The solution of the differential equation \(y d x+\left(x-y^2\right) d y=0\) is :

The area of the region given by \(\left\{(x, y): y \geq x^2, y \leq|x|+2\right\} \backslash-\backslash-\backslash-\backslash-\backslash-\) is

The general solution of the differential equation \(x\left(1+y^2\right) d x+y\left(1+x^2\right) d y=0\) is

Let functions \(f:\{1,3,4\} \rightarrow\{1,2,5\}\) and \(g:\{1,2,5\} \rightarrow\{1,3\}\) be defined as \(f=\{(1,2),(3,5),(4,1)\}\) and \(g=\{(1,3),(2,3),(5,1)\}\) respectively. Then, which one of the following is correct statement for \(g \circ f\)?

A box contains 2 black and 4 red balls and another box contains 4 black and 3 red balls. If a ball is drawn at random from one of the two boxes, then the probability of getting a black ball is

Match List I with List II

LIst - I	List - II
(A) The present value of an immediate perpetuity of ₹R payable at end of any year forever at rate of i per period is:	(I) \(\frac{R}{i}(1+i)^m\)
(B) Present value of deferred perpetuity is	(II) \(\frac{A i}{(1+i)^n-1}\)
(C) Periodic payment R in a sinking fund is given by formula (for Amount A)	(III) \(A(1+i)^{-n}\)
(D) The present value of redemption price A of a bond is given by	(IV) \(\frac{R}{i}\)

If the following data is obtained from a simple random sample : 6, 7, 9, 10, 11, 17
Then the point estimate of population standard deviation is :

Self Inductance of coil causes :

Answer the question on the basis of passage given below:
In the periodic table, the d-block contains the elements of group \(3\) to \(12\). The d-orbitals are progressively filled in each of the four long periods. The elements of d block referred as transition metals have partly filled d orbitals and exhibit certain characteristic properties such as variety of oxidation states, formation of coloured ions, act as catalyst and show paramagnetic behaviour.
The two inner transition metals series \(4f\) and \(5f\) are known as Lanthanoids and Actinoids respectively. The lanthanoids resemble one another more closely as compared to ordinary transition elements in any series.
For the four successive transition elements given below, the stability of +2 oxidation state will be:
A. \(\operatorname{Cr}( Z =24)\)
B. \(Mn ( Z =25)\)
C. \(Fe ( Z =26)\)
D. \(Co ( Z =27)\)
Choose the correct answer from the options given below:

In a 200 m race, Rohan completes the race in 8 seconds and Vivan completes the race in 10 seconds. By how much distance Rohan beats Vivan?

Monochromatic light of wavelength 600 nm is incident from air on to water surface. The frequency of refracted light is

Let \(f:[-2,2] \rightarrow[-2,2]\) be a function defined by \(f(x)=x|x|\), then \(f\) is:

The critical angle for light ray going from medium-1 to medium-2 is \(i_c\). What will be the speed of light in medium-2, if its value in medium-1 is \(u\) ?