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Q) The neutral axis of the cross section of a beam is that axis at which the bending stress is

  • Zero
  • Minimum
  • Maximum
  • Infinity

The neutral axis is an axis in the cross section of a beam along which there are no stress and strains.

Q) Five cubes of identical size and another smaller cube are assembled as shown in Figure A. If viewed from direction X, the planar image of the assembly appears as Figure B. If viewed from direction Y, the planar image of the assembly (Figure A) will appear as?

  •  

Option A is correct.

Q) Visualize a cube that is held with one of the four body diagonals aligned to the vertical axis. Rotate the cube about this axis such that its view remains unchanged. The magnitude of the minimum angle of rotation is

  • 1200
  • 600
  • 900
  • 1800

Q) The plot below shows the relationship between the mortality risk of cardiovascular disease and the number of steps a person walks per day. Based on the data, which one of the following options is true?

  • The risk reduction on increasing the steps/day from 0 to 10000 is less than the risk reduction on increasing the steps/day from 10000 to 20000
  • The risk reduction on increasing the steps/day from 0 to 5000 is less than the risk reduction on increasing the steps/day from 15000 to 20000.
  • For any 5000 increment in steps/day the largest risk reduction occurs on going from 0 to 5000.
  • For any 5000 increment in steps/day the largest risk reduction occurs on going from 15000 to 20000.

Risk reduction value in (0-5000) = 1 – 0.45 = 0.55 which is maximum

Q) Seven identical cylindrical chalk-sticks are fitted tightly in a cylindrical container. The figure below shows the arrangement of the chalk-sticks inside the cylinder. The length of the container is equal to the length of the chalk-sticks. The ratio of the occupied space to the empty space of the container is.

  • 5/2
  • 7/2
  • 9/2
  • 3
1. Occupied Space: The volume of one chalk-stick is \(\pi r^2 h\). For 7 chalk-sticks, the total volume occupied is: \[ V_{\text{occupied}} = 7 \pi r^2 h \] 2. Total Volume of the Container: The radius of the container is \(R = 3r\). Therefore, the volume of the container is: \[ V_{\text{container}} = \pi R^2 h = \pi (3r)^2 h = 9 \pi r^2 h \] 3. Empty Space: The empty space is: \[ V_{\text{empty}} = V_{\text{container}} – V_{\text{occupied}}\] \[= 9 \pi r^2 h – 7 \pi r^2 h = 2 \pi r^2 h \] 4. Ratio of Occupied Space to Empty Space: \[ \text{Ratio} = \frac{V_{\text{occupied}}}{V_{\text{empty}}} = \frac{7 \pi r^2 h}{2 \pi r^2 h} = \frac{7}{2} \] So, the ratio of the occupied space to the empty space is \(\frac{7}{2}\).

Q) If ‘→’ denotes increasing order of intensity, then the meaning of the words [drizzle → rain → downpour] is analogous to [ ______ → quarrel → feud]. Which one of the given options is appropriate to fill the blank?.

  • Bicker
  • Bog
  • Dither
  • Dodge

The correct answer is A. Bicker.

Explanation:
The sequence [drizzle → rain → downpour] shows increasing intensity of rain. In the same way, bicker refers to a small, petty argument, which can escalate into a quarrel (a more serious argument), and then into a feud (a long-lasting, intense conflict). The other options (bog, dither, dodge) are unrelated to the progression of arguments or conflict. Hence, “bicker” fits the analogy perfectly.

Q) Statements: 1. All heroes are winners. 2. All winners are lucky people. Inferences: I. All lucky people are heroes. II. Some lucky people are heroes. III. Some winners are heroes. Which of the above inferences can be logically deduced from statements 1 and 2?

  • Only I and II
  • Only II and III
  • Only I and III
  • Only III

The correct answer is B. Only II and III.

Explanation:
From the statements:

  1. All heroes are winners.
  2. All winners are lucky people.
  • Inference I (All lucky people are heroes) cannot be deduced because not all lucky people are necessarily heroes.
  • Inference II (Some lucky people are heroes) is valid because all heroes are winners, and all winners are lucky people, so some lucky people must be heroes.
  • Inference III (Some winners are heroes) is valid because all heroes are winners.

Thus, only inferences II and III can be logically deduced.

Q) A student was supposed to multiply a positive real number 𝑝 with another positive real number 𝑞. Instead, the student divided 𝑝 by 𝑞. If the percentage error in the student’s answer is 80%, the value of 𝑞 is.

  1. 5
  2. \(\sqrt{2}\)
  3. 2
  4. \(\sqrt{5}\)

The correct answer is \(\sqrt{5}\).
Explanation: Let the correct result be \( p \times q \). Instead, the student calculated \( \frac{p}{q} \). Let the percentage error be \( 80\% \). The percentage error can be expressed as: \[ \text{Percentage Error} = \frac{\left( \frac{p}{q} – p \times q \right)}{p \times q} \times 100 \] This simplifies to: \[ 80 = \frac{\left( \frac{p}{q} – p \times q \right)}{p \times q} \times 100 \] Let’s set up the ratio \( \frac{\frac{p}{q}}{p \times q} \), solve it, and use algebra to find that \( q = \sqrt{5} \).

Q) If the sum of the first 20 consecutive positive odd numbers is divided by $20^2$, the result is.

  • 1
  • 20
  • 2
  • 1/2
The correct answer is A. 1.
Explanation: The sum of the first \( n \) consecutive odd numbers is given by the formula: \[ S_n = n^2 \] For the first 20 odd numbers: \[ S_{20} = 20^2 = 400 \] Now, divide the sum by 202: \[ \frac{400}{202} = \frac{200}{101} = 1.98 \approx 1 \] So, the result is 1.

Q) The ratio of the number of girls to boys in class VIII is the same as the ratio of the number of boys to girls in class IX. The total number of students (boys and girls) in classes VIII and IX is 450 and 360, respectively. If the number of girls in classes VIII and IX is the same, then the number of girls in each class is.

  • 150
  • 200
  • 250
  • 175

Explanation: Given: – Number of girls in both classes is \( X \). – Total students in 8th class = 450. – Total students in 9th class = 360. The ratio condition is: \[\frac{X}{450 – X} = \frac{360 – X}{X}\] Cross-multiplying and solving: \[X^2 = (450 – X)(360 – X)\] Expanding and solving the quadratic equation: \[X^2 = 162000 – 450X – 360X + X^2\] \[0 = 162000 – 810X\] \[X = \frac{162000}{810} = 200\] So, the number of girls in each class is 200.

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