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Physics, Chemistry, Mathematics Test

Physics, Chemistry, Mathematics Test

Comprehensive Examination with +4/-1 Marking Scheme

Marking Scheme: +4 for Correct Answer, -1 for Incorrect Answer

Physics Section

Single Correct: 20 Questions | Numerical: 10 Questions
Question 1
Single Correct (+4/-1)

Given \( y = A \sin \left[ \frac{2\pi}{\lambda} (ct - x) \right] \), where \( y \) and \( x \) are measured in metres. Which of the following statements is true?

A. The unit of \(\lambda\) is same as that of \(x\) and \(A\)
B. The unit of \((ct - x)\) is same as that of \(\frac{2\pi}{\lambda}\)
C. The unit of \(c\) is same as that of \(\frac{2\pi}{\lambda}\)
D. The unit of \(\lambda\) is same as that of \(x\) but not of \(A\)
Question 2
Single Correct (+4/-1)

Two trains, moving along different tracks in opposite directions, are put on the same track by mistake. When 300 m apart, drivers start slowing down. The graphs show decrease in velocities. The separation between trains when both have stopped is:

[Graphs: Train I decreases from 20 m/s to 0 in 10s; Train II decreases from 20 m/s to 0 in 8s]

A. 120 m
B. 20 m
C. 60 m
D. 280 m
Question 21
Numerical (+4/-1)

Total distance traveled by object from speed-time graph.

Chemistry Section

Single Correct: 20 Questions | Numerical: 10 Questions
Question 1
Single Correct (+4/-1)

One among the following is an incorrect statement:

A. Molality of a solution is dependent on the temperature
B. Molarity of a solution is dependent on the temperature
C. Normality of 0.5 M aqueous solution of \( \text{H}_2\text{C}_2\text{O}_4 \cdot 2\text{H}_2\text{O} \) is 1 N
D. Molality of a solution relates moles of solute and mass of solvent
Question 21
Numerical (+4/-1)

3.92 g of ferrous ammonium sulphate react completely with 50 mL of N/10 KMnO₄ solution. The percentage purity of the sample is:

Mathematics Section

Single Correct: 20 Questions | Numerical: 10 Questions
Question 1
Single Correct (+4/-1)

If the complex number \( z \) satisfies the equation \((i - z)(1 + 2i) + (1 - iz)(3 - 4i) = 1 + 7i\), then \( z + \overline{z} + z \overline{z} \) is equal to:

A. 0
B. 1
C. -1
D. None of these
Question 21
Numerical (+4/-1)

If \( A = \begin{bmatrix} -\frac{1+i\sqrt{3}}{2i} & -\frac{1-i\sqrt{3}}{2i} \\ \frac{1+i\sqrt{3}}{2i} & \frac{1-i\sqrt{3}}{2i} \end{bmatrix} \), \( i = \sqrt{-1} \) and \( f(x) = x^2 + 2 \). Then \(\left| \frac{f(A)}{(2+i\sqrt{3})} \right|\) is equal to:

Test Results

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Physics
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Chemistry
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Mathematics
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