RRB NTPC Graduate CBT 1 2024 PYQs

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

1. $61.6=3M-2\times 47.4=3M-94.8$.
2. $3M=156.4$.
3. $M=\frac{156.4}{3}=52.13\approx 52.1$.

Trick: $\text{Median}=\frac{\text{Mode}+2\text{Mean}}{3}=\frac{61.6+94.8}{3}$.

Answer: (B) $52.1$

Concept: Angle sum of a quadrilateral is ${360}^{\circ }$. If two adjacent angles add to ${180}^{\circ }$, the sides opposite their common side are parallel.

1. $2+8+3+7=20$ parts ⇒ 1 part $={18}^{\circ }$: $\angle P={36}^{\circ }$, $\angle Q={144}^{\circ }$, $\angle R={54}^{\circ }$, $\angle S={126}^{\circ }$.
2. $\angle P+\angle Q={180}^{\circ }$ ⇒ $PS\parallel QR$.
3. $\angle Q+\angle R={198}^{\circ }\ne {180}^{\circ }$ ⇒ $PQ$ not parallel to $SR$.
4. Exactly one pair of parallel sides ⇒ trapezium.

Trick: Ratio terms $2+8=3+7=10$ (half of 20) ⇒ co-interior pair ⇒ trapezium; all angles unequal rules out rhombus/square.

Answer: (A) Trapezium

Concept: After paying 40% rent, the remaining 60% of salary covers the other expenses and savings.

1. Other expenses + savings = ₹$442+9115+946$ = ₹10,503.
2. $60\%$ of salary = ₹10,503.
3. Salary = ₹$\frac{10503\times 100}{60}$ = ₹17,505.

Trick: Salary must be a multiple of 5 such that $0.6\times$ salary = 10503 – only 17,505 works ($17505\times 0.6=10503$).

Answer: (C) ₹17,505

Concept: $V=\frac{1}{3}\pi r^{2}h$, $l=\sqrt{r^2+h^2}$, $\text{TSA}=\pi r(r+l)$.

1. $\frac{1}{3}\times \frac{22}{7}\times r^2\times 21=1078$ ⇒ $22r^2=1078$ ⇒ $r^2=49$, $r=7$.
2. $l=\sqrt{49+441}=\sqrt{490}=7\sqrt{10}$.
3. $\text{TSA}=\frac{22}{7}\times 7\times (7+7\sqrt{10})=22\times 7(1+\sqrt{10})=154(1+\sqrt{10}){\text{cm}}^2$.

Trick: With $h=21$, $\frac{1}{3}\pi h=22$, so $r^2=\frac{1078}{22}=49$ instantly.

Answer: (C) $154(1+\sqrt{10}){\text{cm}}^2$

Concept: Take total work = LCM of the days and find each person's daily work.

1. Total work = LCM(2, 52) = 52 units; A = 26 units/day, B = 1 unit/day.
2. B in 26 days: $26\times 1=26$ units; remaining $52-26=26$ units.
3. A's time $=\frac{26}{26}=1$ day.

Trick: B did half the work (26 of 52 days), so A needs half of 2 days = 1 day.

Answer: (C) 1

Concept: Volume of a hollow sphere $=\frac{4}{3}\pi (R^3-r^3)$; mass $=$ density $\times$ volume.

1. $R^3-r^3=729-512=217$.
2. Volume $=\frac{4}{3}\times \frac{22}{7}\times 217=\frac{2728}{3}{\text{cm}}^3$.
3. Mass $=21\times \frac{2728}{3}=19096\text{g}=19.096\text{kg}$.

Trick: $217=7\times 31$ cancels the 7 of $\pi$ and $21$ cancels the 3 → $4\times 22\times 31\times 7=19096$.

Answer: (B) 19.096

Concept: Two consecutive integers are $x$ and $x+1$.

1. Product: $x(x+1)=960$.
2. $x^2+x=960\Rightarrow x^2+x-960=0$.
3. Only the form of the equation is asked, so no need to solve it.

Trick: Consecutive → $x(x+1)$; move the constant to the left with a minus sign.

Answer: (B) $x^2+x-960=0$

Concept: Secant–power theorem: for external point P, $PA\times PB=P{O}^2-r^2$.

1. $PB=PA+AB=8+7=15\text{cm}$.
2. $PA\times PB=8\times 15=120$.
3. ${17}^2-r^2=120\Rightarrow r^2=289-120=169\Rightarrow r=13\text{cm}$.

Trick: $PA·PB$ = (tangent length)${}^2$ = $d^2-r^2$.

Answer: (A) 13 cm

Concept: Follow BODMAS: brackets (with 'of') first, then division.

1. $\frac{9}{9}\text{ of }\frac{9}{8}=1\times \frac{9}{8}=\frac{9}{8}$.
2. $4\times \frac{9}{8}=\frac{9}{2}$.
3. $34÷\frac{9}{2}=34\times \frac{2}{9}=\frac{68}{9}$.

Trick: $\frac{9}{9}=1$ – spot such simplifications at a glance.

Answer: (A) $\frac{68}{9}$

Concept: Sum of numbers = average $\times$ count.

1. Sum $=23\times 3=69$.
2. Third number $=69-(11+25)=69-36=33$.

Trick: Deviation method: $11$ is $-12$, $25$ is $+2$ from 23 → third $=23+10=33$.

Answer: (D) 33

Concept: SP at loss $=\text{CP}\times \frac{100-\text{loss}\%}{100}$.

1. $\text{CP}=\frac{950\times 100}{95}=1000$.
2. Gain $=1360-1000=360$.
3. $x=\frac{360}{1000}\times 100=36\%$.

Trick: 5% loss on ₹950 → CP is a round ₹1000; gain is then read directly.

Answer: (C) 36

Concept: Form two equations and eliminate one variable.

1. $A+4B=34$ … (i); $3A+7B=97$ … (ii).
2. (i) $\times 3$: $3A+12B=102$; subtract (ii): $5B=5\Rightarrow B=1$.
3. $A=34-4=30$; $A+B=31$.

Trick: Multiply the equation with coefficient 1 to match the other's $A$.

Answer: (B) 31

Concept: Successive increases multiply: $P\times (1+\frac{r_1}{100})(1+\frac{r_2}{100})$.

1. After year 1: $110000\times \frac{105}{100}=115500$.
2. After year 2: $115500\times \frac{125}{100}=144375$.

Trick: $25\%=\frac{1}{4}$: add a quarter, $115500+28875=144375$.

Answer: (A) 1,44,375

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

1. Times: $\frac{576}{16}=36$, $\frac{630}{7}=90$, $\frac{315}{9}=35$ → total $161\text{h}$.
2. Distance $=576+630+315=1521\text{km}$.
3. $\frac{1521}{161}=9\frac{72}{161}\text{km/h}$ (since $161\times 9=1449$).

Trick: Never average the speeds; compute each time separately.

Answer: (C) $9\frac{72}{161}$

Concept: SP $=\text{MP}\times \frac{100-d}{100}$; without discount SP = MP.

1. $\text{MP}=\frac{5180}{0.20}=25900$.
2. Selling at MP gives 48% gain: $\text{CP}\times 1.48=25900$.
3. $\text{CP}=\frac{25900}{1.48}=17500$.

Trick: $1.48=\frac{37}{25}$: $25900\times \frac{25}{37}=700\times 25=17500$.

Answer: (D) 17,500

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

1. $(18+8\sqrt{2})(15-2\sqrt{2})=270-36\sqrt{2}+120\sqrt{2}-16\times 2$.
2. $=270-32+84\sqrt{2}=238+84\sqrt{2}$.
3. Mean proportional $=\sqrt{238+84\sqrt{2}}$.

Trick: All options share 238; only the $\sqrt{2}$ term matters: $120-36=84$.

Answer: (A) $\sqrt{238+84\sqrt{2}}$

Concept: For fixed distance, time $\propto \frac{1}{\text{speed}}$.

1. Speed ratio new : usual $=5:7$, so time ratio $=7:5$.
2. Extra time $=7-5=2$ parts $=20$ minutes → 1 part $=10$ minutes.
3. Usual time $=5$ parts $=50$ minutes.

Trick: Speed $\frac{a}{b}$ of normal and late by $t$ → usual time $=\frac{at}{b-a}=\frac{5\times 20}{2}$.

Answer: (C) 50 minutes

Concept: Write everything as powers of 146 and compare exponents.

1. $x^z={146}^{0.93z}$ and $y^7={146}^{0.22\times 7}={146}^{1.54}$.
2. $0.93z=1.54\Rightarrow z=\frac{1.54}{0.93}\approx 1.66$.

Trick: Same base → equate exponents.

Answer: (C) 1.66

Concept: Total = average $\times$ count; difference of totals gives the excluded value.

1. Total of 7 subjects $=75\times 7=525$.
2. Total of 6 subjects $=70\times 6=420$.
3. Science $=525-420=105$.

Trick: Science $=75+6\times (75-70)=105$.

Answer: (A) 105

Concept: Convert each ratio to a decimal (or compare with $\frac{1}{2}$).

1. $\frac{33}{51}\approx 0.647$, $\frac{37}{64}\approx 0.578$.
2. $\frac{32}{86}\approx 0.372$, $\frac{26}{59}\approx 0.441$.
3. Greatest: $33:51$.

Trick: $\frac{32}{86}$ and $\frac{26}{59}$ are below $\frac{1}{2}$; between the other two, $33:51$ has larger numerator and smaller denominator.

Answer: (A) $33:51$