If we reject the null hypothesis when it is true, we might be making

Which of the following is true?

Consider the linear programming problem (LPP):
Minimize \(Z=x+y\)
subject to
\(x+2 y \leq 4,\)
\(3 x+y \geq 3\),
\(4 x+3 y \geq 6\),
\(x, y \geq 0\).
Which of the following is correct for the above linear programming problem (LPP):
(A) The LPP has a bounded feasible region.
(B) The LPP has a unique optimal solution.
(C) The optimal value of the LPP exists at the point (3/2,0)
(D) The corner points of the feasible region are \((3 / 2,0),(3 / 5,6 / 5),(2 / 5,6 / 5)\) and \((4,0)\)
Choose the correct answer from the options given below:

The number of all possible matrices of order 2 × 2 with each entry 0, 1 or 2 are:

Match List I with List II

LIST I	LIST II
A. \(\lim_{x \to 0} \frac{(1 - \cos 2x) \sin 5x}{x^2 \sin 3x}\)	I. 18
B. \(\lim_{x \to \infty} \frac{(3x-5)(2x-7)}{(4x-9)(5x-3)}\)	II. \(\frac{10}{3}\)
C. \(\lim_{x \to 0} \frac{2 \sin^2 3x}{x^2}\)	III. \(\frac{3}{4}\)
D. \(\lim_{x \to \frac{\pi}{4}} \frac{1 - \cos^3 x}{2 \cot x - \cot^3 x}\)	IV. \(\frac{3}{10}\)

Choose the correct answer from the options given below:

General solution of \(\frac{dy}{dx} + \frac{\sqrt{1-y^2}}{\sqrt{1-x^2}} = 0\) is:

Which of the following matrices is symmetric as well as skew-symmetric?

Read the passage carefully and answer:
Organic compounds derived from NH3 by replacing one or more H-atoms with alkyl or aryl groups will form primary, secondary and tertiary amines. The common methods which include their preparations are reduction of nitro group, amide group and nitrile group, Gabriel phthalimide synthesis and ammonolysis of alkyl halides. Amines are basic in nature due to the presence of a lone pair of electrons on the nitrogen atom. Important chemical properties of amines include acylation, alkylation and their interaction with nitrous acid. There are various tests which can distinguish different types of amines from each other, for e.g. carbylamine test, Hinsberg's test, coupling reaction etc. Another important class of compounds which can be derived from primary amines is azo compounds. These compounds are intensely colored and widely used as dyes in textile, leather and food industries.
Conversion of nitro group into primary amine is preferred using

Which among the following is the strongest base in aqueous solution?

A battery of emf 3 V and internal resistance r is connected in series with a resistor of \( 55 \text{ } \Omega \). An ammeter of resistance \( 2 \text{ } \Omega \) connected in circuit reads 50 mA. The value of r is

If \(A=\left[\begin{array}{ccc}1 & -2 & 3 \\ -4 & 2 & 4\end{array}\right]\) and \(B=\left[\begin{array}{cc}1 & -2 \\ 3 & -4 \\ 2 & 4\end{array}\right]\) then product \(A B\) is :

Which of the following statements are correct for a transistor action ?
(A) The input resistance depends upon the current \( I_e \) in the transistor
(B) Collector currents is equal to the sum of base current and emitter current
(C) The emitter junction is forward biased
(D) The collector junction is reverse biased
(E) Both the emitter junction as well as the collector junction are forward biased
Choose the correct answer from the options given below :

In Young's double slit experiment, the ratio of slit widths is 4 : 1. The intensity ratio in the interference pattern would be :