The set of positive integers less than 50 forming the equivalence class of 6 modulo 9 is given by :

If \(y=3 \cos (\log x)+4 \sin (\log x)\), then choose correct option :

The points on the curve \(9 y^2=x^3\) where normal to the curve makes equal intercepts with the axes is/are:

\(A=\left[\begin{array}{lll}0 & 1 & 3 \\ 1 & 2 & x \\ 2 & 3 & 1\end{array}\right]\)
\(A^{-1}=\left[\begin{array}{ccc}\frac{1}{2} & -4 & \frac{5}{2} \\ -\frac{1}{2} & 3 & -\frac{3}{2} \\ \frac{1}{2} & y & \frac{1}{2}\end{array}\right]\)
Find the value of \(8 x+5 y\)

Which of the following statements are true?
(A) Degree of the differential equation \(\frac{d^2 y}{d x^2}+y=1\) is 2.
(B) Number of arbitrary constants in the particular solution the differential equation of order 4 are 4.
(C) \(y^2=a\left(b^2-x^2\right)\) will be the general solution of a differential equation of order 2; where a and b are two arbitrary constants.
(D) \(f(x, y)=\frac{2 x-y}{x+3 y}\) is a homogeneous function of degree 1.
(E) Integrating factor of \(x \frac{d y}{d x}-y=2 x^2\) is \(\frac{1}{x}\).
Choose the correct answer from the options given below:

A person started keeping aside 10,000 each year for his child's college education in a sinking fund. The amount he will receive after 6 years, if the rate of interest is \(10 \%\) p.a., is: [Use \((1.1)^{\wedge} 6=1.771\) ]

The rate of change of volume of a sphere with respect to its surface area, when radius is 4 cm, is equal to

The current flowing through a wire as a function of time is given as : \( I = 3t^2 + 2t + 5 \). The charge flowing through any cross-section of the wire in first 2 s is :

The curves \(x=y^2\) and \(x y= K\), cut at right angles if :

A capacitor charged from a 100 V d.c supply is found to have charge of 20 \(\mu\text{C}\). How much energy is stored in it ?

Answer the question on basis of passage given below :
P block elements are placed in groups 13 to 18 of the periodic table. Their valence shell electronic configuration is \(ns^2 np^{1-6}\). Group 16 of the p block elements are known as the group of chalcogens having \(ns^2 np^4\) as their general electronic configuration. They exhibit number of oxidation states but the stability of \(- 2\) oxidation state decreases down the group. They are sometimes also known as group of chalcogens as the name is derived from the Greek word for brass and points to the association of sulphur and its congeners with copper. Their ionisation enthalpy decreases down the group. Oxygen shows anomalous behaviour due to its small size and high electronegativity.
Identify the epsom salt out of the following salts :

In a Young's double-slit experiment, the slits are separated by 0.28 mm and the wavelength of light used is 6000 A. The fringes are observed on a screen placed 1.4 m away from the slits. The distance between the central bright fringe and the fourth bright fringe will be

Choose the wrong statement from the following :