Let \(P, I\) and \(n\) be the principal of the loan, the total interest on the principal and number of months in the loan period respectively, then the EMI by Flat Rate Method is :

The function \(f(x)=2 x^3-3 x^2-12 x+4\) has:
(A) two points of local maxima.
(B) two points of local minima.
(C) one local maxima and one local minima.
(D) no local maxima or local minima.

Match List - I with List - II.

List - I	List - II
(A) The common region determined by all the constraints of LPP is called	(I) objective function
(B) Minimize \(z=c_1 x_1+c_2 x_2+\cdots+c_n x_n\) is	(II) convex set
(C) A solution that also satisfies the non-negative restrictions of a LPP is called	(III) feasible region
(D) The set of all feasible solutions of a LPP is a	(IV) feasible solution

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If \(f(x)=\left\{\begin{array}{ll}a x-1 & \text { if } x \geq 1 \\ 2 x+1 & \text { if } x<1\end{array}\right.\) is continuous at x = 1, then a equals

The probability distribution of number of heads in two tosses of a coin is:

If the lines \(\frac{1-x}{3}=\frac{3 y-6}{k}=\frac{3-z}{-2}\) and \(\frac{1-x}{2 k}=\frac{y-5}{3}=\frac{6-z}{5}\) are perpendicular, then \(k\) is equal to :

A coin is tossed 3 times. If \(X\) denotes the number of heads, then Match List I with List II

LIST I	LIST II
A. \(P(X=0)\)	I. \(\frac{1}{8}\)
B. \(P(X=1)\)	ㅍ. \(\frac{7}{8}\)
C. \(P(X \leq 2)\)	III. \(\frac{4}{8}\)
D. \(P(X \geq 2)\)	IV. \(\frac{3}{8}\)

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Match List-l with List-ll

List-l (Rate expression)	List-II (Overall order of reaction)
(A) \(r=k[A]^{0.2}[B]^{0.3}[C]\)	(I) \(\frac{3}{10}\)
(B) \(r=k[A]^{0.2}[B]^{-0.3}[C]\)	(II) 1
(C) \(r=k[A][B]^{0.8}[C]^{-1}\)	(III) \(3 / 2\)
(D)\(r=k[A]^{0.2}[B]^{0.3}[C]^{0.5}\)	(IV) \(9 / 10\)

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Select the correct statements from the following:
(A) Mn show the highest oxidation state in first transition series elements
(B) Titanium (II) is more stable than titanium (III) and titanium (IV).
(C) Scandium does not exhibit variable oxidation states.
(D) Zn form complexes with only (II) oxidation state.
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Based on their rate laws, arrange the following reactions in the decreasing sequence of the reaction order.
(A)Rate \(=k[A]^{3 / 2}[B]^{-1}\)
(B)Rate \(=k\left[ CHCl _3\right]\left[ Cl _2\right]^{1 / 2}\)
(C)Rate \(=k\left[ CH _3 COOC _2 H _5\right]\left[ H _2 O \right]^0\)
(D)Rate \(=k[A]^{1 / 2}[B]^{3 / 2}\)
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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.
Atomic number of \(\mathrm{V}, \mathrm{Mn}, \mathrm{Cu}\) and Zn is \(23,25,29\) and 30 respectively. Which of them shows a positive value for the standard electrode potential \(E^{\circ}\left(M^{2+} / M\right)\) ?

An unpolarised light of intensity \( I_0 \) passes through five identical polarisers arranged in such a manner that the transmission axis of each is set at an angle of 30° with respect to its predecessor. The ratio of the intensity of the final emerging light to that of the unpolarised light is

Arrange the following in order of increasing boiling points.
(A) Bromomethane
(B) Bromoform
(C) Chloromethane
(D) Dibromomethane
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