RRB NTPC Undergraduate CBT 1 2024 PYQs

Concept: Same base: $(a^m{)}^n=a^{mn}$; compare exponents.

1. $x^z=({132}^{0.14}{)}^z={132}^{0.14z}$
2. $y^2=({132}^{0.26}{)}^2={132}^{0.52}$
3. Equate powers: $0.14z=0.52\Rightarrow z=\frac{0.52}{0.14}=\frac{26}{7}\approx 3.71$

Trick: Base is the same, so just divide the exponents: $\frac{2\times 0.26}{0.14}$.

Answer: (D) $3.71$

Concept: Profit share $\propto$ capital $\times$ time.

1. $M+N=3519$, $M-N=207\Rightarrow M=1863,N=1656$
2. Ratio $=\frac{1863}{1656}=\frac{9}{8}$
3. Let N's capital $=c$: $\frac{6(c+49000)}{7c}=\frac{9}{8}\Rightarrow 48c+2352000=63c$
4. $c=156800$, so M's capital $=156800+49000=205800$

Trick: Get the profit ratio first ($9:8$), then plug capitals into $\frac{6(c+49000)}{7c}$.

Answer: (C) ₹2,05,800

Concept: $1-2{\sin }^{2}A=\cos 2A$ and $2{\cos }^{2}A-1=\cos 2A$.

1. Numerator $=\sin A(1-2{\sin }^{2}A)=\sin A\cos 2A$
2. Denominator $=\cos A(2{\cos }^{2}A-1)=\cos A\cos 2A$
3. Fraction $=\frac{\sin A}{\cos A}=\tan A$
4. $K\times \tan A=1\Rightarrow K=\cot A$

Trick: Put $A={30}^{\circ }$: fraction $=\frac{1/2-1/4}{3\sqrt{3}/4-\sqrt{3}/2}=\frac{1}{\sqrt{3}}$, so $K=\sqrt{3}=\cot {30}^{\circ }$.

Answer: (A) $\cot A$

Concept: Work on the remaining part step by step.

1. After debt: $100\%-33\%=67\%$ of salary remains
2. Spends $25\%$ of it, saves $75\%$: $0.75\times 0.67=0.5025$ of salary
3. $0.5025S=402\Rightarrow S=\frac{402}{0.5025}=800$

Trick: Check options: $800\times 0.67=536$, $536\times 0.75=402$ ✓.

Answer: (D) $800$

Concept: Same distance: time $\propto \frac{1}{\text{speed}}$.

1. Distance $=100\times 14=1400\text{km}$
2. Disha's time $=\frac{1400}{35}=40$ hours

Trick: $t_2=t_1\times \frac{s_1}{s_2}=14\times \frac{100}{35}=40$.

Answer: (C) 40 hours

Concept: Difference of ratio parts gives one part's value.

1. Largest − smallest $=13-3=10$ parts $=36846$
2. 1 part $=3684.6$
3. Total $=13+3+9=25$ parts $=25\times 3684.6=92115$

Trick: Total $=36846\times \frac{25}{10}=36846\times 2.5$.

Answer: (D) 92,115

Concept: Test each option.

1. Ends in 3 → not divisible by 5; odd → not by 6 or 12
2. Rule of 7: $26753-2\times 3=26747$; $2674-14=2660$; $266-0=266=7\times 38$ ✓
3. Direct: $267533=7\times 38219$

Trick: Odd number kills 6 and 12 at once; last digit kills 5 — only 7 is left.

Answer: (B) 7

Concept: All sides equal + one right angle + parallelogram ⇒ square.

1. Opposite sides parallel and opposite angles equal → parallelogram
2. All sides equal → rhombus
3. One angle ${90}^{\circ }$ → every angle ${90}^{\circ }$ → square

Trick: Rhombus + right angle = square; rectangle needs only opposite sides equal.

Answer: (B) square

Concept: Apply discounts one after another.

1. After 15%: $12000\times 0.85=10200$
2. After 10%: $10200\times 0.9=9180$

Trick: Net discount $=15+10-\frac{15\times 10}{100}=23.5\%$; $12000\times 0.765=9180$.

Answer: (C) ₹9,180

Concept: Average $=\frac{\text{sum}}{\text{number}}$.

1. Sum $=40+49+56+74+37=256$
2. Average $=\frac{256}{5}=51.2$

Trick: Take 50 as base: deviations $-10,-1,+6,+24,-13=+6$; $50+\frac{6}{5}=51.2$.

Answer: (D) $51.2$

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

1. CP per pen $=\frac{180}{12}=15$
2. SP $=22$, profit $=7$
3. $\text{Profit}\%=\frac{7}{15}\times 100=46.67\%$

Trick: $\frac{7}{15}=\frac{1}{3}+\frac{2}{15}=33.33+13.33=46.67$.

Answer: (A) $46.67$

Concept: Total work = LCM of days; find units done.

1. Total $=\text{LCM}(16,22)=176$ units; A $=11$, B $=8$ units/day
2. Together in 2 days: $2\times 19=38$ units
3. Left $=176-38=138$ units $=\frac{138}{176}=\frac{69}{88}$

Trick: Done $=2(\frac{1}{16}+\frac{1}{22})=\frac{19}{88}$, left $=1-\frac{19}{88}$.

Answer: (B) $\frac{69}{88}$

Concept: $A=P{(1+\frac{r}{100})}^n$.

1. $\frac{841}{625}={\left(1.16\right)}^n$
2. $\frac{841}{625}={\left(\frac{29}{25}\right)}^2$ and $\frac{29}{25}=1.16$
3. So $n=2$ years

Trick: $841={29}^2$, $625={25}^2$ — the squares give the time instantly.

Answer: (C) 2 years

Concept: Two successive $10\%$ discounts $=10+10-\frac{10\times 10}{100}=19\%$.

1. Single 20%: $0.20\times 600=120$
2. Successive: $0.19\times 600=114$
3. Difference $=120-114=6$

Trick: Difference $=\frac{10\times 10}{100}\%=1\%$ of 600 $=6$.

Answer: (D) ₹6

Concept: Find each pipe's full-tank time, then net rate.

1. P: $\frac{4}{9}$ in 20 h → full in $20\times \frac{9}{4}=45$ h; Q: $\frac{2}{9}$ in 30 h → full in $135$ h
2. In 3 h: $3(\frac{1}{45}+\frac{1}{135})=3\times \frac{4}{135}=\frac{4}{45}$ filled
3. R empties $\frac{4}{45}$ in 4 h → empties full tank in $45$ h
4. Together: $\frac{1}{45}+\frac{1}{135}-\frac{1}{45}=\frac{1}{135}$ → 135 h

Trick: R cancels P exactly (both 45 h), so the net is just Q: 135 h.

Answer: (B) 135 hours

Concept: Simplify the complex fraction first, then take LCM.

1. $1+\frac{5}{8}=\frac{13}{8}$, so $\frac{1}{13/8}=\frac{8}{13}$
2. $\frac{3}{2}+\frac{8}{13}-\frac{4}{3}$, LCM $=78$
3. $=\frac{117+48-104}{78}=\frac{61}{78}$

Trick: Denominator must contain 13 and 6 → only 78 fits.

Answer: (C) $\frac{61}{78}$

Concept: Lateral surface area of cuboid $=2h(l+b)$.

1. Cube side $=\sqrt[3]{15625}=25\text{cm}$
2. Cuboid: $l=5\times 25=125$, $b=h=25$
3. LSA $=2\times 25\times (125+25)=7500{\text{cm}}^2$

Trick: LSA = 4 long faces $=4\times (125\times 25)=7500$.

Answer: (B) $7500$

Concept: Form two equations in Salaj's speed $s$ and Kevin's time $t$.

1. $\frac{112}{s}=t+3$
2. $\frac{112}{2s}=t-5$
3. Subtract: $\frac{56}{s}=8\Rightarrow s=7\text{km/h}$

Trick: Halving the time saves $8$ h, so normal time $=16$ h; $\frac{112}{16}=7$.

Answer: (B) $7\text{km/hr}$

Concept: Expand and collect like terms.

1. $\frac{6}{3}=2$: $3(2x^2-22x+14)=6x^2-66x+42$
2. $-6(x^2+6x-15)=-6x^2-36x+90$
3. Sum $=-102x+132$

Trick: $x^2$ terms cancel ($6-6=0$); just add $x$ terms and constants.

Answer: (B) $-102x+132$

Concept: Translate statements into equations.

1. $3M=5D+29$
2. $2D=M-9\Rightarrow M=2D+9$
3. $3(2D+9)=5D+29\Rightarrow D=2$, $M=13$
4. Difference $=13-2=11$

Trick: Check: $3\times 13=39=5\times 2+29$ ✓.

Answer: (A) 11