\(f(x)=x^3+p x^2+q x+10\) has a maximum at \(x=-3\) and a minimum at \(x=1\). The values of \(p\) and \(q\) are:

What is the mean of the numbers obtained on throwing a die having written \(1\) on three faces, \(2\) on two faces and \(5\) on \(1\) face?

The number of arbitrary constants in general solution of a differential equation of third order is :

If \(\vec{p}\) and \(\vec{q}\) are two unit vectors such that \(|\vec{p}+\vec{q}|=\sqrt{2}\), then which of the following are correct?
(A) \(|\vec{p}|=|\vec{q}|=1\)
(B) \(\vec{p}\) and \(\vec{q}\) are orthogonal vectors
(C) \(\vec{p}\) and \(\vec{q}\) are collinear vectors
(D) \((4 \vec{p}-\vec{q}) \cdot(2 \vec{p}+\vec{q})=7\)
Choose the correct answer from the options given below :

A random variable X has the following probability distribution

X	2	3	4	5
P(X)	5/k	7/k	9/k	11/k

Then the value of \(\frac{k}{4}\) is

If the points \((2,-3),(\lambda,-1)\) and \((0,4)\) are collinear, then the value of \(\lambda\) is:

Anshu takes a personal loan of ₹\(10,00,000\) at the rate of \(12\%\) per annum for 2 years, then the EMI by using flat rate method is

The radius of curvature of the path of a charged particle in a uniform magnetic field is directly proportional to the

Read the passage carefully and answer the questions
Carboxylic acids are the organic compounds which comprise of carboxyl functional group, -COOH. These are generally found in nature, some higher members are known as fatty acids as they occur in natural fats as esters of glycerol. They can be prepared from oxidation of alcohols and aldehydes, hydrolysis of nitriles and amides and Grignard reagents. They are stronger acids than simple phenols and alcohols. but weaker than mineral acids. Substituents affect the acidity of aliphatic and aromatic carboxylic acids. They undergo reactions involving cleavage of -OH and C-OH bond. Carboxylic acids having an alpha hydrogen get halogenated in the presence of red phosphorus to form alpha halo carboxylic acids. The reaction is known as Hell Volhard Zelinsky reaction. Besides these aromatic carboxylic acids undergo electrophilic substitution reactions. They are versatile and are employed in the manufacture of various useful compounds. For example, methanoic acid is used in rubber, textile, dyeing, leather and electroplating industries. Higher fatty acids are used in the manufacture of soaps and detergents. Esters of Benzoic acid are used in perfumery.
Which carboxylic acid will not undergo HVZ reaction?

The halide which will undergo \(SN ^2\) reaction easily:

Match List - I with List - II.

List - I (Disease)	List - II (Pathogen)
(A) Thalassaemia	(I) Absence of one X chromosome
(B) Phenylketonuria	(II) Inborn error of metabolism
(C) Down’s Syndrome	(III) Autosomal recessive blood disease
(D) Turner’s Syndrome	(IV) Presence of an additional copy of the 21st chromosome

Choose the correct answer from the options given below :

Match List - I with List - II.

LIST I	LIST II
A. \(\left[1+\left(\frac{d y}{d x}\right)^2\right]=\left(\frac{d^2 y}{d x^2}\right)^2\)	I. order \(=2\), degree \(=2\)
B. \(\frac{d^3 y}{d x^3}-3 \frac{d^2 y}{d x^2}+2\left(\frac{d y}{d x}\right)^4=y^4\)	II. order \(=3\), degree \(=2\)
C. \(\left(1+\frac{d y}{d x}\right)^3=\left(\frac{d^3 y}{d x^3}\right)^2\)	III. order \(=2\), degree \(=1\)
D. \(\left[1+\left(\frac{d y}{d x}\right)^2\right]^?=\frac{d^2 y}{d x^2}\)	IV. order \(=3\), degree \(=1\)

Choose the correct answer from the option given below:

If \(f(x) = sin\) \(x - cos\) \(x\), \(x \in[0,2 \pi]\) then
(A) f(x) is increasing in \(\left(0, \frac{3 \pi}{4}\right)\)
(B) f(x) is decreasing in \(\left(0, \frac{3 \pi}{4}\right)\)
(C) f(x) is decreasing in \(\left(\frac{3 \pi}{4}, \frac{7 \pi}{4}\right)\)
(D) f(x) is decreasing in \(\left(\frac{7 \pi}{4}, 2 \pi\right)\)
Choose the correct answer from the options given below: