RRB NTPC Graduate CBT 1 2024 PYQs

Concept: Use ${\sin }^2\beta +{\cos }^2\beta =1$.

1. $\frac{m}{a}={\cos }^3\beta \Rightarrow {\left(\frac{m}{a}\right)}^{\frac{2}{3}}={\cos }^2\beta$
2. $\frac{n}{b}={\sin }^3\beta \Rightarrow {\left(\frac{n}{b}\right)}^{\frac{2}{3}}={\sin }^2\beta$
3. Sum $={\cos }^2\beta +{\sin }^2\beta =1$

Trick: Power $\frac{2}{3}$ turns cube into square: $(x^3{)}^{\frac{2}{3}}=x^2$.

Answer: (C) 1

Concept: LCM takes the highest power of every prime present in the numbers.

1. $7800=2^3\times 3\times 5^2\times 13$
2. $40=2^3\times 5$, $78=2\times 3\times 13$ — the factor $5^2$ is missing, so $x$ must contain $5^2$ and no prime beyond these powers.
3. $200=2^3\times 5^2$ ✔; $180$ has $3^2$, $127$ is prime, $152$ has $19$ — all fail.

Trick: Find the missing prime power first ($5^2=25$); only multiples of 25 can work.

Answer: (B) 200

Concept: Take CP = 100 and find the required SP.

1. MP $=150$, required SP $=108$
2. Discount $=150-108=42$
3. Discount% $=\frac{42}{150}\times 100=28\%$

Trick: Discount% $=\frac{M-P}{100+M}\times 100=\frac{50-8}{150}\times 100=28\%$.

Answer: (C) 28%

Concept: Mean proportional of $a$ and $b$ $=\sqrt{ab}$.

1. $18-6\sqrt{7}=2(9-3\sqrt{7})$
2. $ab=2(9+3\sqrt{7})(9-3\sqrt{7})=2(81-63)=36$
3. $\sqrt{36}=6$

Trick: Spot the conjugate pair: $(x+y)(x-y)=x^2-y^2$.

Answer: (A) 6

Concept: SP = MP × (1 − discount).

1. CP $=100$ ⇒ MP $=170$, SP $=153$
2. $170(1-\frac{X}{100})=153$
3. $\frac{X}{100}=\frac{17}{170}=\frac{1}{10}$ ⇒ $X=10$

Trick: $X=\frac{70-53}{170}\times 100=10$.

Answer: (C) 10

Concept: Work backwards: in the last 11 days only Sharad works.

1. Sharad’s 11 days $=\frac{11}{13}$ of work; remaining $\frac{2}{13}$ done together.
2. Combined rate $=\frac{1}{13}+\frac{1}{9}=\frac{22}{117}$ per day.
3. Time together $=\frac{2}{13}÷\frac{22}{117}=\frac{9}{11}$ day.
4. Total $=11+\frac{9}{11}=11\frac{9}{11}$ days.

Trick: “Left $k$ days before completion” ⇒ start from the end with the remaining worker.

Answer: (C) $11\frac{9}{11}$

Concept: In a regular polygon, interior + exterior $={180}^{\circ }$ and exterior $=\frac{{360}^{\circ }}{n}$.

1. $I+E={180}^{\circ }$, $I-E={140}^{\circ }$
2. $2E={40}^{\circ }$ ⇒ $E={20}^{\circ }$
3. $n=\frac{360}{20}=18$

Trick: $E=\frac{180-\text{difference}}{2}$, then $n=\frac{360}{E}$.

Answer: (C) 18

Concept: Each numerator term is 10 times the matching denominator term.

1. $0.06=10\times 0.006$, $0.66=10\times 0.066$, $0.666=10\times 0.0666$
2. Squares: numerator $={10}^2\times$ denominator
3. Value $=100$

Trick: If $a=kx$, $b=ky$, $c=kz$ then $\frac{a^2+b^2+c^2}{x^2+y^2+z^2}=k^2$.

Answer: (D) 100

Concept: Let son’s present age $=s$.

1. Hitesh $=3s$, daughter $=s-3$; present sum $=5s-3$
2. 3 years ago sum $=5s-3-9=123$
3. $5s=135$ ⇒ $s=27$, Hitesh $=81$

Trick: Sum $n$ years ago = present sum − (people × $n$).

Answer: (A) 81

Concept: Write the expression as a sum of squares.

1. $(x^2-10x+25)+(y^2+26y+169)=25+169-194$
2. $(x-5{)}^2+(y+13{)}^2=0$ ⇒ $x=5$, $y=-13$
3. $x^2+y^2=25+169=194$

Trick: Sum of squares $=0$ ⇒ each square $=0$.

Answer: (B) 194

Concept: Ashish’s rate = combined rate − other rates.

1. $\frac{1}{6}-\frac{1}{9}-\frac{1}{21}$; LCM $=126$
2. $=\frac{21-14-6}{126}=\frac{1}{126}$ ⇒ Ashish alone: 126 hours
3. Twice the work: $2\times 126=252$ hours

Trick: Take total work = LCM(9, 21, 6) = 126 units: Ashish does 1 unit/h.

Answer: (B) 252

Concept: Average = total ÷ number of days.

1. Total $=1200+1300+1400+1100+1300+1200=7500$
2. Average $=\frac{7500}{6}=1250$

Trick: Assume 1200 as base: deviations $0+100+200-100+100+0=300$, $\frac{300}{6}=50$ ⇒ $1250$.

Answer: (B) ₹1,250

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

1. $SI=\frac{2200\times 5\times 2}{100}$
2. $=220$

Trick: $5\%\times 2=10\%$ of 2200 $=220$.

Answer: (A) ₹220

Concept: $A\propto B$ ⇒ $\frac{A}{B}$ is constant.

1. $\frac{210}{51}=\frac{A}{136}$
2. $A=\frac{210\times 136}{51}=\frac{210\times 8}{3}=560$

Trick: $\frac{136}{51}=\frac{8}{3}$, so $A=210\times \frac{8}{3}=560$.

Answer: (B) 560

Concept: Volume of cuboid $=l\times b\times h$.

1. $4\times 46\times h=8832$
2. $184h=8832$ ⇒ $h=48\text{cm}$

Trick: Unit-digit check: $184\times h$ ends in 2 ⇒ $h$ ends in 3 or 8; $184\times 48=8832$ ✔

Answer: (B) 48

Concept: $\text{Median}=l+\frac{\frac{N}{2}-cf}{f}\times h$

1. $N=148$, $\frac{N}{2}=74$
2. Cumulative frequencies: 11, 27, 41, 70, 110 ⇒ median class 60-70.
3. $l=60$, $cf=70$, $f=40$, $h=10$
4. $\text{Median}=60+\frac{74-70}{40}\times 10=61$

Trick: Median class = first class whose cumulative frequency crosses $\frac{N}{2}$.

Answer: (D) 61 years

Concept: Apply BODMAS: powers first, then division/multiplication left to right, then addition/subtraction.

1. $3^2=9$
2. $72÷18\times 9=4\times 9=36$
3. $21\times 12÷3=252÷3=84$
4. $z=36-84+12=-36$

Trick: Solve each product-quotient block separately, then combine: $36-84+12$.

Answer: (D) $-36$

Concept: Moving in opposite directions on a circular track, they meet first when together they cover one full round: $\text{time}=\frac{\text{length}}{\text{sum of speeds}}$.

1. $4.6+X=\frac{2742}{457}$
2. $\frac{2742}{457}=6\text{m/s}$
3. $X=6-4.6=1.4\text{m/s}$

Trick: Opposite directions → add speeds; same direction → subtract.

Answer: (D) $1.4$

Concept: Find the remaining distance and the remaining time, then $\text{speed}=\frac{\text{distance}}{\text{time}}$.

1. Distance covered $=\frac{2}{3}\times 387=258\text{km}$; remaining $=129\text{km}$.
2. Time used $=\frac{6}{9}\times 18=12\text{h}$; time left $=6\text{h}$.
3. Required speed $=\frac{129}{6}=21.5\text{km/h}$

Trick: Remaining $\frac{1}{3}$ distance in remaining $\frac{1}{3}$ time: $\frac{387}{18}=21.5$ — same as the average speed.

Answer: (A) $21.5$

Concept: Take a convenient cost price and apply the changes step by step; $\text{Profit}\%=\frac{\text{SP}-\text{CP}}{\text{CP}}\times 100$.

1. Let CP = 100, so SP = 130.
2. New CP $=100\times 1.3=130$; new SP $=130\times 1.7=221$.
3. Profit $=221-130=91$
4. $\text{Profit}\%=\frac{91}{130}\times 100=70\%$

Trick: Both CP and SP were 130 at different stages; SP rises 70% on the new CP of 130 → profit is exactly 70%.

Answer: (A) $70\%$