Value of \(\frac{e^{\sin \left(\tan ^{-1} x+\cot ^{-1} x\right)}}{e^{\sin \left(\sin ^{-1} x+\cos ^{-1} x\right)}}, x \in[-1,1]\), is:

A cone, whose height is always equal to its diameter, is increasing in volume at the rate of \(40 cm^3 / sec\). The rate at which radius is increasing when circular base area is \(1 m^2\) is :

If \(f(x)=2 x^3-15 x^2+36 x+1, x \in[1,5]\), then the absolute minimum value of \(f(x)\) is:

A coin is tossed twice and outcomes are recorded. If the random variable \(X\) represents the number of heads in the experiment, then the expectation of X will be :

In an LPP, the feasible region represented by the set off constraints \(2 x+3 y \leq 18, x+y \leq 10, x \geq 0, y \geq 0\) is

Let \(A=\left[\begin{array}{cc}0 & 2 \alpha+1 \\ 1 & \beta\end{array}\right]\) and \(B=\left[b_{i j}\right]\) be a skew symmetric matrix of order 2 such that \(b_{12}=1\).
If \(A B=I_2\), where \(I_2\) is the identity matrix of order 2 , then :

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 k/4 is

The reaction of aliphatic and aromatic primary amines with chloroform in the presence of ethanolic potassium hydroxide to produce compound with fouling smell, is known as

After industrialisation in England, the reversed proportion of dark winged moth with white winged moth is an example of __________

Read the given passage carefully and answer the questions
Salmonella typhi is a pathogenic bacterium which causes typhoid fever in human beings. Sustained high fever (39° to 40°C), weakness, stomach pain, constipation, headache and loss of appetite are some of the common symptoms of this disease. Typhoid fever could be confirmed by Widal test. Plasmodium enters the human body as sporozoites. The parasites initially multiply within the liver cells and then attack the red blood cells (RBCs) resulting in their rupture. The rupture of RBCs is associated with release of a toxic substance, haemozoin, which is responsible for the chill and high fever recurring every three to four days. There is lymphoid tissue also located within the lining of the major tracts (respiratory, digestive and urogenital tracts) called mucosa-associated lymphoid tissue (MALT). In our body, cell growth and differentiation is highly controlled and regulated. In cancer cells, there is breakdown of regulatory mechanisms. Normal cells show a property called contact inhibition by virtue of which contact with other cells inhibits their uncontrolled growth. Cancerous cells just continue to divide giving rise to masses of cells called tumors. Tumors are of two types: benign and malignant. Cannabinoids are a group of chemicals, which interact with cannabinoid receptors present principally in the brain. Generally taken by inhalation and oral ingestion, these are known for their effects on cardiovascular system of the body.
In which organ of the human body, cannabinoid receptors are principally present?

Arrange the following steps of sewage treatment in correct sequence:
A. Flocs consume organic matter and reduces the BOD.
B. Removal of floating debris and grit.
C. Bacterial flocs allowed to sediment.
D. Primary effluent passed into aeration tank and agitated mechanically.
E. Effluent after secondary treatment is released into water bodies.
Choose the correct answer from the options given below:

Choose the correct statement:
Three charges \( 2q, -q, -q \) are located at the vertices of an equilateral triangle. At the centroid:

Match List I with List - II. -

List – l (Diseases)	List – II (Causative micro-organisms)
(A) Filariasis	(l) Haemophilus influenzae
(B) Common cold	(II) Wuchereria malayi
(C) Pneumonia	(III) Trichophyton
(D) Ringworm	(IV) Rhino viruses

Choose the correct answer from the options given below: