The maximum value of \(Z=2 x+3 y\) subject to the constraints \(x \geq 0, y \geq 0, x+y \leq 10,3 x+4 y \leq 36\) is:

The area (in sq. units) of the region in the first quadrant bounded by \(y=3 \sqrt{1-x^2}, x \in[0,1]\) and the x-axis is equal to

The function \(f: R \rightarrow R\) defined as \(f(x)=x^2+2 x\) is

If \(x=e^{\cos 2 t}, y=e^{\sin 2 t}\), then \(\frac{d y}{d x}\) equals to

If the binomial distribution \(X \sim B(n, p)\) has mean 3 and variance \(\frac{3}{2},(p+q)=1\), then which of the following is/are TRUE?
(A) \(q=\frac{1}{2}, n=6\)
(B) \(P(X \leq 5)=\frac{63}{64}, p=\frac{1}{2}\)
(C) \(q=\frac{1}{3}, p=\frac{2}{3}\)
(D) \(P(X=4)=\frac{15}{64}, n=6\)
Choose the correct answer from the options given below:

A person has invested Rs. 20,000 in 2020 for 5 years.
If the CAGR for his investment is 11.84%, the end balance of his investment is [Given \((1.1184)^5=1.7498\) ]

The maximum value of \(Z=3 x+4 y\) subject to the constraints: \(x+y \leq 1, x \geq 0, y \geq 0\) is:

Match List I with List II

LIST I	LIST II
A. Soda Water	I. A solution of gas in gas
B. Sugar Solution	II. A solution of solid in solid
C. German Silver	III. A solution of solid in liquid
D. Air	IV. A solution of gas in liquid

Choose the correct answer from the options given below:

The intercept made by the plane \(2 x-3 y+5 z+4=0\) on \(z\)-axis is :

Match List-l with List-II

List-l (Terms)	List-II (Features)
(A) Allele	(I) The position on the chromosome where a gene occurs
(B) Locus	(II) Testing a suspected heterozygote by crossing it with a known homozygous recessive
(C) Gene	(III) One of two or more alternative nucleotide sequences at a single gene locus
(D) Test Cross	(IV) A length of DNA that codes for a particular polypeptide or protein

Choose the correct answer from the options given below:

\(C_2 H_5 OH \xrightarrow{X} C_2 H_5 Cl \xrightarrow{Y} C_2 H_5 CN\)
\(X\) and \(Y\) used in the above reaction are :

Read the following paragraph carefully and answer the given questions.
Certain types of leukocytes (WBC) of our body like polymorpho-nuclear leukocytes (PMNL-neutrophils) and monocytes and natural killer (type of lymphocytes) in the blood as well as macrophages in tissues can phagocytose and destroy microbes. For determining the cause of allergy, the patient is exposed to or injected with very small doses of possible allergens, and the reactions studied. The use of drugs like anti-histamine, adrenalin and steroids quickly reduce the symptoms of allergy. Heroin, commonly called smack is chemically diacetylmorphine which is a white, odourless, bitter crystalline compound. This is obtained by acetylation of morphine. Techniques like radiography (use of X-rays), CT (computed tomography) and MRI (magnetic resonance imaging) are very useful to detect cancers of the internal organs. Different species of Plasmodium (P. vivax, P. malaria and P. falciparum) are responsible for different types of malaria. Of these, malignant malaria caused by Plasmodium falciparum is the most serious one and can even be fatal.
Which of the following drugs are commonly used to quickly reduce the symptoms of allergy?

What is the colour of the third band of a coded resistor of resistance 3.2 \(\times 10^3\) \(\Omega\) ?