The system of equations:
\(x+y+z=5\)
\(x+2 y+3 z=9\)
\(x+3 y+\lambda z=\mu\) has a unique solution, if

Match List-l with List-ll

List-l	List-II
(A) \(\lim _{x \rightarrow 0} \frac{1-\cos 2 x}{x}\)	(I) \(\frac{5}{2}\)
(B) \(\lim _{x \rightarrow 0} \frac{\sin 2 x}{x}\)	(II) 5
(C) \(\lim _{x \rightarrow 1} \frac{x^5-1}{x^2-1}\)	(III) 2
(D) \(\lim _{x \rightarrow 0} \frac{(x+1)^5-1}{x}\)	(IV) 0

Choose the correct answer from the options given below:

The point which lies in the half plane \(2 x-y \geq 6\) is:

Match List I with List II

List - I	List - II
(A) \(|\vec{a} \times \hat{i}|^2+|\vec{a} \times \hat{j}|^2+|\vec{a} \times \hat{k}|^2\)=	(I) \(|\vec{a}|^2\)
(B) \(\frac{(\vec{a} \cdot \vec{b})^2+|\vec{a} \times \vec{b}|^2}{|\vec{b}|^2}=\)	(II) \(\sqrt{3}|\vec{a}|\)
(C) \(\vec{a}, \vec{b}\) and \(\vec{c}\) are three mutually perpendicular vectors of equal magnitude then \(|\vec{a}+\vec{b}+\vec{c}|=\)	(III) \(\frac{1}{2}|\vec{a} \times \vec{b}|\)
(D) Area of parallelogram with diagonals \(\vec{a}\) and \(\vec{b}\)	(IV) \(2|\vec{a}|^2\)

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Let box I contains 3 black and 4 white balls, box II contains 2 black and 2 white balls, box III contains 4 black and 3 white balls. A. box is selected at random and then a ball is randomly drawn from the selected box. If the color of the ball is black, then the probability that the ball is drawn from box III, is:

Match List-I with List-II

List-I	List-II
(A) The minimum value of \(f(x)=(2 x-1)^2+3\)	(I) 4
(B) The maximum value of \(f(x)=-|x+1|+4\)	(II) 10
(C) The minimum value of \(f(x)=\sin (2 x)+6\)	(III) 3
(D) The maximum value of \(f(x)=-(x-1)^2+10\)	(IV) 5

Choose the correct answer from the options given below:

If \(A=\left[\begin{array}{cc}3 & 2 a \\ 1 & 5\end{array}\right]\) and \(B=\left[\begin{array}{ll}2 & 3 \\ b & 5\end{array}\right]\) are singular matrices, then \(a+b\) is :

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.
Which one of the following techniques is used to amplify a specific DNA sequence?

Arrange the following electromagnetic waves in the order of their decreasing frequency.
(A) Radio wave
(B) Gamma rays
(C) Ultraviolet ray
(D) Infrared wave
(E) Visible light
Choose the correct answer from the options given below :

If a p-n junction is forward biased, then what is the direction of diffusion and drift current across the junction?

In hydrogen atom light corresponding to the transition \(n=4\) to \(n=2\) falls on cesium metal. The work function of the metal is 1.9 eV . What is the maximum kinetic energy of the photoelectrons emitted?

Match List-l with List-II

List-l (Complex)	List-II (Property)
(A) \(\left[ CoF _6\right]^{3-}\)	(I) \(d^5\), high spin
(B) \(\left[ Fe ( CN )_6\right]^{4-}\)	(II) \(d^6\), high spin
(C) \(\left[ FeF _6\right]^{3-}\)	(III) \(d^5\), low spin
(D) \(\left[ Mn ( CO )_6\right]^{2+}\)	(IV) \(d^6\), low spin

Choose the correct answer from the options given below :

The rate law for a reaction between substance P \& Q is given by
Rate = k[P]^x [Q]^y
If concentration of P is doubled and concentration of Q is halved, the ratio of the new rate to the earlier rate of reaction will be :