The effective rate that is equivalent to a nominal rate of 16 % compounded semi-annually is :

If \(A = \begin{bmatrix} 1 & 0 \\ -1 & 5 \end{bmatrix}\) and \(I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}\), then the value of k so that \(A^2 = 6A + kI\) is given by:

If \(a, b, c\) are positive real numbers, then the least value of \((a+b+c)(a b+b c+c a)\) is :

Total number of one-one functions from the set \(A=\{1,2,3,4\}\) to the set \(B=\{a, b, c, d\), e \(\}\) are:

Area of the triangle ABC with vertices \(\left(a, a^2\right),\left(b, b^2\right)\) and \(\left(c, c^2\right)\) is equal to :

The area of the region bounded by the curves \(x^2 = 4y\), the line \(x = 3\) and x axis is:

Three pipes \(A, B\) and \(C\) can fill a tank in \(12\) hours, \(15\) hours and \(20\) hours respectively. If A is open all the time and \(B\) and \(C\) are open for one hour each alternately, in how many hours will the tank be full?

Read the passage carefully and answer the questions
Optically active polyhydroxy aldehydes or ketones or molecules which provide such units on hydrolysis are called carbohydrates. They can be broadly classified as monosaccharides, disaccharides and polysaccharides depending on their behavior towards hydrolysis. They are also classified as reducing or non-reducing sugars. Another class of biomolecules is proteins which are polymers of twenty different amino acids linked by peptide bonds. Amino acids can be classified as acidic, basic or neutral depending on the relative number of amino and carboxyl groups in their molecule. The essential amino acids cannot be synthesized by our body and hence must be provided through diet. Nucleic acids are the polymers of nucleotides which in turn consist of a base, pentose sugar and phosphate. There are two types of nucleic acids namely, DNA and RNA which differ in the composition of sugar and a base
The sugar moiety in DNA and RNA molecules, respectively, ar

Read the following passage carefully and answer the given questions.
Plasmodium, a tiny protozoan is responsible for the disease malaria. 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. Innate immunity consist of four types of barriers. These are – (i) Physical barriers- skin on our body is the main barrier which prevents entry of the micro-organisms. (ii) Physiological barriers- Acid in the stomach, saliva in the mouth, tears from eyes-all prevent microbial growth. (iii) Cellular barriers- 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. (iv) Cytokine barriers- virus-infected cells secrete proteins called interferons which protect non-infected cells from further viral infection. Allergy is due to the release of chemicals like histamine and serotonin from the mast cells. The use of drugs like anti-histamine, adrenalin and steroids quickly reduce the symptoms of allergy. Drugs like barbiturates, amphetamines, benzodiazepines, and other similar drugs, that are normally used as medicines to help patients cope with mental illnesses like depression and insomnia, are often abused.
Which one of the following drugs or chemicals can not quickly reduce the symptoms of allergy?

A long wire with a small current element of length 1 cm is placed at the origin and carries a current of 10 A along the x-axis. The magnitude of the magnetic field, due to the element, on the y-axis at a distance \( r = 0.5 \, m \) from it, would be

Two charges \( 5 \mu C \) and \( - 2 \mu C \) (with no external field) are placed at \( (-9 \text{ cm}, 0, 0) \) and \( (9 \text{ cm}, 0, 0) \) respectively. The work required to separate the two charges infinitely away from each other is :

Reaction of Ethene with Bromine in CCl\(_4\) will result in

n the given diagram, the direction of current is given. Due to the presence of the current carrying wire, the loop ABCD will be