A solid sphere of density $\rho$ and radius $R$ is floating in a liquid of density $\sigma$ with half its volume submerged. When the sphere is pressed down slightly and released, it executes simple harmonic motion of time period T. If viscous effects are ignored, then:

• $\sigma = 2 \rho$
• $T = 2 \pi \sqrt{\frac{2R}{3g}}$

For which of the species is Bohr's theory not applicable?

(A) Be$^{3+}$
(B) Li$^{2+}$
(C) He$^{2+}$
(D) H

Which of the following represent 'M is nephew of N'? A $N - K + M$ B $N \times K \div M \div T$ C $N \div K \times M$ D $N \div K + M \times T$ E None of these

The ratio of the longest to the shortest wavelength in the Balmer series of Hydrogen spectrum is:

• 25/9
• 17/6
• 9/5
• 5/4

Choose the correct pathway for systemic circulation:

• Right auricle -> Left ventricle -> Aorta -> Tissues -> Veins
• Right ventricle -> Pulmonary aorta -> Tissues -> Pulmonary veins -> Left auricle
• Left ventricle -> Aorta -> Arteries -> Tissues -> Veins -> Right atrium
• Left auricle -> Left ventricle -> Pulmonary aorta -> Tissues -> Right auricle

A light source of frequency v illuminates a metallic surface and ejects photoelectrons. The photoelectrons having maximum energy are just able to excite the hydrogen atom in ground state. When the whole experiment is repeated with an incident radiation of frequency $\frac{6}{5} \mathrm{v}$, the photoelectrons so emitted are able to excite the hydrogen atom which then emit radiation of six different wavelengths.

• The work function of the metal is $3.15 \mathrm{eV}$
• The work function of the metal is $2.55 \mathrm{eV}$
• The frequency of radiation is $3.08 \times 10^{15} \mathrm{~Hz}$
• The frequency of radiation is $3.08 \times 10^{14} \mathrm{~Hz}$

The voltage $V$ and current I graph for a conductor at two different temperatures $T_{1}$ and $T_{2}$ are shown in the figure. The relation between $T_{1}$ and $T_{2}$ is:

• $T_{1} > T_{2}$
• $T_{1} \approx T_{2}$
• $T_{1} = T_{2}$
• $T_{1} < T_{2}$

Which of the following best describes the conditions for a coalition government?

Option 1: Cooperation between different political parties

Option 2: No cooperation between members of different political parties

Option 3: Cooperation between members of different states

Option 4: Cooperation between members of different countries

$x^{2}-8x+15=0$ $y^{2}-3y+2=0$ $x>y$ $x \geq y$ $x<y$ $x \leq y$ $x=y or the relationship cannot be established.

How many ways are there to arrange the letters in the word GARDEN with the vowels in alphabetical order?

• 240

What can be the general notation of a matrix with 4 rows and 5 columns?
Option 1) 5x4
Option 2) 4x5
Option 3) 4x4
Option 4) 5x5

Solution:

$$ \int_{0}^{1} \sqrt{\frac{1+x}{1-x}} dx $$

The correct answer is $\frac{\pi}{2}$.

A box contains 5 green, 4 yellow, and 3 white marbles. Three marbles are drawn at random. What is the probability that they are not of the same color?

Options: A) $\frac{40}{44}$ B) $\frac{44}{41}$ C) $\frac{41}{44}$ D) $\frac{40}{39}$ E) $\frac{44}{39}$

Find the value of $\frac{x(y+2)}{x}$ if $y=2$.

A) 1
B) 2
C) 3
D) 4

Directions: Study the following information carefully to answer the question given below. A, B, C, D, E, F, G, and H are eight persons working in three different departments viz operations, sales, and finance of an organization with at least two and not more than three in any department. They are on three different scales viz. I, II, and III with at least two in any one scale. Both the employees in the operations department are in scale II. D works in the Sales department and belongs to Scale I. A works in the Finance department and does not belong to Scale I. Two employees in the Sales department belong to one scale. F works with only H in one of the departments. C works with E in one of the departments. B does not work with either C or A in the same department. G does not belong to Scale III. E does not belong to Scale I. Which of the following combinations is correct?

• Operation - F - 1
• Operation - H - III
• Sales - B - II
• Finance - E - III
• All are correct

Write a short note on foreign exchange reforms.

The charge on a $3 \mu \mathrm{F}$ capacitor shown in the figure is 8 $\mu \mathrm{F}$.

The pH range of fresh water suitable for consumption by animals is:

• 2.5 - 3.0
• 4.0 - 5.5
• 6.5 - 7.5
• 9 - 11

Bending of stem towards sunlight in plants is due to:

• Unequal distribution of auxins
• Uniform occurrence of gibberellins
• Inhibition of cytokinin synthesis
• Unequal distribution of cytokinins and gibberellins

Veerapandya Kattabomman was betrayed by which of the following Palayakkarars:

• Palayakkararas of Panchalamkurichi and Pudukottai
• Palayakkararas of Ettayapuram and Pudukottai
• Palayakkararas of Ettayapuram and Nerkattumseval
• Palayakkararas of Panchalamkurichi and Nerkattumseval