Mr. X purchased a house for ₹ 7,00,000 and made a down payment of ₹ 1,50,000 .
He repays the balance in 25 years by equal monthly installments as \(9 \%\) per annum compounded monthly. The equated monthly installment (EMM) is :
[Given that \((1.0075)^{-300}=0.106\) ]

If \(A=\left[\begin{array}{cc}\sin \alpha & -\cos \alpha \\ \cos \alpha & \sin \alpha\end{array}\right]\), and \(A+A^{\prime}=I\), then the value of \({ }^{\prime} \alpha^{\prime}\) is :

The unit vector in the xy-plane, making an angle of \(60^{\circ}\) with the positive direction of x-axis is:

The value of \(\int_{-a}^a f(x) d x\) where \(f(x)=\frac{7^x}{1+7^x}\), is :

The differential equation representing the family of curves \(y=A x+\frac{B}{x}, x \neq 0\), where A and B are arbitrary constants, is given by

\(\int_1^4|x-2| d x\) is equal to:

The vector equation of line passing through (2, -1, 3) and perpendicular to the lines \(\frac{x-2}{3}=\frac{y-1}{1}=\frac{z+2}{2} \quad\) and \(\quad \frac{x+3}{-4}=\frac{y-5}{-3}=\frac{z+1}{2}\)
(Here \(\lambda\) is a parameter)

If \(A=\left[\begin{array}{cc}1 & 0 \\ 0 & -1\end{array}\right]\)and \(B=\left[\begin{array}{ll}0 & 2 \\ 2 & 0\end{array}\right]\) ,then the matrix AB is equal to

If \(K\) is such that the area of triangle \(A B C\) is 3 , where \(A(1,3), B(0,0)\) and \(C(K, 0)\), then the value(s) of \(K\) is/are:

Read the passage carefully and answer the Questions
According to Valence Bond theory, the metal atom or ion under the influence of ligands can use its ( \(n-1\) )d, ns, np or ns, np, nd orbitals for hybridisation to yield a set of equivalent orbitals of definite geometry such as octahedral, tetrahedral, square planar and so on. These hybridised orbitals are allowed to overlap with ligand orbitals that can donate electron pairs for bonding. While the VB theory, to a larger extent, explains the formation, structures and magnetic behaviour of coordination compounds, it suffers from the many shortcomings. The Crystal field theory (CFT) is an electrostatic model which considers the metal-ligand bond to be ionic arising purely from electrostatic interactions between the metal ion and the ligand. The five \(d\) orbitals in an isolated gaseous metal atom/ion have same energy, i.e., they are degenerate. This degeneracy is maintained if a spherically symmetrical field of negative charges surrounds the metal atom/ion. However, when this negative field is due to ligands in a complex, it becomes asymmetrical and the degeneracy of the \(d\) orbitals is lifted. It results in splitting of the \(d\) orbitals. The pattern of splitting depends upon the nature of the crystal field.
Which among the following are diamagnetic complexes?
\(\left[Ni(CN)_4\right]^{2-},\left[Co\left(C_2O_4\right)_3\right]^{3-},\left[Fe(CN)_6\right]^{4-},\left[CoF_6\right]^{3-},\left[Mn(CN)_6\right]^{3-}\)

Which enzyme is used to join DNA fragments during recombinant DNA formation?

Match List-l with List-ll

List-I	List-II
(A) The measurable characteristic of a population is called	(I) sample
(B) The measurable characteristics of a sample is called	(II) Alternative hypothesis
(C) A smaller group of a population selected to represent a population is caller	(III) Parameter
(D) The assumption made opposite to the null hypothesis is called	(IV) statistic

Choose the correct answer from the options given below:

Select the correct statement/s from the following:
A. Spermatogonia always undergo meiotic cell division.
B. Primary spermatocytes divide by mitotic cell division.
C. Secondary spermatocytes have 23 chromosomes and undergo second meiotic division
D. Spermatozoa are transformed into spermatids.
Choose the correct answer from the options given below: