If \(y=a x^2+b x\) has minima at \(x=2\) and the minimum value is -12 , then which of the following are correct?
(A) \(a=3\)
(B) \(a=-3\)
(C) \(b=12\)
(D) \(b=-12\)
Choose the correct answer from the options given below :

The solution of \(\frac{7 x+12}{x-9}<4, x \neq 9\) is:

Given \(\sum p_0 q_0=800, \sum p_0 q_1=1500, \sum p_1 q_1=1300\) and \(\sum p_1 q_0=900\), where subscripts 0 and 1 are used for base year and current year respectively. The Paasche's

Match List-1 with List-2

List-1	List-2
(A) A fire in a factory causing production delay for some time is	(I) Secular trend
(B) Technological progress is	(II) Seasonal trend
(C) The rise in prices before big festival is example of	(III) Irregular trend
(D) Rise and fall of share market is	(IV) Cyclic trend

Choose the Correct answer from the options given below :-

If \(\left|\begin{array}{ccc}1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c\end{array}\right|\), where \(a, b\) and \(c\) are non zero constants, then the value of \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\) is

The area (in sq. units) bounded by the parabola \(y^2=16 x\) and its latus rectum is

A coin is biased so that the head is three times as likely to occur as tail. If the coin is tossed twice, the mean of the number of tails is:

\(n _1\) identical capacitors, each of capacitance \(C _1\), are connected in series and charged by a source of potential difference \(3 V . n _2\) identical capacitors, each of capacitance \(C_2\), are connected in parallel and charged by a source of potential difference 2 V . Total energy stored in both the combinations is the same. What is the value of capacitance \(C _2\) in terms of \(C _{ 1 }\) ?

9 cells each of emf e = 3 V and internal resistance r = 1 \( \Omega \) are connected in m = 3 rows, each having n = 3 cells in series. The current flowing in the external resistance of R = 5 \( \Omega \) connected across this arrangement of the cells is

Let \(A=\{1,2,3\}\). Then, the number of relations containing \((1,2)\) and \((1,3)\), which are reflexive and symmetric but not transitive, is:

A measurable characteristic of a population is called:

Identify the correct statement for Zygote Intra-Fallopian Transfer (ZIFT).

p-block elements are placed in groups 13 to 18 of the periodic table. Group 15 is nitrogen family.
Nitrogen makes various compounds like \(NH _3, HNO _3, N_2 O , NO _2\) etc. Phosphorus exists in the form of white and red phosphorus. White phosphorus glows in dark. \(PH _3\) gas is used as smoke screen. Group 16 is called oxygen family. Dry air contains \(21% O_2\) gas by volume. Combined sulphur exists as sulphates such as gypsum, epsome salt, baryte etc. The allotropic forms of sulphur are Rhombic and monoclinic sulphur. \(S_2\) is paramagnetic like \(O_2\) and it stable at high temperature. Group 17 is Halogen family. \(F _2\) is highly reactive, \(Cl _2\) is greenish yellow gas. Both \(SO _2\) and \(Cl _2\) are used for bleaching. Group 18 is Noble gas family but some noble gases also form compounds.
Complete hydrolysis of \(XeF _6\) gives HF and \(XeO _3\) as main products. The permanent bleaching effect is caused by :