If ( y = 2 \sin x ), then ( \frac{dy}{dx} ) will be:

A) ( 2 \cos x )
B) ( -2 \cos x )
C) ( \cos x )
D) None

If ( a = \sin \frac{\pi}{18} \sin \frac{5 \pi}{18} \sin \frac{7 \pi}{18} ), and ( x ) is the solution of the equations ( y = 2[x] + 2 ) and ( y = 3[x - 2] ), where ( [x] ) denotes the integral part of ( x ), then ( a ) is equal to
A ( [x] )
B ( \frac{1}{[x]} )
C ( 2[x] )
D ( [x]^2 )

If $\left[\begin{array}{lll}1 & 2 & 3 \\ 3 & 1 & 2 \\ 2 & 3 & 1\end{array}\right]\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{cc}4 & -2 \\ 0 & -6 \\ -1 & 2\end{array}\right]\left[\begin{array}{l}2 \\ 1\end{array}\right]$, then $(x, y, z)=$

A $(-4, 2, 2)$
B $(4, -2, -2)$
C $(4, 2, 2)$
D $(-4, -2, -2)$

Ionic compounds exist in solid state at room temperature because they have strong electrostatic forces of attraction.

A. solid

B. liquid

C. electrostatic forces

D. van der Waals forces

The teacher asked Sushma that in ethyl ethanoate (CH₃COOC₂H₅) the two oxygen atoms have the same number of electrons but different numbers of neutrons. Which of the following is the correct reason for it?
A. One of the oxygen atoms has gained electrons
B. The oxygen atoms are isotopes
C. One of the oxygen atoms has gained two neutrons
D. The two oxygen atoms are isobars

Which of the following is/are true regarding pyrolysis?
Option 1: It is carried out in the presence of oxygen.
Option 2: It is less effective than incineration.
Option 3: The residues generated by the process of pyrolysis are useful.
Option 4: All of the above.

If I move 5 units towards the east direction and then move 7 units towards the north direction starting from the origin. What will be my coordinates? (Positive x-axis = direction of east)

Option 1) (5, -7)
Option 2) (-5, 7)
Option 3) (5, 7)
Option 4) (-5, -7)

Determine the direction cosines of the normal to the plane and the distance from the origin:

5y + 8 = 0.

Calculate the value of X.

X = (-10) + (15) + (-4)

Option 1) 10
Option 2) -1
Option 3) 1
Option 4) 9

Which number do we get if we skip two numbers on the right side of -1 on a number line?

Option 1) -4
Option 2) 2
Option 3) 1
Option 4) 3

Which of the following is a way to conserve rainwater?

Option 1) Rainwater harvesting

Option 2) Deforestation

Option 3) Use of groundwater for daily usage

Option 4) Building new houses

An elevator starts at the basement with 9 people (excluding the elevator operator) and discharges them all by the time it reaches the top floor, which is floor number 6. In how many ways could the operator have perceived the people leaving the elevator if all the people look the same? (There are a total of 6 floors excluding the basement.)

Option 1) 2002

Option 2) 1009

Option 3) 1576

Option 4) 2492

In which of the given processes does the entropy decrease?
(A) ( 3 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{O}_{3}(\mathrm{g}) )
(B) Boiling of an egg
(C) ( 2 \mathrm{SO}_{3}(\mathrm{g}) \rightarrow 2 \mathrm{SO}_{2}(\mathrm{g}) + \mathrm{O}_{2}(\mathrm{g}) )
(D) ( \mathrm{NH}_{4} \mathrm{Cl}(\mathrm{s}) \rightarrow \mathrm{NH}_{3}(\mathrm{g}) + \mathrm{HCl}(\mathrm{g}) )

Drop in the force of contraction of muscles due to prolonged stimulation is called:

1. Muscle tonicity
2. Muscle atrophy
3. Muscle fatigue
4. Muscle dystrophy

Myxomycetes include members that are:

1. Saprobes or parasites having mycelia, asexual reproduction by fragmentation, sexual reproduction by fusion of gametes.
2. Slimy mass of multinucleate protoplasm having pseudopodia-like structures for engulfing food, reproduction through fragmentation and spore formation.
3. Prokaryotic organisms, cellular or acellular, saprophytic or autotrophic, reproduction by binary fission.
4. Eukaryotic single-celled or filamentous saprobes or autotrophs, asexual reproduction by division of haploid individuals, sexual reproduction by fusion of two cells or their nuclei.

The organic chloro compound which shows complete stereochemical inversion during an SN₂ reaction is:

A) CH₃Cl
B) (C₂H₅)₂CHCl
C) (CH₃)₃CCl
D) (CH₃)₂CHCl

Find the number of integers that lie between the roots of the equation (x^{2}+7x+12=0).

A) 1
B) 7
C) 12
D) 0

Let ( I_{n} = \int_{0}^{\infty} e^{-x} (\sin x)^{n} dx, n \in \mathbb{N}, n > 1 ). Then ( \frac{I_{2008}}{I_{2006}} ) equals

A ( \frac{200 \times 2006}{2008^{2}+1} )

B ( \frac{2008 \times 200}{2008^{2}+1} )

C ( \frac{2006 \times 2004}{2008^{2}-1} )

D ( \frac{2008 \times 2007}{2008^{2}-1} )

Plasmid is a:

Option 1) Part of plasma membrane

Option 2) Extra chromosomal DNA in bacterial cell

Option 3) Fungus

Option 4) Plastid

The driver of a train traveling at 40 m/s applies the brakes as the train enters a station. The train slows down at a rate of 2 m/s². The distance traveled by the train before stopping is:

A. 200 m
B. 300 m
C. 400 m
D. 500 m