\(\int \frac{x+e^{2 z}}{x^2+e^{2 x}} d x=\)

Mr. \(X\) wishes to purchase a house for ₹ \(\ 14,51,400\) from a bank and decided to repay the loan by equal monthly installments (EMI) in \(10\) years. If bank charges interest at 9 % per annum compounded monthly, then the EMI is:
[Given that \((1.0075)^{120}=2.4514\) ]

If \(\vec{a}\) and \(\vec{b}\) are two vectors such that \(|\vec{a}|=10,|\vec{b}|=2\) and \(\vec{a} \cdot \vec{b}=12\), then \(|\vec{a} \times \vec{b}|\) is equal to

A doctor is to visit a patient.
The probabilities that he comes by train, bus, scooter or other means are
\(\frac{3}{10}, \frac{1}{5}, \frac{1}{10}\) and \(\frac{2}{5}\) respectively.
The probabilities that he will be late are
\(\frac{1}{4}\) if he comes by train,
\(\frac{1}{3}\) if he comes by bus,
\(\frac{1}{12}\) if he comes by scooter.
If he comes by other means of transport, he will not be late.
When he arrives, he arrives late.
The probability that he comes by bus is:

The value of is \(\left|\begin{array}{cc}x^2-x+1 & x-1 \\ x+1 & x+1\end{array}\right|\) equal to

Given \(A=\left[\begin{array}{ll}2 & 3 \\ 1 & 4\end{array}\right]\) and \(B=\left[\begin{array}{ll}x & y \\ 1 & 4\end{array}\right]\), If \(A=B\), then \(x\) and \(y\) are :

Which of the following functions is onto?

Answer the question on the basis of passage given below:
Second period elements of p-Block differs from the rest of their group members due to their small atomic size, high electronegativity, high ionization enthalpy and absence of d-orbitals. The elements from the second period like C, N, O have unique property of forming \(p \pi-p \pi\) multiple bonds whereas other heavier elements of p-block form \(d \pi-p \pi\) multiple bonds. This changes the properties of second period elements to great extent. Also the single bond strength of the p-block elements with their own atoms gets affected by their atomic size and presence of lone pairs.
Inert pair effect also affects the properties of the p-Block elements especially for those elements which are present from 4th period onward and this happens due to poor screening effect of inner (n-1)d subshell electrons.
The decreasing order of melting point of the following elements will be:
A. Nitrogen (N)
B. Phosphorus (P)
C. Arsenic (As)
D. Antimony (Sb)
E. Bismuth (Bi)
Choose the correct answer from the options given below:

A mark placed on the surface of a sphere is viewed through glass from a position directly opposite. If the diameter of the sphere is 10 cm and refractive index of glass is 1.5, the image would be at

When a dielectric material placed in uniform electric field, which of the following option is NOT CORRECT:

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

Mr. Jain wishes to purchase a shop for ₹25,00,000 with down payment of ₹2, 00, 000. If he can amortize the balance at 9% per annum compounded monthly for 25 years, what will be his monthly installment if it is given that \(\left(a_{\frac{300}{0.0075}}=119.1616\right)\)?

Given below are two statements:
Statement I : There is a need to translate the original low frequency base band signal into high radio frequency before transmission
Statement II : To transmit a signal an antenna is required. As frequency increases size of antenna decreases.
In the light of the above statements, choose the most appropriate answer from the options given below.