RRB NTPC Undergraduate CBT 1 2024 PYQs

Concept: $1+{\cot }^2\theta ={\csc }^2\theta$ and $1+{\tan }^2\theta ={\sec }^2\theta$.

1. $\frac{1+{\cot }^2\theta }{1+{\tan }^2\theta }=\frac{{\csc }^2\theta }{{\sec }^2\theta }$.
2. $=\frac{{\cos }^2\theta }{{\sin }^2\theta }={\cot }^2\theta$.
3. ${\cot }^2\theta ={\csc }^2\theta -1$.

Trick: Put $\theta ={45}^{\circ }$: expression $=1$; only ${\csc }^2\theta -1=2-1=1$ fits.

Answer: (A) ${\csc }^2\theta -1$

Concept: Successive change: net $\%=a-b-\frac{ab}{100}$ for $+a\%$ then $-b\%$.

1. $24-13-\frac{24\times 13}{100}=11-3.12=7.88\%$.
2. Check: $100\to 124\to 124\times 0.87=107.88$.

Trick: Take CP = 100; MP = 124; SP = $124-16.12=107.88$.

Answer: (C) 7.88%

Concept: For equal distances at speeds $a$ and $b$: average speed $=\frac{2ab}{a+b}$.

1. $\frac{2\times 9\times 18}{9+18}=\frac{324}{27}=12$.

Trick: Take distance 18 km: time $2+1=3$ h, total 36 km → $\frac{36}{3}=12$.

Answer: (B) 12

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

1. $2M=5D+25$ and $3D=M-9\Rightarrow M=3D+9$.
2. $2(3D+9)=5D+25\Rightarrow D=7$.
3. $M=30$; difference $=30-7=23$.

Trick: Check options quickly using $M=3D+9$: difference $=2D+9$ must be odd.

Answer: (D) 23

Concept: A number is divisible by 9 if its digit sum is divisible by 9.

1. Digit sum $=4+8+8+3+0+9+1+3+9=45$, divisible by 9 ✓.
2. Not by 10 (last digit 9).
3. By 11: alternating sum $=(9+1+0+8+4)-(3+9+3+8)=22-23=-1$, not divisible.

Trick: Digit sum 45 → divisible by both 3 and 9.

Answer: (A) 9

Concept: Make decimal places equal, find LCM of the integers, then put back the decimal places.

1. $2.600$ and $0.084$ → 2600 and 84 (3 decimal places).
2. $2600=2^3\times 5^2\times 13$, $84=2^2\times 3\times 7$.
3. LCM $=2^3\times 3\times 5^2\times 7\times 13=54600$ → $54.600=54.6$.

Trick: LCM of decimals must be a multiple of the bigger number 2.6: $54.6=2.6\times 21$ ✓.

Answer: (D) 54.6

Concept: For the same time period, profit is shared in the ratio of investments.

1. Total investment $=1220+1370+1110=3700$.
2. Kiran's share $=\frac{1110}{3700}\times 1160=0.3\times 1160=348$.

Trick: $\frac{1110}{3700}=\frac{3}{10}$ exactly — 30% of 1160.

Answer: (D) ₹348

Concept: Overall average = total runs ÷ total matches.

1. Runs in 23 matches $=23\times 43=989$.
2. Runs in 10 matches $=10\times 13=130$.
3. Average $=\frac{989+130}{33}=\frac{1119}{33}\approx 33.91$.

Trick: Deviation method: $43-\frac{10\times 30}{33}=43-9.09=33.91$.

Answer: (D) 33.91

Concept: Overhead (decoration) is added to cost price. $\text{Loss}\%=\frac{\text{Loss}}{\text{CP}}\times 100$.

1. CP $=670+10=680$.
2. SP $=290$ → loss $=680-290=390$.
3. $\text{Loss}\%=\frac{390}{680}\times 100=\frac{975}{17}\%$ (≈ 57.35%).

Trick: SP is less than CP → only the 'loss' options; then divide 39000 by 680.

Answer: (D) $\frac{975}{17}\%$ loss

Concept: Together, rates add: $\frac{1}{T}=\frac{1}{16}+\frac{1}{21}+\frac{1}{11}$.

1. LCM $=16\times 21\times 11=3696$.
2. $\frac{231+176+336}{3696}=\frac{743}{3696}$ tank per hour.
3. $T=\frac{3696}{743}=4\frac{724}{743}$ hours.

Trick: All options share the fraction $\frac{724}{743}$; only the whole part $3696÷743=4$ is needed.

Answer: (C) $4\frac{724}{743}$ hours

Concept: Decode each symbol and build the family tree.

1. G ÷ I: G is the brother of I.
2. I × L: I is the daughter of L.
3. L + N: L is the husband of N; N − P: N is the mother of P.
4. So I and P are children of L and N, and G (male) is their brother → G is P's brother.

Trick: Brother of P's sibling (same parents) is P's brother.

Answer: (C) Brother

Concept: Draw the least-overlap Venn diagram; a conclusion follows only if it is true in every possible diagram.

1. All towel are handkerchief → Towel inside Handkerchief.
2. Some cloth are handkerchief → Cloth overlaps Handkerchief, but may avoid Towel → (I) does not follow.
3. Towel is inside Handkerchief, not the reverse → (II) does not follow.

Yaad rakhein: 'All A are B' never gives 'All B are A'.

Answer: (B) Neither conclusion (I) nor (II) follows.

Concept: Scan for the pattern Symbol – Number – Symbol.

1. Series: 2 4 & # $ 4 7 6 6 & 1 * $ 2 © 9 4 8 € $ * 4.
2. & 1 * ✓
3. $ 2 © ✓
4. No other number has symbols on both sides; total = 2.

Trick: Look only at numbers standing alone between symbols — runs like 4 7 6 6 can never qualify.

Answer: (A) 2

Concept: When positions are counted from opposite ends and do not overlap: persons between = Total − (left rank + right rank).

1. Toni is 12th from left; Into is 11th from right = $126-11+1=116$th from left.
2. Between them $=116-12-1=103$.

Trick: $126-(12+11)=103$ directly.

Answer: (D) 103

Concept: Plot each move on axes (East +x, North +y) and compare the final point with A.

1. A(0, 0) → 4 W → (−4, 0) → left = South 7 → (−4, −7).
2. Right = West 5 → (−9, −7) → left = South 3 → (−9, −10).
3. Left = East 12 → (3, −10) → left = North 10 → (3, 0).
4. End point is 3 km east of A → drive 3 km towards the west.

Trick: Net E–W: $-4-5+12=3$ (east); net N–S: $-7-3+10=0$.

Answer: (C) 3 km towards the west

Concept: Swap the signs first, then apply BODMAS.

1. After swapping: $13+5\times 5÷5-13÷13+9÷3\times 3+108$.
2. $5\times 5÷5=5$, $13÷13=1$, $9÷3\times 3=9$.
3. $13+5-1+9+108=134$.

Trick: Rewrite the whole expression once with new signs before calculating — avoids mixing old and new signs.

Answer: (D) 134

Concept: Letters common to both words take the digits common to both codes.

1. VAST = 7892, SAVE = 8629.
2. Common letters V, A, S ↔ common digits 8, 9, 2.
3. Leftover: T = 7 in VAST, E = 6 in SAVE.

Trick: Uncommon letter ↔ uncommon digit.

Answer: (C) 6

Concept: Find the gaps between letter positions (A = 1 … Z = 26).

1. LNH: 12, 14, 8 → +2, −6.
2. OQK: 15, 17, 11 → +2, −6; TVP: 20, 22, 16 → +2, −6.
3. KNZ: 11, 14, 26 → +3, +12 → odd one.

Trick: Skip one letter forward, then six back — KNZ breaks it at the first step.

Answer: (B) KNZ

Concept: The only letter common to both words gets the only digit common to both codes.

1. WAVE = 3257, VOLT = 1346.
2. Common letter: V; common digit: 3.
3. So V = 3.

Trick: One common letter ↔ one common digit.

Answer: (C) 3

Concept: Some A are B + All B are C ⇒ Some A are C (definite).

1. Some wigs are roses, and every rose is a bug → those wigs are bugs → (I) follows.
2. All roses are bugs does not mean all bugs are roses → (II) does not follow.

Yaad rakhein: Some + All = Some (with the first term of 'Some').

Answer: (C) Only conclusion (I) follows.