RRB NTPC Undergraduate CBT 1 2024 PYQs

Concept: $\text{SI}=\frac{P\times R\times T}{100}$, with $R$ and $T$ in the same time unit.

1. Rate $4\%$ per month, time $7$ months
2. $\text{SI}=\frac{1200\times 4\times 7}{100}=336$
3. (If the rate were $4\%$ per annum, $\text{SI}=1200\times \frac{4}{100}\times \frac{7}{12}=28$.)

Trick: Always check whether the rate is per month or per annum before plugging in.

Answer: (A) ₹336

Concept: $\text{Side}=\frac{\text{Perimeter}}{4}$, $\text{Area}={\text{side}}^2$.

1. $\text{Side}=\frac{52}{4}=13\text{m}$
2. $\text{Area}={13}^2=169{\text{m}}^2$

Trick: Area $=\frac{{\text{Perimeter}}^2}{16}=\frac{2704}{16}=169$.

Answer: (C) $169$

Concept: Total work in man-days equals total work in woman-days; compare to find relative efficiency.

1. $4\times 18=72$ man-days $=9\times 8=72$ woman-days
2. So 1 man $=$ 1 woman
3. 3 women + 3 men $=6$ persons
4. $\text{Days}=\frac{72}{6}=12$

Trick: $M_1{D}_1=M_2{D}_2$ – equal products mean equal efficiency.

Answer: (C) 12 days

Concept: $a^m÷a^n=a^{m-n}$ and $a^m\times a^n=a^{m+n}$; work left to right.

1. ${66}^{-5}÷{66}^{11}={66}^{-5-11}={66}^{-16}$
2. ${66}^{-16}\times {66}^{-12}={66}^{-16-12}={66}^{-28}$

Trick: Exponent $=-5-11+(-12)=-28$.

Answer: (C) ${66}^{-28}$

Concept: Expand each bracket and combine like terms.

1. $3(\frac{7}{3}{x}^2-28x+14)=7x^2-84x+42$
2. $-7(x^2+4x-14)=-7x^2-28x+98$
3. Sum: $(7x^2-7x^2)+(-84x-28x)+(42+98)=-112x+140$

Trick: The $x^2$ terms cancel; the $x$-coefficient is negative and the constant positive – only one option fits.

Answer: (D) $-112x+140$

Concept: Multiply numerator and denominator by $(1+\cos A)$ and use $1-{\cos }^{2}A={\sin }^{2}A$.

1. $\sqrt{\frac{(1+\cos A{)}^2}{1-{\cos }^{2}A}}=\sqrt{\frac{(1+\cos A{)}^2}{{\sin }^{2}A}}$
2. $=\frac{1+\cos A}{\sin A}$
3. $=\frac{1}{\sin A}+\frac{\cos A}{\sin A}=cosecA+\cot A$

Trick: Put $A={90}^{\circ }$: expression $=1$; $cosec{90}^{\circ }+\cot {90}^{\circ }=1+0=1$ ✓

Answer: (D) $cosecA+\cot A$

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

1. $\sqrt{25\times 36}=\sqrt{900}$
2. $=30$ (or $5\times 6=30$)

Trick: $\sqrt{ab}=\sqrt{a}\times \sqrt{b}=5\times 6$.

Answer: (B) $30$

Concept: Count days excluding the deposit day and including the withdrawal day; 2024 is a leap year (366 days).

1. Feb: $29-10=19$, March: $31$, April: $11$ → $61$ days
2. $\text{SI}=\frac{4000\times 7.5\times 61}{100\times 366}$
3. $=\frac{300\times 61}{366}=\frac{300}{6}=50$

Trick: $366=6\times 61$ – the 61 cancels neatly, confirming the day count.

Answer: (D) $50$

Concept: After a $7\%$ decrease, $93\%$ of the number remains.

1. $93\%\text{ of }x=2790$
2. $x=\frac{2790\times 100}{93}=30\times 100=3000$

Trick: $2790÷93=30$, so the number is $3000$.

Answer: (A) $3000$

Concept: Test odd numbers in the range for divisibility by primes up to $\sqrt{486}\approx 22$.

1. Odd numbers: $473=11\times 43$, $475=5\times 95$, $477=9\times 53$
2. $481=13\times 37$, $483=3\times 161$, $485=5\times 97$
3. $479$ is not divisible by $2,3,5,7,11,13,17,19$ → prime

Trick: Remember tricky composites like $481=13\times 37$ and $473=11\times 43$.

Answer: (A) $1$

Concept: For consecutive numbers $n(n+1)=650$, $n$ is close to $\sqrt{650}$.

1. $\sqrt{650}\approx 25.5$, so try $25$ and $26$.
2. $25\times 26=650$ ✓
3. Greater number $=26$.

Trick: Product ending in 0 with numbers near $\sqrt{N}$: $25\times 26$ (5 × even → ends in 0).

Answer: (D) $26$

Concept: Total = average × number of persons.

1. $R+An+Am=3\times 45=135$
2. $R+An=2\times 44=88$, $An+Am=2\times 42=84$
3. Adding: $R+2An+Am=172$
4. $An=172-135=37\text{kg}$

Trick: Common person = (sum of pair totals) − (total of all) $=88+84-135=37$.

Answer: (A) $37$

Concept: $a^m÷a^n=a^{m-n}$ and $a^m\times a^n=a^{m+n}$ (left to right).

1. ${69}^{-4}÷{69}^{15}={69}^{-4-15}={69}^{-19}$
2. ${69}^{-19}\times {69}^{-9}={69}^{-19-9}={69}^{-28}$

Trick: Add the powers with their signs: $-4-15-9=-28$.

Answer: (D) ${69}^{-28}$

Concept: Selling price = marked price × $\frac{100-\text{discount}\%}{100}$.

1. $\text{SP}=46000\times \frac{84}{100}$
2. $=460\times 84=38640$

Trick: $16\%$ of $46000=7360$; $46000-7360=38640$.

Answer: (A) ₹38,640

Concept: Let Vinay take $t$ hours. Doubling the speed halves the time.

1. Amit's time $=t+8$; with double speed $\frac{t+8}{2}=t-9$
2. $t+8=2t-18\Rightarrow t=26$
3. Amit's time $=34\text{h}$
4. Amit's speed $=\frac{102}{34}=3\text{km/h}$

Trick: Check options: speed $3\Rightarrow 34\text{h}$ and $17\text{h}$; difference $34-17=17=8+9$ ✓.

Answer: (B) $3\text{km/h}$

Concept: Use $\sec A-\tan A=\frac{1-\sin A}{\cos A}$, $\text{cosec}A+\cot A=\frac{1+\cos A}{\sin A}$ and $1-{\sin }^{2}A={\cos }^{2}A$, $1-{\cos }^{2}A={\sin }^{2}A$.

1. Numerator: $(1+\sin A)\frac{1-\sin A}{\cos A}=\frac{{\cos }^{2}A}{\cos A}=\cos A$
2. Denominator: $\text{cosec}A(1-\cos A)\frac{1+\cos A}{\sin A}=\text{cosec}A·\frac{{\sin }^{2}A}{\sin A}=\text{cosec}A\sin A=1$
3. Value $=\frac{\cos A}{1}=\cos A$

Trick: Put $A={60}^{\circ }$: numerator $=\frac{1}{2}$, denominator $=1$ → $\frac{1}{2}=\cos {60}^{\circ }$.

Answer: (D) $\cos A$

Concept: Form two equations in mother's age $M$ and daughter's age $D$.

1. $2M=6D+26\Rightarrow M=3D+13$
2. $4D=M-4\Rightarrow M=4D+4$
3. $4D+4=3D+13\Rightarrow D=9$, $M=40$
4. Difference $=40-9=31$ years

Trick: Check: $2\times 40=80=6\times 9+26$ ✓ and $4\times 9=36=40-4$ ✓.

Answer: (C) $31$

Concept: $\text{SI}=\frac{P\times R\times T}{100}$, Amount $=P+\text{SI}$.

1. $2\frac{7}{8}=\frac{23}{8}$ years: $8671=\frac{P\times 2.9\times 23}{800}\Rightarrow P=\frac{8671\times 800}{66.7}=104000$
2. New SI $=\frac{104000\times 4.5\times 4.4}{100}=104000\times 0.198=20592$
3. Amount $=104000+20592=124592$

Trick: Rate × time $=4.5\times 4.4=19.8\%$ of $P$; $P\times 1.198=124592$.

Answer: (D) ₹1,24,592

Concept: Expand the brackets; the $x^2$ terms cancel, leaving a linear equation.

1. $9x^2-18-9x^2-15x+21=19$
2. $3-15x=19$
3. $-15x=16\Rightarrow x=-\frac{16}{15}$

Trick: Watch the sign: $-3\times (-7)=+21$.

Answer: (C) $-\frac{16}{15}$

Concept: For equal time periods, profit is shared in the ratio of investments.

1. Ratio $=1130:1030:1840=113:103:184$ (sum $400$)
2. Uday's share $=\frac{184}{400}\times 1800=184\times 4.5=828$

Trick: Uday's fraction $=\frac{1840}{4000}=46\%$; $46\%$ of $1800=828$.

Answer: (D) ₹828