If \(|\vec{a}|=a\), then the value of \(|\vec{a} \times \hat{i}|^2+|\vec{a} \times \hat{j}|^2+|\vec{a} \times \hat{k}|^2\) is :

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

Applied Mathematics
Which of the following are NOT correct about "Sinking Fund"?
(A) It does not have any specific purpose.
(B) It can be used in any emergency.
(C) Any amount, any time can be deposited in it.
(D) It is set up for a particular upcoming expense.
Choose the correct answer from the options given below:

If the probability that an individual suffers a bad reaction from an injection of a given serum is 0.001, the probability that out of 2000 individuals, more than two individuals suffer from bad reaction.
[Given that \(e^{-2}=0.13534\) ]

If CAGR stands for Compound Annual Growth Rate, F.V stands for final value of an investment, P.V stands for present value of an investment and \(n\) is the number of years then

If \(e^y=\log x\), then which of the following is true?

If \(\theta\) is an acute angle and the vector \(\vec{a}=(\sin \theta) \hat{i}+(\cos \theta) \hat{j}\) is perpendicular to the vector \(\vec{b}=\hat{i}-\sqrt{3} \hat{j}\) then \(\theta\) is equal to:

Which of the following reaction will not produce ketones?

Read the passage carefully and answer the given questions.
Recombinant DNA Technology
Asexual reproduction preserves the genetic information, while sexual reproduction permits variation. Traditional hybridization procedures used in plants and animals breeding very often lead to inclusion and multiplication of undesirable genes along with the desired genes. The techniques of genetic engineering, which include creation of recombinant DNA, use of gene cloning and gene transfer, overcome this limitation and allow us to isolate and introduce only one or a set of desirable genes without introducing genes into the target organism.
In Recombinant DNA Technology, what is the role of the "selectable marker gene"?

A hot wire voltmeter measures the voltages across the inductor, the capacitor and the resistor as 150 V, 100 V and 50 V across a series, LCR circuit. If resistance is \( 100 \, \Omega \), the current in the circuit is :

A sum of ₹ 60,000 invested at \(r \%\) compounded quarterly will provide payments at ₹ 600 each at the end of every three months. Then the value of \(r\) is :

For an astronomical telescope with 10 m focal length objective and 10 cm eyepiece, tube length and magnification are :

Answer the question on basis of passage given below:
Transition metals form a large number of complexes or coordination compounds in which the metal atoms are bound to a number of anions or neutral molecules. The valence bond theory explain the formation, magnetic behaviour and geometrical shapes while the crystal field theory explains the effect of different crystal fields on the degeneracy of d-orbitals energies of the central metal atom/ion. This provides for the quantitative estimation of orbital separation energies, magnetic moments and spectral and stability parameters.