^2$; circumference $=2\pi r$.

1. $169\times 154=26026{\text{m}}^2$
2. $\frac{22}{7}{r}^2=26026\Rightarrow r^2=8281\Rightarrow r=91$
3. $2\pi r=2\times \frac{22}{7}\times 91=572\text{m}$

Trick: $154=22\times 7$, so $r^2=169\times 49\Rightarrow r=13\times 7=91$ instantly.

Answer: (C) 572

Concept: Find each root by prime factorisation / known powers.

1. $\sqrt[6]{729}=\sqrt[6]{3^6}=3$
2. $\sqrt[4]{65536}=\sqrt[4]{{16}^4}=16$
3. $\sqrt[3]{5832}=18$ (as ${18}^3=5832$)
4. $\sqrt{1764}=42$; sum $=3+16+18+42=79$

Trick: $65536=2^{16}$, so its 4th root is $2^4=16$.

Answer: (D) 79

Concept: $\text{Speed}=\frac{\text{Distance}}{\text{Time}}$; use the remaining distance and remaining time.

1. Covered: $\frac{2}{3}\times 387=258\text{km}$ in $\frac{5}{7}\times 21=15\text{h}$
2. Left: $387-258=129\text{km}$ in $21-15=6\text{h}$
3. Speed $=\frac{129}{6}=21.5\text{km/h}$

Trick: Remaining distance $=\frac{1}{3}$, remaining time $=\frac{2}{7}$ of total.

Answer: (A) 21.5

Concept: $SI=\frac{P\times R\times T}{100}$

1. $SI=\frac{350\times 20\times 1.5}{100}$
2. $=\frac{10500}{100}=105$

Trick: 20% per year for 1.5 years = 30% of ₹350 = ₹105.

Answer: (C) ₹105

Concept: Empirical relation: $\text{Mode}=3\text{Median}-2\text{Mean}$.

1. $2\text{Mean}=3\times 65-52.7=195-52.7=142.3$
2. $\text{Mean}=71.15\approx 71.2$

Trick: $\text{Mean}=\frac{3\text{Median}-\text{Mode}}{2}$

Answer: (A) 71.2

Concept: Mean proportional of $a$ and $b$ is $\sqrt{ab}$, i.e. $m^2=ab$.

1. ${68}^2=272x$
2. $4624=272x$
3. $x=17$

Trick: $272=4\times 68$, so $x=\frac{68}{4}=17$.

Answer: (A) 17