Ram invested Rs. 20,000 in a mutual fund in the year 2012.
The value of the mutual fund increased to Rs. 32,000 in the year 2017.
The compound annual growth rate (CAGR) of his investment is (Given : \((1.6)^{\frac{1}{5}}=1.098\))

The mean of the numbers obtained on throwing a die having 1 on three faces, 2 on two faces and 5 on one face is:

Match List-I with List-II (Where R is the set of real numbers)

List-I	List-II
(A) \(sin\) \(x\) is continuous on :	(I) \(R -\{0\}\)
(B) \(tan\) \(x\) is continuous on :	(II) \(R\)
(C) \(\cot x\) is continuous on :	(III) \(R -\{n \pi: n \in Z \}\)
(D) \(x^{-n}, n \in N\) is continuous on:	(IV) \(R -\left\{(2 n+1) \frac{\pi}{2}: n \in Z \right\}\)

Choose the correct answer from the options given below :

Consider the relation R in the set Z of integers which is given by \(R=\{(a, b): 2\) divides \(a-b\}\).
Choose the correct option for the relation \(R\) :

The value of \(\left|\begin{array}{lll}2^x & 1 & 6^x \\ 4^x & 1 & 3^x \\ 2^x & 1 & 6^x\end{array}\right|\), where \(x \neq 0 ;\) is:

The remainder, when \(5^{60}\) is divided by 7 , is :

The degree of the differential equation \(\left(\frac{d y}{d x}\right)^3+\left(\frac{d^2 y}{d x^2}\right)^2=0\) is:

Which refining method is represented by the following equations ?
\(Zr+2I_2 \rightarrow ZrI_4\)
\(ZrI_4 \rightarrow Zr+ 2I_2\)

The sex determination in honey bee is based on the number of sets of chromosomes an individual receives. So, the males are ______ having ______ .

If the magnetic field \(\vec{B} = \hat{i} - 0.3\hat{j}\) and the area \(\vec{A} = \hat{i} + 6\hat{j} - 3\hat{k}\) then the magnetic flux through this area is:

Answer the question on the basis of passage given below :
One of the notable features of the transition element is the great variety of oxidation states it may show in its compounds. The elements which give the greatest number of oxidation states occur in or near the middle of the series. Manganese, for example exhibits all the oxidation states from +2 to +7. The lesser number of oxidation states at the extreme ends is either due to losing or sharing of few electrons (Sc, Ti) or too many d electrons of higher valence. Early in the first series scandium (II) is virtually unknown and titanium (IV) which is more stable than Ti (III) or Ti (II). On the other end, the only oxidation state of zinc is \(+ 2\).
Fe shows extra stability as \(Fe ^{3+}\) due to:

The thermostable DNA polymerase is isolated from the bacterium:

In a series LCR circuit an ac voltage source is connected. When inductor is removed from the circuit, the phase difference between the voltage and the current in the circuit is \( \frac{\pi}{3} \). If capacitor is removed from the circuit instead of inductor, the phase difference is again \( \frac{\pi}{3} \). What is the power factor of the circuit?