For fixed radii of curvature of a lens, power is proportional to :

A is a \(2 \times 2\) non-singular matrix such that adj \(A=\left[\begin{array}{cc}\sin \theta-\cos \theta & -\sin \theta \sec \theta \\ 2 \cos ^2 \theta & \sin \theta-\cos \theta\end{array}\right]\) then \(|A|\) is:

If the matrix \(\left[\begin{array}{ccc}-1 & x-y & 4 \\ 2 & 0 & 5 \\ x+y & z & 6\end{array}\right]\) is symmetric, then \(x+3 y+2 z\) is equal to

The integrating factor of the differential equation \(\frac{d y}{d x}=x+x y\) is:

\(\int \frac{d x}{9 x^2-16}\) is equal to:

The differential equation of the family of curves \(y=A e^{3 x}+B e^{-3 x}\) where A and B are arbitrary constants, is

The maximum value of the \(f(x)=\frac{1}{4 x^2+2 x+1}\) is :

Match List-I (Name of the Base) with List-II (Structure)

List-I (Name of the Base)	List-II (Structure)
(A). Adenine (A)	(I).
(B). Cytosine (C)	(II).
(C). Thymine (T)	(III).
(D). Guanine (G)	(IV).

Choose the correct answer from the options given below :

The points on the curve \(\frac{x^2}{9} + \frac{y^2}{16} = 1\) at which the tangents are parallel to x-axis :

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:

The 'lungs of the planet' name is given to :

Match List-I with List-II

List-I (Series)	List-II (Values of \( n_1 \) and \( n_2 \) in Bohr's formula)
(A) Lyman	(I) \( n_1=4, n_2 \geq 5 \)
(B) Balmer	(II) \( n_1=3, n_2 \geq 4 \)
(C) Paschen	(III) \( n_1=2, n_2 \geq 3 \)
(D) Brackett	(IV) \( n_1=1, n_2 \geq 2 \)

Choose the correct answer from the options given below:

The number of unpaired electrons in gaseous ions \(Mn ^{3+}, V ^{3+}, Cr ^{3+}\) are respectively: