RRB NTPC Graduate CBT 1 2024 PYQs

Concept: For 2 years, $\text{CI}=P[{(1+\frac{R}{100})}^2-1]$ and $\text{SI}=\frac{P\times R\times T}{100}$.

1. At $5\%$: $(1.05{)}^2-1=0.1025$
2. $0.1025P=102.5\Rightarrow P=1000$
3. $\text{SI}=\frac{1000\times 5\times 2}{100}=100$

Trick: 2-year CI at $R\%$ = SI $+$ interest on interest: $\text{CI}-\text{SI}=P{\left(\frac{R}{100}\right)}^2$. Here $\text{CI}=\text{SI}(1+\frac{R}{200})$ → $\text{SI}=\frac{102.5}{1.025}=100$.

Answer: (C) ₹$100$

Concept: $(a+b{)}^3=a^3+b^3+3a^{2}b+3a{b}^2$.

1. Take $a=4x$, $b=3y$: $3a^{2}b=3(16x^2)(3y)=144x^{2}y$ and $3a{b}^2=3(4x)(9y^2)=108x{y}^2$ ✓
2. So the expression $=(4x+3y{)}^3$
3. $4(5)+3(-5)=20-15=5$, and $5^3=125$

Trick: Cube roots of the first and second terms ($4x$, $3y$) tell you the bracket instantly.

Answer: (B) $125$

Concept: Solve brackets inside-out, then ÷ and ×, then subtraction; track the signs carefully.

1. $(-31-58-19)=-108$; $\{7+(-2)(-6)\}=19$; $[9\times 19]=171$
2. $(-98)\times (-108)=10584$
3. $10584÷171=\frac{10584}{171}=\frac{1176}{19}$
4. $72-\frac{1176}{19}=\frac{1368-1176}{19}=\frac{192}{19}$

Trick: All options have denominator $19$; cancel the $9$ first: $\frac{10584}{9}=1176$.

Answer: (A) $\frac{192}{19}$

Concept: For a cubic $a{x}^3+b{x}^2+cx+d=0$, product of roots $=-\frac{d}{a}$.

1. Here $a=k$, $d=k$.
2. Product $=-\frac{k}{k}=-1$

Trick: Cubic signs: sum $=-\frac{b}{a}$, pair-sum $=+\frac{c}{a}$, product $=-\frac{d}{a}$ (signs alternate $-,+,-$).

Answer: (B) $-1$

Concept: $\text{Average}=\frac{\text{Sum of values}}{\text{Number of values}}$

1. Sum $=250+300+275+325+350=1500$
2. Average $=\frac{1500}{5}=300$

Trick: Take $300$ as base: deviations $-50,0,-25,+25,+50$ sum to $0$ → average $=300$.

Answer: (C) ₹$300$

Concept: $\text{SP}=\text{CP}\times \frac{100+\text{gain}\%}{100}$ and $\text{SP}=\text{MP}\times \frac{100-\text{discount}\%}{100}$.

1. $\text{SP}=1301\times \frac{141}{100}=1834.41$
2. $\text{MP}\times \frac{47}{100}=1834.41$
3. $\text{MP}=\frac{1834.41\times 100}{47}=3903$

Trick: $\text{MP}=\text{CP}\times \frac{141}{47}=1301\times 3=3903$, since $141=3\times 47$.

Answer: (D) ₹$3903$

Concept: Write each ratio as a fraction/decimal and compare.

1. $\frac{9}{11}\approx 0.82$, $\frac{10}{27}\approx 0.37$, $\frac{31}{38}\approx 0.82$
2. $\frac{11}{11}=1$
3. Every other ratio has antecedent smaller than consequent, so each is less than $1$.

Trick: A ratio equal to $1$ beats every ratio whose first term is smaller than its second.

Answer: (C) $11:11$

Concept: $\text{Mode}=l+\frac{f_1-f_0}{2f_1-f_0-f_2}\times h$, where $l$ is the lower limit of the modal (highest-frequency) class.

1. Highest frequency $37$ → modal class $50$–$60$: $l=50$, $h=10$, $f_1=37$, $f_0=34$, $f_2=32$.
2. $\text{Mode}=50+\frac{37-34}{74-34-32}\times 10=50+\frac{3}{8}\times 10$
3. $=50+3.75=53.75$

Trick: The mode always lies inside the modal class; among the options only $53.75$ lies in $50$–$60$.

Answer: (B) $53.75$

Concept: $l^2=r^2+h^2$ and $V=\frac{1}{3}\pi r^{2}h$.

1. $l=2r\Rightarrow h=\sqrt{4r^2-r^2}=\sqrt{3}r$
2. $V=\frac{1}{3}\pi r^2·\sqrt{3}r=\frac{\sqrt{3}}{3}\pi r^3=401\pi$
3. $r^3=\frac{3\times 401}{\sqrt{3}}=401\sqrt{3}$

Trick: $\frac{3}{\sqrt{3}}=\sqrt{3}$, so $r^3=401\sqrt{3}$ directly.

Answer: (A) $401\sqrt{3}$

Concept: Sum of interior angles $=(n-2)\times {180}^{\circ }$; number of diagonals $=\frac{n(n-3)}{2}$.

1. $(n-2)\times 180=1260\Rightarrow n-2=7\Rightarrow n=9$
2. Diagonals $=\frac{9\times 6}{2}=27$

Trick: $\frac{1260}{180}=7$ → add $2$ → $9$ sides (nonagon).

Answer: (B) $27$

Concept: Convert averages to totals; the common member is counted twice in the pair totals.

1. $A+B+C=3\times 45=135$
2. $A+B=2\times 39=78$, $B+C=2\times 48=96$
3. $B=(A+B)+(B+C)-(A+B+C)=78+96-135=39$

Trick: Common member $=$ sum of the two pair totals $-$ group total.

Answer: (B) $39$

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

1. $R=\frac{700\times 100}{1400\times 5}$
2. $=\frac{70000}{7000}=10\%$

Trick: SI is half the principal in 5 years → $50\%$ in 5 years → $10\%$ per year.

Answer: (A) $10\%$

Concept: Number to add $=$ divisor $-$ remainder.

1. $67\times 207=13869$, so $13874÷67$ leaves remainder $13874-13869=5$
2. Number to add $=67-5=62$
3. Check: $13874+62=13936=67\times 208$ ✓

Trick: $67\times 200=13400$; $13874-13400=474$; $474=67\times 7+5$ → remainder $5$.

Answer: (D) $62$

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

1. First part: $23\times 4.5=103.5\text{km}$
2. New speed $=23+11=34\text{km/h}$; second part $=34\times 1=34\text{km}$
3. Total distance $=137.5\text{km}$, total time $=5.5\text{h}$
4. Average $=\frac{137.5}{5.5}=25\text{km/h}$

Trick: Never average the two speeds directly; always divide total distance by total time.

Answer: (B) $25$

Concept: Difference of ratio parts corresponds to the given money difference.

1. Ratio A : B : C : D $=10:4:8:5$
2. C − B $=8-4=4$ parts $=$ ₹24, so 1 part $=$ ₹6
3. A $=10\times 6=$ ₹60

Trick: Value of 1 part = difference ÷ difference of parts.

Answer: (C) ₹60

Concept: Mode is the value that occurs most often in the data.

1. Count repeats: 43 appears 4 times.
2. 53 appears 3 times; 42 and 54 appear 2 times each; others once.
3. Highest frequency is 4, for 43.

Trick: Sort mentally or tally only the repeated numbers – no need to count singles.

Answer: (D) $43$

Concept: Covered : remaining $=5:4$, so the covered part is $\frac{5}{9}$ of the total.

1. Distance covered $=\frac{5}{9}\times 39=\frac{65}{3}\approx 21.67\text{km}$
2. Time $=5\text{h}5\text{min}=5\frac{5}{60}=\frac{61}{12}\text{h}$
3. Speed $=\frac{65}{3}÷\frac{61}{12}=\frac{65\times 12}{3\times 61}=\frac{260}{61}\approx 4.26$
4. Rounded: $4.3\text{km/h}$

Trick: 'a/b of remaining' ⇒ covered $=\frac{a}{a+b}$ of total.

Answer: (B) $4.3$

Concept: $\text{TSA}=2\pi r(r+h)$, $V=\pi r^{2}h$

1. $2\times \frac{22}{7}\times 7\times (7+h)=396$
2. $44(7+h)=396\Rightarrow 7+h=9\Rightarrow h=2\text{cm}$
3. $V=\frac{22}{7}\times 7^2\times 2=22\times 7\times 2=308{\text{cm}}^3$

Trick: With $r=7$, $2\pi r=44$ – divide TSA by 44 to get $r+h$ instantly.

Answer: (B) $308$

Concept: Find both values separately and subtract.

1. $60\%\text{ of }40=\frac{60}{100}\times 40=24$
2. $\frac{3}{5}\text{ of }15=9$
3. Difference $=24-9=15$

Trick: $60\%=\frac{3}{5}$, so the answer is $\frac{3}{5}\times (40-15)=15$.

Answer: (B) $15$

Concept: Angle sum of a quadrilateral $={360}^{\circ }$; the angle between bisectors of two adjacent angles $=\frac{1}{2}(\text{sum of the other two angles})$.

1. $\angle S+\angle T={360}^{\circ }-({52}^{\circ }+{44}^{\circ })={264}^{\circ }$
2. In $△TES$: $\frac{\angle S}{2}+\frac{\angle T}{2}={132}^{\circ }$
3. $\angle TES={180}^{\circ }-{132}^{\circ }={48}^{\circ }$

Trick: $\angle TES=\frac{\angle Q+\angle R}{2}=\frac{{96}^{\circ }}{2}={48}^{\circ }$.

Answer: (A) ${48}^{\circ }$