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RRB JE Mechanical study materials
RRB JE Mechanical study resources

RRB JE Mechanical practice questions

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Question 1Mathematics (CBT 1)

A mechanical workshop uses 240 litres of lubricating oil per month. After a maintenance drive, consumption falls by 15%. How many litres per month are saved?

  1. 24 litres
  2. 36 litres Correct answer.
  3. 60 litres
  4. 48 litres

Explanation

Saving is 15% of the monthly consumption, so calculate 0.15 × 240 = 36 litres. The remaining consumption would be 204 litres, but the question asks for the amount saved, not the new total.

Question 2Mathematics (CBT 1)

In a machine shop, the ratio of skilled workers to unskilled workers is 5:3. If there are 40 skilled workers, how many unskilled workers are there?

  1. 24 Correct answer.
  2. 32
  3. 30
  4. 20

Explanation

The ratio 5:3 means 5 parts correspond to 40 skilled workers, so one part equals 40 ÷ 5 = 8 workers. The unskilled group has 3 parts, giving 3 × 8 = 24 workers.

Question 3Mathematics (CBT 1)

The daily production of a lathe over five days is 42, 48, 45, 50, and 55 units. What is the average daily production?

  1. 48 units Correct answer.
  2. 49 units
  3. 46 units
  4. 47 units

Explanation

Add the five daily production figures to get 240 units, then divide by the number of days, which is 5. The average is 240 ÷ 5 = 48 units per day.

Question 4Mathematics (CBT 1)

A sum of ₹12,000 is invested at 10% per annum compound interest, compounded annually. What is the amount after 2 years?

  1. ₹14,520 Correct answer.
  2. ₹14,400
  3. ₹14,640
  4. ₹14,500

Explanation

Compound interest applies interest on the previous year's amount, so the multiplier per year is 1.10. Amount = 12,000 × (1.10)² = 12,000 × 1.21 = ₹14,520.

Question 5Mathematics (CBT 1)

A and B can complete a repair job in 12 days and 18 days respectively. Working together, in how many days will they complete the job?

  1. 7.5 days
  2. 6.8 days
  3. 8 days
  4. 7.2 days Correct answer.

Explanation

In one day, A completes 1/12 of the job and B completes 1/18. Together they complete 1/12 + 1/18 = 5/36 per day, so the time is the reciprocal, 36/5 = 7.2 days.

Question 6Mathematics (CBT 1)

A train 150 m long passes a stationary pole in 9 seconds. What is its speed in km/h?

  1. 45 km/h
  2. 60 km/h Correct answer.
  3. 54 km/h
  4. 72 km/h

Explanation

The train covers its own length while passing the pole, so speed = 150 m ÷ 9 s = 16.67 m/s. Converting to km/h by multiplying by 3.6 gives 60 km/h.

Question 7Mathematics (CBT 1)

The volume of a cylindrical tank is 1,232 m³. If its radius is 7 m, what is its height? (Use π = 22/7)

  1. 6 m
  2. 9 m
  3. 8 m Correct answer.
  4. 7 m

Explanation

For a cylinder, volume = πr²h. Substitute the values: 1,232 = (22/7) × 7² × h = 154h, so h = 1,232 ÷ 154 = 8 m.

Question 8Mathematics (CBT 1)

If x + 1/x = 3, then x² + 1/x² equals:

  1. 7 Correct answer.
  2. 6
  3. 8
  4. 5

Explanation

Square the given equation: (x + 1/x)² = x² + 2 + 1/x². Since the left side equals 3² = 9, we get x² + 1/x² = 9 − 2 = 7.

Question 9Mathematics (CBT 1)

The angle of elevation of the top of a tower from a point on the ground is 30°. On walking 20 m towards the tower, the angle of elevation becomes 60°. What is the height of the tower?

  1. 10 m
  2. 30 m
  3. 10√3 m Correct answer.
  4. 20√3 m

Explanation

Let the height be h. From the first position, distance = h/tan30° = h√3. After moving 20 m, distance = h/tan60° = h/√3. Equating h√3 − 20 = h/√3 gives 2h = 20√3, so h = 10√3 m.

Question 10Mathematics (CBT 1)

A box contains 4 defective and 6 non-defective bolts. Two bolts are drawn at random without replacement. What is the probability that both are defective?

  1. 2/15 Correct answer.
  2. 3/10
  3. 4/15
  4. 1/5

Explanation

The probability of the first bolt being defective is 4/10. Given that, 3 defective bolts remain among 9 bolts, so the second probability is 3/9. Multiply: (4/10) × (3/9) = 12/90 = 2/15.

Question 11Mathematics (CBT 1)

Evaluate: 3/4 of 2/5 ÷ 1/2 + 1/3.

  1. 11/15
  2. 7/10
  3. 14/15 Correct answer.
  4. 1

Explanation

Apply BODMAS: first find 3/4 of 2/5 = 3/10. Then divide by 1/2, which is the same as multiplying by 2, giving 3/5. Finally add 1/3: 9/15 + 5/15 = 14/15.

Question 12Mathematics (CBT 1)

The HCF of two numbers is 12 and their LCM is 240. If one number is 48, what is the other number?

  1. 72
  2. 45
  3. 60 Correct answer.
  4. 80

Explanation

For any two numbers, the product of the numbers equals HCF × LCM. Thus the product is 12 × 240 = 2,880, and the other number is 2,880 ÷ 48 = 60.

Question 13Mathematics (CBT 1)

A workshop buys a machine part for ₹1,200 and sells it at a loss of 8%. What is the selling price?

  1. ₹1,116
  2. ₹1,296
  3. ₹1,104 Correct answer.
  4. ₹1,080

Explanation

A loss of 8% means the selling price is 92% of the cost price. So SP = 0.92 × ₹1,200 = ₹1,104. Alternatively, loss = 8% of ₹1,200 = ₹96, and SP = ₹1,200 − ₹96 = ₹1,104.

Question 14Mathematics (CBT 1)

A cone-shaped hopper has base radius 7 cm and slant height 25 cm. Using π = 22/7, what is its curved surface area?

  1. 1,100 cm²
  2. 550 cm² Correct answer.
  3. 704 cm²
  4. 154 cm²

Explanation

The curved surface area of a cone is πrl, where r is the base radius and l is the slant height. Substituting gives (22/7) × 7 × 25 = 550 cm².

Question 15Mathematics (CBT 1)

Two goods trains, 120 m and 180 m long, run in opposite directions at 54 km/h and 36 km/h. How long do they take to cross each other completely?

  1. 10 s
  2. 15 s
  3. 18 s
  4. 12 s Correct answer.

Explanation

When moving in opposite directions, relative speed = 54 + 36 = 90 km/h = 90 × 5/18 = 25 m/s. Total length to be crossed = 120 + 180 = 300 m. Time = 300 ÷ 25 = 12 s.

Question 16Mathematics (CBT 1)

If α and β are the roots of x² − 7x + 10 = 0, what is α² + β²?

  1. 39
  2. 29 Correct answer.
  3. 49
  4. 19

Explanation

For the quadratic, α + β = 7 and αβ = 10. Using the identity α² + β² = (α + β)² − 2αβ gives 49 − 20 = 29.

Question 17Mathematics (CBT 1)

In triangle ABC, angle A = 50° and angle B = 60°. What is the exterior angle at C?

  1. 120°
  2. 70°
  3. 130°
  4. 110° Correct answer.

Explanation

The interior angle at C is 180° − (50° + 60°) = 70°. The exterior angle at C is therefore 180° − 70° = 110°, which also equals the sum of the remote interior angles 50° + 60°.

Question 18Mathematics (CBT 1)

A and B invest ₹20,000 and ₹30,000 in a workshop partnership. After 6 months, A withdraws half his capital. At the end of the year, the profit is ₹12,000. What is A's share?

  1. ₹5,000
  2. ₹8,000
  3. ₹4,000 Correct answer.
  4. ₹6,000

Explanation

A's capital-months are 20,000 × 6 + 10,000 × 6 = 1,80,000, while B's are 30,000 × 12 = 3,60,000. The ratio is 1:2, so A receives one-third of ₹12,000, which is ₹4,000.

Question 19Mathematics (CBT 1)

What is the remainder when 3²⁰⁰ is divided by 7?

  1. 1
  2. 2 Correct answer.
  3. 4
  4. 6

Explanation

Powers of 3 modulo 7 follow the cycle 3, 2, 6, 4, 5, 1 with period 6. Since 200 = 6 × 33 + 2, the remainder is the same as 3² modulo 7, which is 2.

Question 20Mathematics (CBT 1)

A committee of 3 is selected at random from 5 mechanical engineers and 4 electrical engineers. What is the probability that exactly 2 mechanical engineers are selected?

  1. 5/12
  2. 5/14
  3. 1/2
  4. 10/21 Correct answer.

Explanation

Total ways to choose 3 from 9 people = C(9,3) = 84. Favourable ways with exactly 2 mechanical engineers = C(5,2) × C(4,1) = 10 × 4 = 40. The probability is 40/84 = 10/21.

Question 21Mathematics (CBT 1)

A sum of money invested at simple interest doubles itself in 8 years. What is the annual rate of interest?

  1. 13.25%
  2. 12.25%
  3. 12.5% Correct answer.
  4. 11.25%

Explanation

Let the principal be P. For the amount to double, the simple interest earned must equal P, so P = P × R × 8 / 100. Solving gives R = 100/8 = 12.5% per annum.

Question 22Mathematics (CBT 1)

An alloy used for machine bushes contains copper and zinc in the ratio 7 : 3 by mass. In an 80 kg batch of this alloy, what mass of zinc is present?

  1. 32 kg
  2. 28 kg
  3. 56 kg
  4. 24 kg Correct answer.

Explanation

Total parts = 7 + 3 = 10. Zinc is 3 parts out of 10, so zinc mass = (3/10) × 80 kg = 24 kg.

Question 23Mathematics (CBT 1)

What is the least non-negative integer that must be added to 1,056 so that the result is exactly divisible by 23?

  1. 3
  2. 2 Correct answer.
  3. 5
  4. 1

Explanation

The multiples of 23 near 1,056 are 23 × 45 = 1,035 and 23 × 46 = 1,058. The next multiple above 1,056 is 1,058, so the required addition is 1,058 − 1,056 = 2.

Question 24Mathematics (CBT 1)

A motorboat travels 24 km downstream in 2 hours and returns the same distance upstream in 3 hours. What is the speed of the stream?

  1. 3 km/h
  2. 1 km/h
  3. 2 km/h Correct answer.
  4. 4 km/h

Explanation

Downstream speed = 24/2 = 12 km/h and upstream speed = 24/3 = 8 km/h. The stream speed is half the difference, (12 − 8)/2 = 2 km/h.

Question 25Mathematics (CBT 1)

Two inlet pipes can fill a sump in 12 minutes and 18 minutes respectively, while an outlet pipe can empty it in 36 minutes. If all three are opened together when the sump is empty, in what time will it be filled?

  1. 9 min Correct answer.
  2. 8 min
  3. 7.2 min
  4. 10 min

Explanation

Net filling rate = 1/12 + 1/18 − 1/36 = 3/36 + 2/36 − 1/36 = 4/36 = 1/9 sump per minute. Hence the sump fills in 9 minutes.

Question 26Mathematics (CBT 1)

A solid steel sphere of radius 6 cm is melted and drawn into a wire of radius 0.5 cm. Assuming no loss of metal, what is the length of the wire?

  1. 5.76 m
  2. 2.88 m
  3. 11.52 m Correct answer.
  4. 23.04 m

Explanation

Volume of sphere = (4/3)π(6)^3 = 288π cm³. If L is wire length, π(0.5)^2 L = 288π, so L = 288/0.25 = 1,152 cm = 11.52 m.

Question 27Mathematics (CBT 1)

Simplify: (x² − 9)/(x² + 6x + 9), where x ≠ −3.

  1. (x − 3)²/(x + 3)
  2. (x + 3)/(x − 3)
  3. (x − 3)/(x + 3) Correct answer.
  4. (x − 9)/(x + 9)

Explanation

Factor the numerator as (x − 3)(x + 3) and the denominator as (x + 3)². Cancelling the common factor (x + 3) gives (x − 3)/(x + 3), valid because x ≠ −3.

Question 28Mathematics (CBT 1)

What is the units digit of 7^105?

  1. 9
  2. 7 Correct answer.
  3. 1
  4. 3

Explanation

The units digits of powers of 7 repeat in the cycle 7, 9, 3, 1 with period 4. Since 105 leaves remainder 1 on division by 4, the units digit is the first value in the cycle, which is 7.

Question 29Mathematics (CBT 1)

Two circles have radii 5 cm and 3 cm and touch each other externally. What is the length of their direct common tangent?

  1. 8 cm
  2. 2√15 cm Correct answer.
  3. 4√2 cm
  4. 2√10 cm

Explanation

For externally touching circles, the distance between centres is d = 5 + 3 = 8 cm. The direct common tangent length is √(d² − (r₁ − r₂)²) = √(8² − 2²) = √60 = 2√15 cm.

Question 30Mathematics (CBT 1)

A card is drawn at random from a standard pack of 52 playing cards. What is the probability that it is either a king or a heart?

  1. 1/13
  2. 1/4
  3. 17/52
  4. 4/13 Correct answer.

Explanation

There are 4 kings and 13 hearts, but the king of hearts is counted in both groups. Thus favourable cards = 4 + 13 − 1 = 16, and probability = 16/52 = 4/13.

Question 31General Intelligence and Reasoning (CBT 1)

Find the next term of the number series: 3, 7, 15, 31, 63, ?

  1. 127 Correct answer.
  2. 129
  3. 121
  4. 125

Explanation

Each term is obtained by doubling the previous term and adding 1: 3 × 2 + 1 = 7, 7 × 2 + 1 = 15, 15 × 2 + 1 = 31, and 31 × 2 + 1 = 63. Applying the same rule to the last given term gives 63 × 2 + 1 = 127. So the missing term is 127.

Question 32General Intelligence and Reasoning (CBT 1)

Three of the following four numbers share a common property. Identify the number that does not belong to that group: 121, 144, 169, 180.

  1. 144
  2. 180 Correct answer.
  3. 121
  4. 169

Explanation

121 = 11², 144 = 12² and 169 = 13², so these three are consecutive perfect squares. The number 180 lies between 13² = 169 and 14² = 196 and is not a perfect square at all. Hence 180 is the odd one out.

Question 33General Intelligence and Reasoning (CBT 1)

Pointing to a photograph, Ramesh said, "She is the daughter of my grandfather's only son." How is the girl in the photograph related to Ramesh?

  1. Cousin
  2. Sister Correct answer.
  3. Aunt
  4. Daughter

Explanation

Ramesh's grandfather has only one son, and that son is Ramesh's father. The girl is the daughter of Ramesh's father, which makes her Ramesh's sister. The word "only" removes any possibility of the girl being a cousin through another son of the grandfather.

Question 34General Intelligence and Reasoning (CBT 1)

In a certain code, MACHINE is written as NBDIJOF. Using the same code, how will TURBINE be written?

  1. UVSDJOF
  2. VUSCJOF
  3. UVSCJOG
  4. UVSCJOF Correct answer.

Explanation

Comparing MACHINE with NBDIJOF shows that every letter is replaced by the letter immediately following it in the alphabet: M→N, A→B, C→D, and so on. Applying the same shift of one place forward to TURBINE gives U, V, S, C, J, O, F, that is UVSCJOF.

Question 35General Intelligence and Reasoning (CBT 1)

A man walks 5 km towards the north, turns right and walks 3 km, turns right again and walks 5 km, then turns left and walks 2 km. How far and in which direction is he now from his starting point?

  1. 3 km East
  2. 5 km West
  3. 7 km East
  4. 5 km East Correct answer.

Explanation

Taking the start as the origin, the man reaches (0, 5), then (3, 5) after moving east, then (3, 0) after moving south, and finally (5, 0) after turning left from south, which means moving east. His final position is 5 km due east of the starting point.

Question 36General Intelligence and Reasoning (CBT 1)

Statements: All engines are machines. Some machines are turbines. Conclusions: I. Some engines are turbines. II. Some machines are engines. Which conclusion logically follows?

  1. Both I and II follow
  2. Only I follows
  3. Neither I nor II follows
  4. Only II follows Correct answer.

Explanation

The statement "All engines are machines" allows conversion to "Some machines are engines", so conclusion II follows. The turbines that are machines may lie entirely outside the engine group, so conclusion I is only a possibility and cannot be concluded with certainty.

Question 37General Intelligence and Reasoning (CBT 1)

Five friends A, B, C, D and E sit in a row facing north. E is at the extreme left end. C sits second to the right of E. A sits immediately to the right of C, and B sits at the extreme right end. Who sits exactly in the middle of the row?

  1. D
  2. E
  3. A
  4. C Correct answer.

Explanation

Numbering the seats 1 to 5 from the left, E occupies seat 1, C takes seat 3 (second to the right of E), A takes seat 4 and B takes seat 5. The only remaining person D occupies seat 2, so the middle seat, seat 3, belongs to C.

Question 38General Intelligence and Reasoning (CBT 1)

A clock shows the time 3:30. What is the smaller angle between the hour hand and the minute hand at that instant?

  1. 105°
  2. 60°
  3. 75° Correct answer.
  4. 90°

Explanation

At 3:30 the minute hand points at 6, covering 30 × 6 = 180° from 12. The hour hand has moved 3 × 30° plus half of 30° for the extra 30 minutes, giving 90° + 15° = 105°. The difference between the two positions is 180° − 105° = 75°.

Question 39General Intelligence and Reasoning (CBT 1)

Study the letter series AZ, CX, EV, GT and identify the next pair.

  1. IQ
  2. IR Correct answer.
  3. HR
  4. IS

Explanation

In the first letter of each pair the alphabet advances by two places: A, C, E, G, so the next first letter is I. In the second letter the alphabet moves back by two places: Z, X, V, T, so the next second letter is R. The required pair is therefore IR.

Question 40General Intelligence and Reasoning (CBT 1)

If '+' means '×', '−' means '÷', '×' means '−' and '÷' means '+', what is the value of 8 + 4 − 2 × 6 ÷ 3?

  1. 10
  2. 11
  3. 16
  4. 13 Correct answer.

Explanation

Replacing each symbol by its stated meaning turns the expression into 8 × 4 ÷ 2 − 6 + 3. Working left to right within the multiplication and division block, 8 × 4 = 32 and 32 ÷ 2 = 16. Then 16 − 6 + 3 = 13.

Question 41General Intelligence and Reasoning (CBT 1)

Thermometer : Temperature :: Tachometer : ?

  1. Electric current
  2. Speed Correct answer.
  3. Volume
  4. Pressure

Explanation

A thermometer measures temperature, while a tachometer measures the rotational speed of a shaft or engine. The same instrument-to-quantity relationship therefore gives speed as the answer.

Question 42General Intelligence and Reasoning (CBT 1)

Which item is different in kind from the other three: lathe, drill, grinder, bolt?

  1. Lathe
  2. Grinder
  3. Bolt Correct answer.
  4. Drill

Explanation

A lathe, a drill and a grinder are machine tools that shape or remove material from a workpiece. A bolt is a threaded fastener used to join parts, so it is different in kind.

Question 43General Intelligence and Reasoning (CBT 1)

If FAN is coded as 6-1-14, how is PUMP coded using the same letter-position code?

  1. 16-21-14-16
  2. 15-21-13-16
  3. 16-20-13-16
  4. 16-21-13-16 Correct answer.

Explanation

In letter-position coding, A is 1, B is 2, and so on. PUMP becomes P = 16, U = 21, M = 13, P = 16, giving 16-21-13-16.

Question 44General Intelligence and Reasoning (CBT 1)

A is the father of B. C is the mother of A. D is the sister of B. How is C related to D?

  1. Great-grandmother
  2. Aunt
  3. Mother
  4. Grandmother Correct answer.

Explanation

C is A's mother, and A is the father of both B and D because D is B's sister. Therefore C is D's grandmother.

Question 45General Intelligence and Reasoning (CBT 1)

A person facing north turns 90° clockwise and then 180° anticlockwise. Which direction is the person facing now?

  1. North
  2. West Correct answer.
  3. South
  4. East

Explanation

Facing north, a 90° clockwise turn points the person east. A further 180° anticlockwise turn from east points west.

Question 46General Intelligence and Reasoning (CBT 1)

Statements: All gears are wheels. No wheel is a belt. Conclusions: I. No gear is a belt. II. All belts are wheels. Which conclusion follows?

  1. Both I and II follow
  2. Only conclusion I follows Correct answer.
  3. Only conclusion II follows
  4. Neither I nor II follows

Explanation

All gears lie inside the set of wheels, and no wheel is a belt, so no gear can be a belt. The second conclusion says belts are wheels, which contradicts the stated exclusion rather than following from it.

Question 47General Intelligence and Reasoning (CBT 1)

In a row of 40 students, Ravi is 12th from the left and Meena is 15th from the right. How many students are between Ravi and Meena?

  1. 15
  2. 12
  3. 14
  4. 13 Correct answer.

Explanation

Meena's position from the left is 40 − 15 + 1 = 26. Ravi is at position 12, so the number between them is 26 − 12 − 1 = 13.

Question 48General Intelligence and Reasoning (CBT 1)

If 1 January 2024 was a Monday, what day of the week was 1 March 2024?

  1. Monday
  2. Wednesday
  3. Thursday
  4. Friday Correct answer.

Explanation

2024 is a leap year, so January and February together contain 31 + 29 = 60 days. Since 60 leaves a remainder of 4 when divided by 7, four weekdays after Monday is Friday.

Question 49General Intelligence and Reasoning (CBT 1)

A cube is painted on all faces and then cut into 64 equal smaller cubes. How many smaller cubes have exactly two faces painted?

  1. 8
  2. 16
  3. 24 Correct answer.
  4. 32

Explanation

Cutting into 64 equal cubes gives 4 cubes along each edge. Cubes with exactly two painted faces lie on edges but not at corners, so there are 12 × (4 − 2) = 24.

Question 50General Intelligence and Reasoning (CBT 1)

Arrange the following workshop terms in the order in which they would appear in a dictionary: Bearing, Belt, Bolt, Bush, Bushing.

  1. Belt, Bearing, Bolt, Bush, Bushing
  2. Bearing, Belt, Bush, Bushing, Bolt
  3. Bearing, Bolt, Belt, Bush, Bushing
  4. Bearing, Belt, Bolt, Bush, Bushing Correct answer.

Explanation

Dictionary order compares letters from left to right. 'Bearing' precedes 'Belt' because a comes before l, 'Belt' precedes 'Bolt' because e comes before o, and 'Bush' precedes 'Bushing' because it is the shorter prefix.