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FRV Written Selection Test study materials
FRV Written Selection Test study resources

FRV Written Selection Test practice questions

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Question 1Integrated english, quant, formal, spatial, mechanics foundations

A 3x3 grid contains shapes in a sequence. The top row has: a circle, a square, and a triangle. The middle row has: a square, a triangle, and a circle. The bottom row has: a triangle, a circle, and a blank space. Which shape logically completes the bottom row?

  1. Circle
  2. Triangle
  3. Square Correct answer.
  4. Diamond

Explanation

Each row and column in the 3x3 grid must contain exactly one circle, one square, and one triangle. In the bottom row, we have a triangle and a circle, meaning the missing shape must be a square. This represents a Latin square pattern, which is a common visual logic puzzle in abstract reasoning tests.

Question 2Integrated english, quant, formal, spatial, mechanics foundations

A sequence of four shapes is shown. The first is a triangle pointing up. The second is a square. The third is a regular pentagon pointing up. The fourth is a regular hexagon. What is the fifth shape in this sequence?

  1. Regular heptagon pointing up Correct answer.
  2. Regular octagon
  3. Circle
  4. Pentagon pointing down

Explanation

The sequence progresses by increasing the number of sides of the polygon by one for each step. The sequence of sides is: triangle (3), square (4), pentagon (5), and hexagon (6). Therefore, the fifth shape must have seven sides (a heptagon) pointing up, maintaining the progression.

Question 3Integrated english, quant, formal, spatial, mechanics foundations

An arrow inside a circle rotates clockwise in a sequence: first pointing at 12 o'clock, then pointing at 2 o'clock, then pointing at 5 o'clock, and then pointing at 9 o'clock. Where does the arrow point in the next step?

  1. 11 o'clock
  2. 12 o'clock
  3. 1 o'clock
  4. 2 o'clock Correct answer.

Explanation

The rotation interval increases by 1 hour (or 30 degrees) at each step. The first step rotates clockwise by 2 hours (12 to 2). The second step rotates by 3 hours (2 to 5). The third step rotates by 4 hours (5 to 9). The next step must rotate clockwise by 5 hours, moving from 9 o'clock to 2 o'clock.

Question 4Integrated english, quant, formal, spatial, mechanics foundations

Identify the odd one out among the following groups of lines: Group A has 4 horizontal lines. Group B has 4 vertical lines. Group C has 4 diagonal lines parallel to each other. Group D has 4 lines that intersect at a single central point.

  1. Group A
  2. Group B
  3. Group C
  4. Group D Correct answer.

Explanation

Groups A, B, and C consist entirely of parallel lines that never cross each other. Group D features lines that intersect at a single point, meaning they are not parallel. This difference in geometric relationship makes Group D the odd one out.

Question 5Integrated english, quant, formal, spatial, mechanics foundations

A net of a cube is shown. It has symbols on its faces: a dot, a cross, a triangle, a square, a star, and a circle. When folded into a 3D cube, if the face with the dot is on top and the face with the cross is on the bottom, which of the following is mathematically impossible?

  1. The face with the triangle is opposite the face with the square
  2. The face with the star is opposite the face with the circle
  3. The face with the dot is adjacent to the face with the cross Correct answer.
  4. The face with the triangle is adjacent to the face with the star

Explanation

Since the question establishes that the dot is on top and the cross is on the bottom, these two faces are opposite each other in the folded cube. By definition, opposite faces can never touch or share an edge, making it impossible for the dot to be adjacent to the cross. All other relationships are spatially possible depending on the layout of the remaining four faces around the sides.

Question 6Integrated english, quant, formal, spatial, mechanics foundations

A matrix pattern contains lines. Row 1 has 1 vertical line, 2 vertical lines, and 3 vertical lines. Row 2 has 1 horizontal line, 2 horizontal lines, and 3 horizontal lines. Row 3 has 1 diagonal line, 2 diagonal lines, and a blank space. What completes the blank space?

  1. 3 horizontal lines
  2. 3 vertical lines
  3. 3 diagonal lines Correct answer.
  4. 4 diagonal lines

Explanation

The pattern in each row shows shapes of the same orientation increasing in count from 1 to 2 to 3. In Row 3, the orientation is diagonal, starting with 1 diagonal line, then 2 diagonal lines. Therefore, the blank space must contain 3 diagonal lines to complete the numerical progression.

Question 7Integrated english, quant, formal, spatial, mechanics foundations

A circle and a square intersect. In the first frame, they do not overlap. In the second frame, they overlap slightly, creating 3 distinct regions. In the third frame, the circle moves completely inside the square. How many distinct regions exist in the third frame?

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

Explanation

When the circle is completely inside the square, the regions are: (1) the area inside the circle, and (2) the area inside the square but outside the circle. This creates exactly 2 distinct regions. The options are 0-indexed, meaning '2' is at index 1.

Question 8Integrated english, quant, formal, spatial, mechanics foundations

A square grid contains black dots. In the first grid, there is 1 dot in the top-left. In the second, there are 2 dots: top-left and top-right. In the third, there are 3 dots: top-left, top-right, and bottom-right. If the pattern continues clockwise around the corners, where are the dots in the fourth grid?

  1. All four corners contain a dot Correct answer.
  2. Top-left, top-right, and bottom-left
  3. Top-right, bottom-right, and bottom-left
  4. Top-left, bottom-right, and bottom-left

Explanation

The dots are added one by one in a clockwise direction around the corners of the grid: top-left, top-right, bottom-right. The fourth corner in the clockwise sequence is the bottom-left. Therefore, the fourth grid will have dots in all four corners (top-left, top-right, bottom-right, and bottom-left).

Question 9Integrated english, quant, formal, spatial, mechanics foundations

A regular hexagon contains a shaded triangle. In the first frame, the top triangle is shaded. In the second frame, the adjacent triangle to the right is shaded. In the third frame, the next triangle to the right is shaded. What describes the rotation of the shaded region?

  1. Clockwise rotation of 60 degrees Correct answer.
  2. Counter-clockwise rotation of 60 degrees
  3. Clockwise rotation of 120 degrees
  4. Counter-clockwise rotation of 120 degrees

Explanation

A regular hexagon is divided into 6 equal triangular segments, each representing 60 degrees (360 degrees / 6). Since the shaded region moves to the adjacent triangle to the right at each step, this represents a clockwise rotation of 1 step, which corresponds to exactly 60 degrees.

Question 10Integrated english, quant, formal, spatial, mechanics foundations

A shape resembles the letter 'L'. In the first frame, it is upright. In the second frame, it is reflected horizontally (mirrored). In the third frame, it is flipped vertically (inverted). In the fourth frame, it is reflected horizontally again. How does the shape compare to the first frame?

  1. It is identical to the first frame
  2. It is flipped vertically (inverted) compared to the first frame Correct answer.
  3. It is reflected horizontally (mirrored) compared to the first frame
  4. It is rotated 90 degrees clockwise compared to the first frame

Explanation

Let's track the transformations: Start (Upright) -> Horizontally Reflected -> Vertically Flipped (now both mirrored and upside down) -> Horizontally Reflected (cancels out the mirroring, leaving only the vertical flip). Therefore, the final state is just vertically flipped (inverted) compared to the first frame.

Question 11Integrated english, quant, formal, spatial, mechanics foundations

A visual addition rule states that the two input shapes are overlaid and every line from both is kept; where identical lines coincide they merge into a single line (they are not duplicated). If a square with a vertical line through the center is 'added' to a square with a horizontal line through the center, what is the resulting shape?

  1. A blank square
  2. A square with a cross (both vertical and horizontal lines) Correct answer.
  3. A square with only a vertical line
  4. A circle with a cross

Explanation

The first shape has the outline of a square and a vertical line. The second has the outline of a square and a horizontal line. The two square outlines coincide exactly, so they merge into one square outline. The internal lines are non-overlapping (one vertical, one horizontal), so both are kept inside the square, forming a cross.

Question 12Integrated english, quant, formal, spatial, mechanics foundations

A transparent cube is shown in different perspectives. Face A is adjacent to Faces B, C, D, and E. Face F is opposite Face A. Which face must be opposite Face B?

  1. Face C
  2. Face D
  3. Face E
  4. Cannot be determined without knowing the adjacent relationships of B Correct answer.

Explanation

We know Face A is adjacent to B, C, D, and E, and F is opposite A. B, C, D, and E form a ring of four faces around the axis of A and F. However, without knowing the specific sequential order of B, C, D, and E around the cube, we cannot determine which of C, D, or E is opposite B. Therefore, the relationship cannot be determined with the given information.

Question 13Integrated english, quant, formal, spatial, mechanics foundations

A five-pointed star has vertices numbered 1 to 5 clockwise. The shaded point starts at vertex 1. Each move skips one vertex clockwise. Which list shows the initial position followed by the positions after four successive moves?

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

Explanation

Starting at 1, we skip 2 to land on 3. From 3, we skip 4 to land on 5. From 5, we skip 1 (since it is a 5-point loop) to land on 2. From 2, we skip 3 to land on 4. The sequence is therefore 1, 3, 5, 2, 4.

Question 14Integrated english, quant, formal, spatial, mechanics foundations

A grid sequence has a circle that moves down 1 unit at each step, while a triangle moves right 1 unit at each step. If they start at the top-left coordinate (1,1) of a 4x4 grid, at which coordinate will they first intersect?

  1. (2,2)
  2. (3,3)
  3. (4,4)
  4. They will never intersect Correct answer.

Explanation

Let's track their coordinates over time. Coordinate format is (row, column). Step 0: Circle at (1,1), Triangle at (1,1) - they start intersected. Step 1: Circle moves down to (2,1), Triangle moves right to (1,2). Step 2: Circle at (3,1), Triangle at (1,3). Step 3: Circle at (4,1), Triangle at (1,4). Beyond this, they hit the boundaries. Thus, after the start at Step 0, they will never intersect because the circle is constrained to column 1 and the triangle is constrained to row 1.

Question 15Integrated english, quant, formal, spatial, mechanics foundations

In a 3x3 matrix, the top row shows three shapes with 3, 4, and 5 sides. The second row shows shapes with 4, 5, and 6 sides. The third row starts with a shape of 5 sides, followed by a shape of 6 sides. What is the number of sides of the final shape in the third row?

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

Explanation

The matrix follows an addition pattern where the number of sides increases by 1 across each column. Row 1: 3 -> 4 -> 5. Row 2: 4 -> 5 -> 6. Row 3: 5 -> 6 -> ?. The next number in the progression is 7, so the final shape must have 7 sides (a heptagon).

Question 16Integrated english, quant, formal, spatial, mechanics foundations

A pattern consists of arrows. Arrow 1 points Up. Arrow 2 points Right. Arrow 3 points Down. Arrow 4 points Left. If this cycle repeats, what is the direction of Arrow 99?

  1. Up
  2. Right
  3. Down Correct answer.
  4. Left

Explanation

The pattern has a cycle length of 4 (Up, Right, Down, Left). To find the direction of Arrow 99, we divide 99 by 4 and look at the remainder: 99 = 24 * 4 + 3. A remainder of 3 corresponds to the third position in the cycle, which is Down.

Question 17Integrated english, quant, formal, spatial, mechanics foundations

A square piece of paper is folded in half diagonally to form a triangle. It is then folded in half again to form a smaller triangle. A single circular hole is punched through the center of this folded triangle. When the paper is completely unfolded, how many holes will be visible?

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

Explanation

Each fold doubles the thickness of the paper layers. The first fold (in half) creates 2 layers. The second fold (in half again) creates 4 layers. Punching a hole through the 4-layered paper goes through all 4 layers, resulting in 4 separate circular holes when the sheet is unfolded.

Question 18Integrated english, quant, formal, spatial, mechanics foundations

A 3x3 matrix has shaded grids. The top row has: 1 shaded square, 2 shaded squares, 3 shaded squares. The middle row has: 2 shaded squares, 3 shaded squares, 4 shaded squares. The bottom row has: 3 shaded squares, 4 shaded squares, and a blank space. How many squares should be shaded in the blank space?

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

Explanation

The number of shaded squares increases by 1 as you move from left to right in each row, and also increases by 1 as you move from top to bottom in each column. Row 3: 3 -> 4 -> ?. Following the arithmetic progression, the missing grid must have 5 shaded squares.

Question 19Integrated english, quant, formal, spatial, mechanics foundations

A sequence of figures consists of lines. Figure 1 has 1 line segment. Figure 2 has 3 segments (forming a triangle). Figure 3 has 5 segments (two connected triangles sharing an edge). Figure 4 has 7 segments. What is the pattern of growth in the number of segments?

  1. Multiply by 2 at each step
  2. Increase by 2 at each step Correct answer.
  3. Increase by 1, then 2, then 3
  4. Double the previous number and subtract 1

Explanation

The number of line segments in the sequence is: 1, 3, 5, 7. This is an arithmetic progression of odd numbers where the common difference between consecutive terms is exactly 2. Thus, the pattern is to increase by 2 at each step.

Question 20Integrated english, quant, formal, spatial, mechanics foundations

Shape A is a square. Shape B is a square divided into 4 equal quadrants by a cross. Shape C is a circle. What is the logical analogue to Shape D?

  1. A circle divided into 4 quadrants by a cross Correct answer.
  2. A square inside a circle
  3. A circle inside a square
  4. An undivided circle

Explanation

The relationship between Shape A (square) and Shape B is that the shape is divided into 4 equal quadrants by a cross. Applying this same transformation to Shape C (a circle) results in a circle divided into 4 quadrants by a cross, which must be Shape D.

Question 21Integrated english, quant, formal, spatial, mechanics foundations

A logical grid operates like an XOR gate: where lines overlap in the two input shapes, they are deleted in the output. If Input 1 is a large circle containing a small circle, and Input 2 is a large circle containing a small square, what is the output?

  1. A large circle containing both the small circle and the small square
  2. A blank shape
  3. Only the small circle and the small square (the large circle is deleted) Correct answer.
  4. A small circle inside a small square

Explanation

According to the XOR rule, lines that appear in both inputs are deleted, while lines that appear in only one input are kept. The large circle appears in both inputs, so its outline is deleted (cancels out). The small circle appears only in Input 1, and the small square appears only in Input 2. Both are kept, leaving only the small circle and the small square in the output.

Question 22Integrated english, quant, formal, spatial, mechanics foundations

A domino sequence has top and bottom numbers. Domino 1: [1/2]. Domino 2: [2/4]. Domino 3: [3/6]. Domino 4: [4/1]. (Note: domino values wrap around from 6 to 1). What is the value of Domino 5?

  1. [5/2]
  2. [5/3] Correct answer.
  3. [6/2]
  4. [6/3]

Explanation

The top numbers follow a simple arithmetic sequence: 1, 2, 3, 4, so the fifth must be 5. The bottom numbers increase by 2 at each step and wrap around through a 7-value cycle: 2, 4, 6, then 6 + 2 = 8 which wraps to 1, then 1 + 2 = 3. So the fifth domino's bottom value is 3, making the domino [5/3].

Question 23Integrated english, quant, formal, spatial, mechanics foundations

A sequence of polygons starts with a triangle, then a square, then a pentagon, then a hexagon. Inside each polygon, there are half as many diagonal lines as the polygon has sides (rounded down). How many diagonals are inside the hexagon?

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

Explanation

A hexagon has 6 sides. The rule states that the number of diagonal lines inside is half the number of sides, rounded down. Half of 6 is exactly 3. Therefore, the hexagon has 3 diagonal lines inside.

Question 24Integrated english, quant, formal, spatial, mechanics foundations

A shape subtraction gate operates as follows: any lines present in the first shape that are also present in the second shape are removed. If Shape 1 is a square with a horizontal line and a vertical line (a cross), and Shape 2 is a vertical line, what is the output shape?

  1. A square with a horizontal line Correct answer.
  2. A square with a vertical line
  3. A blank square
  4. A horizontal line only

Explanation

Shape 1 contains: (a) the square outline, (b) a horizontal line, and (c) a vertical line. Shape 2 contains only a vertical line. According to the subtraction rule, the vertical line is present in both shapes, so it is removed from Shape 1. The square outline and the horizontal line are not in Shape 2, so they remain. The output is a square with a horizontal line.

Question 25Integrated english, quant, formal, spatial, mechanics foundations

A single shaded square sits in the top-left cell of a 3x3 grid. The entire grid is rotated 90 degrees clockwise, and then rotated a further 90 degrees clockwise (a total of 180 degrees). In which cell does the shaded square end up?

  1. Top-right cell
  2. Bottom-left cell
  3. Bottom-right cell Correct answer.
  4. Center cell

Explanation

A 180-degree rotation maps each cell to the cell diagonally opposite through the centre. The top-left cell therefore moves to the bottom-right cell. (Tracing the two 90-degree steps: top-left moves to top-right after the first clockwise rotation, then top-right moves to bottom-right after the second, confirming bottom-right.)

Question 26Integrated english, quant, formal, spatial, mechanics foundations

A balanced lever is 2 meters long with a central pivot. A 10 kg mass is placed 0.5 meters to the left of the pivot. What mass must be placed 1 meter to the right of the pivot to maintain static balance?

  1. 5 kg Correct answer.
  2. 10 kg
  3. 15 kg
  4. 20 kg

Explanation

Static balance in a lever requires the anticlockwise moment to equal the clockwise moment (Moment = Force * Distance). The left moment is 10 kg * 0.5 m = 5 kg-m. To balance this on the right side at a distance of 1 meter, we calculate: Mass * 1 m = 5 kg-m, which gives Mass = 5 kg.

Question 27Integrated english, quant, formal, spatial, mechanics foundations

Two gears, A and B, are in direct mesh. If Gear A rotates in a clockwise direction, which of the following describes the motion of Gear B?

  1. It rotates clockwise
  2. It rotates counter-clockwise Correct answer.
  3. It remains stationary
  4. It slides along its axle without rotating

Explanation

Directly meshed gears always rotate in opposite directions due to the forces acting at the contact point of their teeth. Because Gear A is rotating clockwise, the teeth of Gear A push the teeth of Gear B in a direction that forces Gear B to rotate counter-clockwise.

Question 28Integrated english, quant, formal, spatial, mechanics foundations

A block and tackle pulley system has three supporting rope segments directly holding a load of 120 kg. Neglecting friction, what is the minimum effort force required to lift the load?

  1. 30 kg
  2. 40 kg Correct answer.
  3. 60 kg
  4. 120 kg

Explanation

The mechanical advantage (MA) of a block and tackle pulley system is determined by the number of rope segments that directly support the moving pulley and load. With three supporting segments, MA = 3. Effort Force = Load / MA = 120 kg / 3 = 40 kg.

Question 29Integrated english, quant, formal, spatial, mechanics foundations

According to Pascal's Principle, if a force of 10 N is applied to a small piston with an area of 2 cm^2 in a closed hydraulic system, what is the resulting pressure transmitted throughout the fluid?

  1. 5 N/cm^2 Correct answer.
  2. 10 N/cm^2
  3. 20 N/cm^2
  4. 50 N/cm^2

Explanation

Pascal's law states that pressure applied to an enclosed fluid is transmitted undiminished in all directions. Pressure (P) is calculated as Force (F) divided by Area (A). P = F / A = 10 N / 2 cm^2 = 5 N/cm^2.

Question 30Integrated english, quant, formal, spatial, mechanics foundations

Gear A has 12 teeth and rotates at a speed of 100 revolutions per minute (RPM). It drives Gear B, which has 24 teeth. What is the rotational speed of Gear B?

  1. 50 RPM Correct answer.
  2. 100 RPM
  3. 200 RPM
  4. 240 RPM

Explanation

The rotational speed of two meshed gears is inversely proportional to their number of teeth: Speed A * Teeth A = Speed B * Teeth B. Rearranging the formula gives: Speed B = (Speed A * Teeth A) / Teeth B = (100 RPM * 12) / 24 = 1200 / 24 = 50 RPM.

Question 31Integrated english, quant, formal, spatial, mechanics foundations

Which of the following materials is the most efficient conductor of heat?

  1. Wood
  2. Glass
  3. Copper Correct answer.
  4. Air

Explanation

Copper is a metal with high thermal conductivity due to the presence of free electrons that can easily transfer thermal kinetic energy. Wood, glass, and air have low thermal conductivities and act as insulators rather than conductors.

Question 32Integrated english, quant, formal, spatial, mechanics foundations

A heavy object is placed on a flat surface. In which of the following configurations will the object be the most stable against tipping over?

  1. Narrow base and a high center of gravity
  2. Narrow base and a low center of gravity
  3. Wide base and a high center of gravity
  4. Wide base and a low center of gravity Correct answer.

Explanation

An object's stability depends on the size of its base of support and the height of its center of gravity. A wide base of support requires the object to be tilted through a larger angle before its center of gravity falls outside the base. A low center of gravity minimizes the height of the weight vector, making it harder to tip. Therefore, the combination of a wide base and low center of gravity provides maximum stability.

Question 33Integrated english, quant, formal, spatial, mechanics foundations

Water flows through a pipe that constricts to a narrower diameter in the middle section. According to Bernoulli's Principle, how do the speed and fluid pressure in the narrow section compare to the wider section?

  1. Higher speed and higher pressure
  2. Higher speed and lower pressure Correct answer.
  3. Lower speed and higher pressure
  4. Lower speed and lower pressure

Explanation

According to the continuity equation, fluid speed must increase in a constricted area to maintain a constant flow rate. Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in static pressure. Therefore, the narrow section experiences higher speed and lower pressure.

Question 34Integrated english, quant, formal, spatial, mechanics foundations

Two identical light bulbs are connected to a battery. In Configuration A, they are connected in series. In Configuration B, they are connected in parallel. How does the brightness of the bulbs in Configuration A compare to Configuration B?

  1. Bulbs in A are brighter than B
  2. Bulbs in A are dimmer than B Correct answer.
  3. Bulbs in A and B have the same brightness
  4. Bulbs in A will flash, while bulbs in B remain steady

Explanation

In a series circuit (A), the total resistance is the sum of the individual resistances (R + R = 2R), which reduces the current flowing from the battery. Each bulb also receives only half of the battery's voltage. In a parallel circuit (B), each bulb is connected directly across the battery, receiving full voltage and drawing more current. Consequently, the bulbs in series (A) are dimmer than those in parallel (B).

Question 35Integrated english, quant, formal, spatial, mechanics foundations

A simple pendulum swings back and forth. Which of the following changes will increase the time period (the time taken for one complete swing) of the pendulum?

  1. Increasing the mass of the bob
  2. Increasing the length of the string Correct answer.
  3. Decreasing the mass of the bob
  4. Decreasing the length of the string

Explanation

The time period (T) of a simple pendulum is given by the formula T = 2 * pi * sqrt(L / g), where L is the length of the string and g is the acceleration due to gravity. The period is directly proportional to the square root of the length, so increasing the string length will increase the time period. The mass of the bob does not affect the period of a simple pendulum.

Question 36Integrated english, quant, formal, spatial, mechanics foundations

A hydraulic jack has an input piston with an area of 5 cm^2 and an output piston with an area of 100 cm^2. If an input force of 50 N is applied to the small piston, what is the output force exerted by the large piston?

  1. 50 N
  2. 250 N
  3. 1000 N Correct answer.
  4. 2000 N

Explanation

The mechanical advantage (MA) of a hydraulic system is the ratio of the area of the output piston to the input piston: MA = Area_out / Area_in = 100 / 5 = 20. Output Force = Input Force * MA = 50 N * 20 = 1000 N. This allows a small input force to lift a much heavier load.

Question 37Integrated english, quant, formal, spatial, mechanics foundations

Two identical springs, each with a spring constant 'k' of 10 N/mm, are connected in series to support a load. What is the effective spring constant of the combined series system?

  1. 5 N/mm Correct answer.
  2. 10 N/mm
  3. 20 N/mm
  4. 40 N/mm

Explanation

When springs are connected in series, the overall system is less stiff. The formula for the effective spring constant (K_eff) of two springs in series is: 1 / K_eff = 1 / k1 + 1 / k2. Here, 1 / K_eff = 1/10 + 1/10 = 2/10 = 1/5. Therefore, K_eff = 5 N/mm.

Question 38Integrated english, quant, formal, spatial, mechanics foundations

A pair of scissors is an example of which class of lever?

  1. First-class lever Correct answer.
  2. Second-class lever
  3. Third-class lever
  4. Fourth-class lever

Explanation

Levers are classified by the relative positions of the fulcrum, effort, and load. In a first-class lever, the fulcrum (pivot point) is positioned in the middle, between the effort force (handles) and the load (cutting blades). A pair of scissors fits this exact description.

Question 39Integrated english, quant, formal, spatial, mechanics foundations

A wheelbarrow carries a load of 90 kg. The distance from the wheel axle (fulcrum) to the center of the load is 0.4 meters, and the distance from the axle to the handles (where effort is applied) is 1.2 meters. What effort force is required to lift the handles?

  1. 30 kg Correct answer.
  2. 45 kg
  3. 60 kg
  4. 90 kg

Explanation

A wheelbarrow acts as a second-class lever. Using the law of moments: Load * Load Distance = Effort * Effort Distance. Thus, 90 kg * 0.4 m = Effort * 1.2 m. Effort = (90 * 0.4) / 1.2 = 36 / 1.2 = 30 kg.

Question 40Integrated english, quant, formal, spatial, mechanics foundations

A belt drive connects two pulleys. The belt is crossed (twisted in an 'X' shape between the pulleys). If the driving pulley rotates clockwise, in which direction does the driven pulley rotate?

  1. Clockwise
  2. Counter-clockwise Correct answer.
  3. It fluctuates direction continuously
  4. It will not rotate because a crossed belt locks the system

Explanation

In an open belt drive, both pulleys rotate in the same direction. However, crossing the belt reverses the direction of the belt path between the pulleys, causing the driven pulley to rotate in the opposite direction. Since the driving pulley rotates clockwise, the driven pulley will rotate counter-clockwise.

Question 41Integrated english, quant, formal, spatial, mechanics foundations

A solid block of wood floats in water with exactly half of its volume submerged. What can be inferred about the density of the wood block compared to the density of water?

  1. The wood is twice as dense as water
  2. The wood is half as dense as water Correct answer.
  3. The wood has the same density as water
  4. Density cannot be determined without knowing the mass of the block

Explanation

According to Archimedes' principle, a floating object displaces a weight of fluid equal to its own weight. If the block floats with half of its volume submerged, it means the weight of water displaced by half of the block's volume equals the total weight of the block. Therefore, the density of the wood must be exactly half (50%) the density of water.

Question 42Integrated english, quant, formal, spatial, mechanics foundations

A screw is used to hold two wooden blocks together. If the pitch of the screw thread is decreased (meaning the threads are closer together), how does this affect the effort required to turn the screw and the mechanical advantage?

  1. Requires more effort, lower mechanical advantage
  2. Requires less effort, higher mechanical advantage Correct answer.
  3. Requires more effort, higher mechanical advantage
  4. Requires less effort, lower mechanical advantage

Explanation

A screw is essentially an inclined plane wrapped around a cylinder. Decreasing the pitch reduces the slope of this inclined plane. A gentler slope requires less effort force to rotate the screw, which corresponds to a higher mechanical advantage, though it requires more turns to insert the screw to the same depth.

Question 43Integrated english, quant, formal, spatial, mechanics foundations

A wooden crate rests on a ramp. The angle of the ramp is slowly increased. At an angle of 30 degrees, the crate just begins to slide down. What physical property determines this threshold?

  1. The coefficient of static friction Correct answer.
  2. The coefficient of kinetic friction
  3. The surface area of the crate in contact with the ramp
  4. The atmospheric pressure surrounding the ramp

Explanation

The point at which an object just begins to slide down an inclined plane is determined by the coefficient of static friction (μ_s). Specifically, sliding starts when the component of gravity acting down the ramp (mg * sinθ) exceeds the maximum static frictional force (μ_s * mg * cosθ), which simplifies to μ_s = tanθ. Once movement begins, kinetic friction applies.

Question 44Integrated english, quant, formal, spatial, mechanics foundations

A car drives around a circular track. If the car doubles its speed while keeping the same turning radius, how does the centrifugal force acting on the passengers change?

  1. It remains the same
  2. It doubles
  3. It triples
  4. It quadruples Correct answer.

Explanation

Centrifugal (or centripetal) force is given by the formula F = m * v^2 / r, where m is mass, v is velocity, and r is the radius of the turn. Since velocity is squared in the formula, doubling the speed (2v) results in (2)^2 = 4 times the force. Therefore, the force quadruples.

Question 45Integrated english, quant, formal, spatial, mechanics foundations

An engineer chooses to use an I-beam instead of a solid rectangular beam of the same material and weight to support a bridge. Why is the I-beam structurally preferred?

  1. It is more flexible and bends easily
  2. It concentrates the material in the areas of maximum stress (flanges) Correct answer.
  3. It has a lower density than a solid beam
  4. It prevents wind from blowing through the structure

Explanation

An I-beam is designed to maximize the moment of inertia for a given weight. Bending stress is highest at the top and bottom edges (outer fibers) of a beam, while the center (neutral axis) experiences zero bending stress. The flanges of the I-beam place most of the material at the outer edges where stress is highest, providing high resistance to bending with minimal weight.

Question 46Integrated english, quant, formal, spatial, mechanics foundations

A bimetallic strip consists of a strip of brass bonded to a strip of iron. When heated, the bimetallic strip bends toward the iron side. What does this indicate?

  1. Brass expands more than iron when heated Correct answer.
  2. Iron expands more than brass when heated
  3. Iron conducts heat faster than brass
  4. Brass has a lower melting point than iron

Explanation

When heated, the metals expand. Since they are bonded together, they must bend. The metal that expands more (larger coefficient of thermal expansion) will become longer and form the outer curve of the bend. Since the strip bends toward the iron side, the brass must be on the outside, indicating that brass expands more than iron.

Question 47Integrated english, quant, formal, spatial, mechanics foundations

A simple truss bridge supports a load in the middle. Which of the following describes the forces acting on the top chord and bottom chord of the truss?

  1. Top chord is in tension, bottom chord is in compression
  2. Top chord is in compression, bottom chord is in tension Correct answer.
  3. Both chords are in tension
  4. Both chords are in compression

Explanation

Under a downward load, a truss bridge behaves similarly to a bending beam. The top chord is squeezed together, placing it under compressive stress (compression). The bottom chord is pulled apart, placing it under tensile stress (tension). This combination resists the bending moment of the load.

Question 48Integrated english, quant, formal, spatial, mechanics foundations

How does atmospheric pressure change as altitude above sea level increases?

  1. It increases linearly
  2. It decreases Correct answer.
  3. It remains constant
  4. It increases exponentially

Explanation

Atmospheric pressure is caused by the weight of the air column above a given point. As altitude increases, there is less air above that point, resulting in a decrease in atmospheric pressure. This decrease is non-linear (exponentially decaying) because air is compressible and is denser near the Earth's surface.

Question 49Integrated english, quant, formal, spatial, mechanics foundations

A belt drive system uses a tensioner pulley. To maximize belt grip and reduce slippage, on which side of the belt drive should the tensioner pulley be installed?

  1. The tight side (the side pulled by the driving pulley)
  2. The slack side (the side returning to the driving pulley) Correct answer.
  3. Directly on the driving pulley itself
  4. It does not matter, as tension is uniform throughout the belt

Explanation

In a belt drive, one side is under high tension (tight side) as it is pulled by the driver. The other side is loose (slack side) as it returns. Placing the tensioner on the slack side is optimal because it absorbs the slack, increases the belt wrap angle around the pulleys, and avoids the high forces present on the tight side, which would wear out the tensioner bearing rapidly.

Question 50Integrated english, quant, formal, spatial, mechanics foundations

Choose the word that is closest in meaning (synonym) to 'resilient' as used in a professional context: 'Despite the grueling nature of the training program, the recruits proved to be highly resilient.'

  1. Fragile
  2. Stubborn
  3. Adaptable Correct answer.
  4. Hostile

Explanation

In a professional or stressful context, 'resilient' means able to withstand or recover quickly from difficult conditions. 'Adaptable' is the closest synonym among the choices, representing the capacity to adjust and recover. 'Fragile' is an antonym, while 'stubborn' and 'hostile' carry negative connotations that do not match 'resilient'.