List of practice Questions

The value of the following expression is: \[ \cos \left( \frac{\pi}{2^2} \right) \cdot \cos \left( \frac{\pi}{2^3} \right) \cdot \cos \left( \frac{\pi}{2^4} \right) ... \cdot \cos \left( \frac{\pi}{2^{10}} \right) \]

If $ \sin(\alpha + \beta) = 5 \sin(\alpha - \beta) $, then $ \frac{\sin 2\beta}{5 - \cos 2\beta} $ is:

Match the items of List - A with those of the entries of List - B.

If $ \sin x \cosh y = \cos \theta $ and $ \cos x \sinh y = \sin \theta $, then find $ \sin^2 x + \cosh^2 y $.

If $ \alpha, \beta, \gamma $ are the roots of the equation $ x^3 + 3x^2 + 4x + 5 = 0 $, then the cubic equation whose roots are $ 1 + 4\alpha, 1 + 4\beta, 1 + 4\gamma $ is:

The coefficient of $ x^2 $ in the expansion of \[ (1 - 3x)^{\frac{-1}{4}} \] is

The number of natural numbers less than 500 in which no two digits are repeated is:

If $ N(n) = n \prod_{r=1}^{2023} (n^2 - r^2) $ where $ n > 2023 $, then the value of $ {}^{n}C_{N-1} $ when $ n = 2024 $ is:

Arg \[ \frac{4 + 2i}{1 - 2i} + \frac{3 + 4i}{2 + 3i} \] lies in the interval \[ \text{Arg} \left( \frac{4 + 2i}{1 - 2i} + \frac{3 + 4i}{2 + 3i} \right) \]

The multiplicative inverse of $ z $ is:

The number of elements in the set $ S = \{x \in \mathbb{Z} : x^2 - 7x + 6 \le 0 \text{ and } x^2 - 3x>0 \} $ is

Match the following

List I		List II
A.	Pollen germination	i.	Sulphur
B.	Synthesis of Auxins	ii.	Calcium
C.	Stabilization of protein structure	iii.	Boron
D.	Synthesis of cell wall	iv.	Zinc

Match the following

List I		List II
I.	Helical virus	A.	Bacteriophage
II.	Glycoprotein	B.	Rabies virus
III.	Complex viruses	C.	Influenza virus
IV.	Enveloped virus	D.	Measles virus

Match the following

Set I		Set II		Set III
I.	DNA Ligase	A.	Polymerisation	i.	Okazaki fragments
II.	DNA Polymerase	B.	Introns	ii.	Reactive & unstable
III.	Splicing	C.	Joining	iii.	mRNA
IV.	Ribozyme	D.	RNA Enzyme	iv.	One direction

Mention the Nitrogen base sequence name, restriction cut sites and type of cut ends in the above DNA fragment.
5' - GAATTC - 3'
3' - CTTAAG - 5'

Assertion (A): Bioterrorism involves the actual use or threat to use biological agents to spread fear or inflict death and death of large populations.
Reason (R): It paves way for the development of new vaccines and therapies.

Composition of biogas produced during sewage treatment is

The method of representing phylogeny by branching diagrams was introduced by

Match the following

List I		List II
A.	Red panda	i.	Grus leucogeranus
B.	Siberian crane	ii.	Antelope cervicapra
C.	The black buck	iii.	Sus salvanius
D.	Pygmy hog	iv.	Ailurus ochraceus

Match the following

List I		List II
A.	Gorgonia	i.	Marine leech
B.	Pontobdella	ii.	Sea Urchin
C.	Balanus	iii.	Sea Fan
D.	Echinus	iv.	Rock barnacle

Match the following:
List I and List II

List I	List II
A. Family planning programme	i. 1970
B. Pre-natal Diagnostic Techniques act	ii. 1971
C. Legalisation of Medical Termination of Pregnancy	iii. 1951
D. Advant of amniocentesis	iv. 1994

Experimental verification of chromosomal theory of inheritance was done by_____.

The electric potential at a point is given by $ V = \left(-5x + 3y + \sqrt{15z} \right) \, \text{volt}$.
The magnitude of the electric field at that point is

The metal and metalloid in the $5^{th}$ period of the long form of the periodic table are respectively

Number of electrophiles from the following: CH₄, CO₂, NH₃, H₂O, SO₃, H⁺, BF₃