Identify the correct option regarding the term used to measure an element's ability to lose electrons.

Option 1: Electropositivity
Option 2: Electronegativity
Option 3: Valency
Option 4: Density

If velocity V, acceleration A, and force B are chosen as fundamental quantities, then the dimensional formula of angular momentum in terms of v, A, and F would be:

A) FA(^{-1}) V
B) Fv(^{3}) A(^{-2})
C) Fv(^{2}) A(^{-1})
D) F(^{2}) v(^{2}) A(^{-1})

A sinusoidal wave on a string is described by the wave function

$$ y = 0.3 \sin (1.6 x - 100 t) $$

where ( x ) and ( y ) are in metres and ( t ) is in seconds. The mass per unit length of this string is ( 10 , \text{g/m} ). Determine the power transmitted to the wave.

A. 260 J
B. 360 J
C. 281 J
D. 320 J

Which of the following organisms is an example of a producer?
Option 1) Waterlily
Option 2) Crab
Option 3) Snake
Option 4) Fungi

What practical difficulties are encountered by a trader due to the incompleteness of accounting records?

A closed vessel with rigid walls contains 1 mol of ( _{92}^{238} \mathrm{U} ) and 1 mol of air at 298 K. Considering complete decay of ( _{92}^{238} \mathrm{U} ) to ( _{82}^{206} \mathrm{Pb} ), the ratio of the final pressure to the initial pressure of the system at 298 K is

The transfer of pollen grains from anther to stigma is called pollination.

1. fragmentation
2. pollination
3. fertilisation
4. budding

One side of a rhombus is 5 units. What is its perimeter?
Option 1) 10
Option 2) 20
Option 3) 5
Option 4) None of these

A wire, when bent in the form of a square, encloses an area of 196 cm². If the same wire is bent to form a circle, find the area of the circle.

A has one dimension.
Option 1) line segment
Option 2) sheet of paper
Option 3) cardboard box

Which of the following statements is/are correct?

Option 1) Flood can be defined as a large flow of water.
Option 2) When a flood occurs within six hours of heavy rainfall, it is called a coastal flood.
Option 3) Floods may lead to contamination of drinking water.
Option 4) Effects of floods can be minimized by increasing vegetation cover.

Let ( S_{n} = \tan \theta + 2 \tan 2 \theta + 4 \tan 4 \theta + \cdots + n ) terms and ( F(\theta) = \int S_{n} d \theta ). If ( \lim_{\theta \rightarrow 0} F(\theta) = 1 ), then ( F(\theta) ) is:

A ( \ln \left| \frac{2^{n} \sin \theta}{\sin \left(2^{n} \theta\right)} \right| )
B ( \ln \left| \frac{e 2^{n} \sin \theta}{\sin \left(2^{n} \theta\right)} \right| )
C ( \ln \left| \frac{10 \cdot 2^{n} \sin \theta}{\sin \left(2^{n} \theta\right)} \right| )
D ( \ln \left| \frac{\sin \theta}{\sin \left(2^{n} \theta\right)} \right| )

Srivani plucked a lotus plant from a lake near her school. She observed that it has a long hollow stem. What is the function of the stem?

Option 1) To help leaves float on water

Option 2) To absorb water

Option 3) To fix the plant to the bottom of the pond

Option 4) To produce flowers around it.

If ( f(x) = \sqrt{x} g(x) ), where ( g(4) = 2 ) and ( g'(4) = 3 ), find ( f'(4) ).

To find ( f'(x) ), we can use the product rule: [ f'(x) = \frac{d}{dx}(\sqrt{x}) \cdot g(x) + \sqrt{x} \cdot g'(x) ]

The derivative of ( \sqrt{x} ) is: [ \frac{d}{dx}(\sqrt{x}) = \frac{1}{2\sqrt{x}} ]

Thus, we can write: [ f'(x) = \frac{1}{2\sqrt{x}} g(x) + \sqrt{x} g'(x) ]

Now, we will evaluate ( f'(4) ): [ f'(4) = \frac{1}{2\sqrt{4}} g(4) + \sqrt{4} g'(4) ]

We know that ( g(4) = 2 ) and ( g'(4) = 3 ). Plugging in these values: [ f'(4) = \frac{1}{2 \cdot 2} \cdot 2 + 2 \cdot 3 ]

This simplifies to: [ f'(4) = \frac{2}{4} + 6 = \frac{1}{2} + 6 = \frac{1}{2} + \frac{12}{2} = \frac{13}{2} ]

So, ( f'(4) = 6.5 ).

Auxin, cytokinin, and ethylene are examples of:

1. Antibiotics
2. Animal hormones
3. Plant hormones
4. Enzymes

When a solenoid that is carrying current is freely suspended, it comes to rest along a particular direction. This happens because:

Option 1) The solenoid becomes a bar magnet with fixed polarities at its ends under the influence of the Earth's magnetic field.

Option 2) The solenoid behaves like a bar magnet with fixed polarities at its ends when current flows through it.

Option 3) The solenoid becomes a bar magnet with alternating polarities at its ends under the influence of the Earth's magnetic field.

Option 4) The solenoid behaves like a bar magnet with alternating polarities at its ends when current flows through it.

All receipts from the sale of consumable items are treated as:

Option 1) Revenue Receipt

Option 2) Capital Receipt

Option 3) Revenue Expenditure

Option 4) Capital Expenditure

How many molecules of H₂ gas are present in a container of dimensions 2 m × 2 m × 3 m at STP?
(A) 32.22 × 10²⁵
(B) 32.22 × 10²⁵
(C) 32.22 × 10²²
(D) 32.22 × 10²¹

A solid sphere is rotating freely about its symmetry axis in free space. The radius of the sphere is increased while keeping its mass the same. Which of the following physical quantities would remain constant for the sphere?

1. Angular velocity
2. Moment of inertia
3. Rotational kinetic energy
4. Angular momentum

Cloaca of Rana receives

1. Alimentary canal
2. Reproductive tract
3. Urinary tract
4. All of these