The number of arbitrary constants in general solution of a differential equation of third order is :

Silicon can be doped to get an n-type semiconductor by using :
(A) Arsenic (As)
(B) Phosphorus (P)
(C) Boron (B)
(D) Antimony (Sb)

Pipe A can independently empty a half-filled tank in 3 hours whereas pipe B can alone fill the same tank in 4 hours, when the tank is completely empty. In how much time.

\(\int \frac{d x}{\sqrt{5-x}}=\) (where \(C\) is arbitrary constant.)

If the difference of two unit vectors is again a unit vector, then the angle between them is ______________

A T.V. panel costing Rs 18000 has a useful life of 12 years. If the annual depreciation is Rs 1000, then its scrap value by linear method is :

The product of the order and degree of the following differential equation :
\(x \left( \frac{d^2y}{dx^2} \right)^2 + \left( \frac{dy}{dx} \right)^3 + y^2 = 0\)

Considering the following statements; identify the correct statements:
(A) Scandium is regarded as a transition element, but zinc is not.
(B) \(V _2 O _3\) is amphoteric and \(V _2 O _5\) is basic oxide.
(C) The similar radii of Zr and Hf is a consequence of the lanthanoid contraction.
(D) The oxidation state of chromium in chromate and dichromate ion is same.
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Read the passage carefully and answer the Questions
The term vitamin was coined from the word vital +amine since the earlier identified compounds had amino groups. Later work showed that most of them didn't contain amino groups. They are very essential for the body. They has to be taken various diet or in the form of medicines also.
Vitamins are classified into two groups depending upon their solubility in water or fat.
Fat soluble vitamins are soluble in fat and oils but insoluble in water. They are stored in liver and adipose (fat storing) tissues Water-soluble vitamins are soluble in water. These must be supplied regularly in diet because they are readily excreated in urine and cannot be stored in our body.
Deficiency of Scurvy disease leads to

Let A and B be two events. Then which of the following statements are TRUE?
(A) \(P(B \mid A)=\frac{P(A \cap B)}{P(A)}\), provided \(P(A) \neq 0\)
(B) \(P\left(B^{\prime}\right)=1+P(B)\)
(C) \(P(A \cup B)=P(A)+P(B)+P(A \cap B)\)
(D) \(P(A \cap B)=P(A) \cdot P(B)\) if A and B are independent events
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Match List-I with List-II

List-I	List-II
(A) Electric Field	(I) [ LTA ]
(B) Electric Flux	(II) \( [ L^2 ] \)
(C) Electric Dipole Moment	(III) \( [ M L T^{-3} A^{-1} ] \)
(D) Area Vector Element	(IV) \( [ M L^3 T^{-3} A^{-1} ] \)

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During electrolysis of acidified water, 2.8 Litre of oxygen gas is released (at STP). The charge passed through the anode is -

consider the linear programming problem: Maximise \(z=3 x+y\) subject to the constraints \(x+y \leq 6, x \geq 0, y \geq 0\). Which of the following statements are true?
(A) \(x \geq 0, y \geq 0\) are non-negative restrictions.
(B) The point \((1,1)\) does not lie in the half plane \(x+y \leq 6\).
(C) There are 2 corner points of the feasible region of given LPP.
(D) Maximum value of \(z\) is 18.
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