If \(P\left[\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6\end{array}\right]=\left[\begin{array}{ccc}-7 & -8 & -9 \\ 2 & 4 & 6\end{array}\right]\), then matrix \(P\) is equal to :

An automobile dealer wishes to buy four luxury cars of different brands with some down payment and balance in equal monthly instalments for 10 years
The bank charges \(9 \%\) interest per annum compounded monthly
Given \(\frac{0.0075(1.0075)^{120}}{(1.0075)^{120}-1}=0.01266\)

Luxury Car	Price of the Car (in Rs.)	Down payment (in Rs.)
P	25,00,000	5,00,000
Q	35,00,000	12,00,000
R	45,00,000	15,00,000
S	42,00,000	15,00,000

Match List I with List II

List-I (Luxury Car)	List-II (EMI (in Rs.))
(A) P	(i) 34,182
(B) Q	(ii) 37,980
(C) R	(iii) 29,118
(D) S	(iv) 25,320

Choose the correct answer from the options given below :

If X, Y, Z, W \& P are matrices of order 2 × n, 3 × k, 2 × p, n × 3 and p × k respectively. The restrictions on n,k \& p so that PY + WY be defined are:

Which of the following terms are associated with a linear programming problem?
(A) Constraints
(B) Independent events
(C) Feasible region
(D) Objective function
Choose the correct answer from the options given below :

Match List I with List II

LIST I	LIST II
A. \(\lim _{x \rightarrow 0} \frac{1-\cos 2 x}{3 x^2}\)	I. 2
B. \(\lim _{x \rightarrow 4} \frac{x^2-16}{x-4}\)	II. 8
C. \(\lim _{x \rightarrow 0} \frac{\sin a x+4 x}{a x+\sin 4 x}\)	III. 1
D. \(\lim _{z \rightarrow 1} \frac{z^{1 / 3}-1}{z^{1 / 6}-1}\)	IV. \(\frac{2}{3}\)

In a linear programming problem, the linear constraints are as follows :
\(x-3 y \geq 0, y \geq 0,0 \leq x \leq 6 \)
where \(z=x+2 y\)
Which of the following statement/s is/are correct ?
(A) The feasible region is not the first quadrant
(B) The feasible region is unbounded in the first quadrant
(C) The feasible region is bounded in the first quadrant
(D) The feasible region is a triangular region
(E) The maximum value of \(z\) is 10
Choose the correct answer from the options given below :

The edge of a cube is increasing at a rate of 7 cm/s. The rate of change of area of the cube when its side is 3 cm is:

A function \(f: R \rightarrow\{x \in R:-1< x<1\}\) is defined as \(f(x)=\frac{x}{1+|x|}\), then \(f\) is :

Read the passage carefully and answer the questions
Nearly all the transition elements display typical metallic properties such as high tensile strength, ductility, malleability, high thermal and electrical conductivity and metallic lustre. The transition metals (with the exception of Zn, Cd and Hg) are very hard and have low volatility. Their melting and boiling points are high. They have high enthalpies of atomization. lons of the same charge in a given series show progressive decrease in radius with increasing atomic number. However, the variation within a series is quite small. The filling of 4f before 5d orbital results in a regular decrease in atomic radii called Lanthanoid contraction which essentially compensates for the expected increase in atomic size with increasing atomic number. The net result of the lanthanoid contraction is that the second and the third d series exhibit similar radii (e.g., Zr 160 pm, Hf 159 pm) and have very similar physical and chemical properties. There is an increase in ionisation enthalpy along each series of the transition elements from left to right. The first ionisation enthalpy, in general, increases, but the magnitude of the increase in the second and third ionisation enthalpies for the successive elements, is much higher along a series. One of the notable features of a transition elements is the great variety of oxidation states these may show in their compounds.
Among \(\mathrm{Cr}(\mathrm{Z}=24), \mathrm{Co}(\mathrm{Z}=27), \mathrm{Mn}(\mathrm{Z}=25)\) and \(\mathrm{Fe}(\mathrm{Z}=26)\); which will show the maximum variety of oxidation states?

Which is not an application of Total Internal Reflection:

A thermal power plant produces electric power of 1000 kW at 10000 V, which is to be transmitted 20 km away from the power plant. The transmission line has resistance of 0.5 ohm per kilometre, the percentage power dissipation during transmission is :

A plane electromagnetic wave of frequency 75 Hz travels in free space along the X -direction. At a particular point in space and time \(\vec{E}=9.6 \hat{j}\). What is \(\vec{B}\) at that point ?
( \(E=\) Electric field, \(B=\) Magnetic field)

The order and degree of the differential equation \(\left(1+3 \frac{d y}{d x}\right)^{\frac{2}{3}}=4 \frac{d^3 y}{d x^3}\) respectively are: