RRB ALP CBT 1 2025 PYQs

Concept: Mitochondria carry out aerobic respiration and make ATP, the energy currency of the cell.

1. Krebs cycle (matrix) and electron transport chain (inner membrane) produce ATP
2. NADPH is mainly made in chloroplasts (photosynthesis)

Short trick: Hook: "Mito = Power plant, ATP = electricity bill".

Answer: (A) Generation of ATP

Concept: Refraction = change in direction of light when it passes obliquely from one medium to another, because its speed changes.

1. Mirror → reflection; air molecules → scattering; prism splitting → dispersion
2. Rarer → denser: bends towards the normal

Short trick: Hook: "Re-fraction = from one medium to another".

Answer: (B) Change in direction of light when it passes from one medium to another

Concept: Colloidal particles (1–1000 nm) are too small to settle under gravity; Brownian motion and like charges keep them dispersed.

1. They do not dissolve completely (that is a true solution)
2. They pass through filter paper, so filtration cannot separate them
3. They do not react with the medium

Short trick: Hook: "Milk never settles like muddy water" – colloid stable, suspension unstable.

Answer: (C) Its particles do not settle down when left undisturbed.

Concept: The World Para Athletics Championships 2025 were held in New Delhi (Jawaharlal Nehru Stadium), 27 Sept – 5 Oct 2025.

1. It was the first time India hosted this championship
2. India achieved its best-ever medal haul at the event

Short trick: Hook: "Para-games at the capital" – Delhi, JLN Stadium.

Answer: (B) New Delhi

Concept: A provision of the Constitution can be changed only by a Constitutional Amendment under Article 368 (Part XX).

1. The amendment bill is passed by Parliament (special majority, and state ratification where required)
2. Ordinances, executive orders or court rulings cannot amend the Constitution text

Short trick: Hook: "3-6-8 = only Parliament can amend" – Article 368.

Answer: (C) Constitutional Amendment

Concept: Bring all sine terms to one side and divide by $\cos y$.

1. $\sqrt{9}=3$, so $6\sin y+\cos y=3\sin y$.
2. $3\sin y=-\cos y$.
3. Divide by $3\cos y$: $\tan y=-\frac{1}{3}$.

Short trick: In $a\sin y+b\cos y=0$, $\tan y=-\frac{b}{a}$ directly: here $a=6-3=3,b=1$.

Answer: (A) $-\frac{1}{3}$

Concept: Write $\tan ,\cot$ in $\sin ,\cos$ and use $1-{\cos }^{2}A=(1-\cos A)(1+\cos A)$.

1. First term $=\frac{{\sin }^{2}A}{\cos A(1-\cos A)}=\frac{(1-\cos A)(1+\cos A)}{\cos A(1-\cos A)}=\frac{1+\cos A}{\cos A}=\sec A+1$.
2. Second term $=\frac{{\cos }^{2}A}{\sin A(1-\sin A)}=\frac{1+\sin A}{\sin A}=\mathrm{cosec}A+1$.
3. Difference $=\sec A-\mathrm{cosec}A$.

Short trick: Put $A={60}^{\circ }$: value $=(2+1)-(\frac{2}{\sqrt{3}}+1)\approx 0.845$, and $\sec {60}^{\circ }-\mathrm{cosec}{60}^{\circ }=2-1.155=0.845$ ✓ (B, C give negative values; D gives 0.366).

Answer: (A) $\sec A-\mathrm{cosec}A$

Concept: Unengraved area = total surface area of cube − area of all spots.

1. TSA $=6a^2=6\times {50}^2=15000{\text{cm}}^2$.
2. Number of spots $=1+2+3+4+5+6=21$.
3. Spot area $=21\times \pi \times 5^2=525\pi \approx 1649.3{\text{cm}}^2$.
4. Required $=15000-1649.3\approx 13351{\text{cm}}^2$.

Short trick: Spots $=\frac{6\times 7}{2}=21$; $525\pi \approx 1650$ → $15000-1650\approx 13350$ → only 13351 is close.

Answer: (B) 13351

Concept: Change in total = change in average × number of students.

1. Total decreased by $59-23=36$.
2. $n\times \frac{9}{7}=36$.
3. $n=36\times \frac{7}{9}=28$.

Short trick: $n=\frac{\text{error}}{\text{change in average}}$; and $n$ must be a multiple of 7 (denominator) → only 28 or 35; $28\times \frac{9}{7}=36$ ✓.

Answer: (B) 28

Concept: Mode = the value that occurs most often.

1. Frequencies of option values: 64 → 4 times, 81 → 3, 82 → 3, 89 → 2.
2. Highest frequency is 4 for 64.

Short trick: Only count the four option values – no need to tally all 25 numbers.

Answer: (B) 64

Concept: Product of two numbers = HCF × LCM.

1. Other number $=\frac{12\times 924}{84}$.
2. $=\frac{11088}{84}=132$.

Short trick: $\frac{924}{84}=11$, so other $=12\times 11=132$. Also the answer must be a multiple of 12 and divide 924 → 132 only.

Answer: (D) 132

Concept: Time together $=\frac{ab}{a+b}$ when both work in the same direction.

1. Emptying per minute $=\frac{1}{30}+\frac{1}{15}=\frac{3}{30}=\frac{1}{10}$.
2. Time $=10$ minutes.

Short trick: $\frac{30\times 15}{30+15}=\frac{450}{45}=10$; also it must be less than 15 (faster tap alone) → only 10 fits.

Answer: (A) 10 minutes

Concept: SP = MP × (1 − d₁)(1 − d₂); CP = SP ÷ (1 + profit%).

1. SP $=10000\times 0.8\times 0.7=5600$ → ₹5600.
2. CP $=\frac{5600}{1.12}=5000$ → ₹5000.

Short trick: SP must equal 1.12 × CP: only (D) has 5600 = 1.12 × 5000 – no calculation of discounts needed.

Answer: (D) Cost price = ₹5,000, Selling price = ₹5,600

Concept: Compare how much each fraction exceeds ½.

1. $\frac{25}{43}-\frac{1}{2}=\frac{7}{86}\approx 0.081$; $\frac{18}{31}-\frac{1}{2}=\frac{5}{62}\approx 0.0806$.
2. $\frac{21}{36}-\frac{1}{2}=\frac{6}{72}=\frac{1}{12}\approx 0.083$; $\frac{17}{30}-\frac{1}{2}=\frac{4}{60}\approx 0.067$.
3. Largest excess → $21:36$ $(=0.583)$.

Short trick: $21:36=7:12$; cross-multiply with 25:43 → $25\times 12=300<43\times 7=301$, so 7:12 is larger.

Answer: (C) 21 : 36

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

1. Ratio $62:70:83$, total $=215$.
2. Profit to share $=75500\times 0.86=64930$.
3. Ashok $=64930\times \frac{83}{215}=302\times 83=25066$.

Short trick: $\frac{64930}{215}=302$ exactly; then $302\times 83$: unit digit $2\times 3=6$ → only 25,066 ends in 6.

Answer: (C) 25,066

Concept: For equal distances, average speed $=\frac{2xy}{x+y}$.

1. $\frac{2\times 13\times 10}{13+10}=\frac{260}{23}$.
2. $=11\frac{7}{23}$ km/h.

Short trick: Average lies a little below the arithmetic mean 11.5 → $11\frac{7}{23}\approx 11.3$ ✓ (while $11\frac{16}{23}\approx 11.7$ is above 11.5).

Answer: (A) $11\frac{7}{23}$

Concept: Empirical relation: Mode $=3$Median $-2$Mean.

1. $36=3\times 42-2\text{Mean}$.
2. $2\text{Mean}=126-36=90$ → Mean $=45$.

Short trick: Mean $=\frac{3\text{Median}-\text{Mode}}{2}$; also Mean − Median $=\frac{\text{Median}-\text{Mode}}{2}=3$ → $42+3=45$.

Answer: (B) 45

Concept: Undo the operations in reverse order.

1. $\frac{x}{3}+17=72$ → $\frac{x}{3}=55$.
2. $x=165$; digit sum $=1+6+5=12$.

Short trick: $(72-17)\times 3=165$ in one line.

Answer: (D) 12

Concept: Net change $=a+b+\frac{ab}{100}$.

1. $20+10+\frac{20\times 10}{100}=32\mathrm{\%}$.

Short trick: Multiplier method: $1.2\times 1.1=1.32$ → 32% increase.

Answer: (A) 32%

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

1. $P=\frac{480\times 100}{6\times 2}=\frac{48000}{12}=4000$.

Short trick: Total rate for 2 years $=12\mathrm{\%}$; 12% of P = 480 → 1% = 40 → P = 4000.

Answer: (C) 4000