A cell of emf 1.1 V and internal resistance \(0.5 \Omega\) is connected to a \(0.5 \Omega\) wire. Another cell of same emf is added in series, but current remains unchanged. The second cell's internal resistance is :

The relation R in R (set of real numbers) is defined by \(R=\left\{(a, b): a \leq b^3\right\}\), then \(R\) is

The minimum value of \(\left|\begin{array}{ccc}2 & 2 & 2 \\ 2 & 2+x & 2 \\ 2 & 2 & 2+x\end{array}\right|, x \in R\) is

The maximum value of \(\sin x+\cos x, x \in R\) is:

The differential equation that represents the family of lines parallel to x + y = 2 is:

If \(\vec{a}, \vec{b}, \vec{c}\) are unit vectors such that \(\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}\), then the value of \(\vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a}\) is:

The number of square matrices of order 2 using numbers 1 and -1 exactly once and the number 0 twice is :

Match List - I with List - II

List - I (Complex)	List - II (Hybridisation)
(A) \([CoF_6]^{3-}\)	(I) \(sp^3\)
(B) \([Co(NH_3)_6]^{3+}\)	(II) \(dsp^2\)
(C) \([NiCl_4]^{2-}\)	(III) \(d^2sp^3\)
(D) \([Ni(CN)_4]^{2-}\)	(IV) \(sp^3d^2\)

Choose the correct answer from the options given below :

The value of \(\tan ^2\left(\sec ^{-1} 2\right)\) is:

Read the passage carefully and answer the questions
Carboxylic acids are the organic compounds which comprise of carboxyl functional group, -COOH. These are generally found in nature, some higher members are known as fatty acids as they occur in natural fats as esters of glycerol. They can be prepared from oxidation of alcohols and aldehydes, hydrolysis of nitriles and amides and Grignard reagents. They are stronger acids than simple phenols and alcohols. but weaker than mineral acids. Substituents affect the acidity of aliphatic and aromatic carboxylic acids. They undergo reactions involving cleavage of -OH and C-OH bond. Carboxylic acids having an alpha hydrogen get halogenated in the presence of red phosphorus to form alpha halo carboxylic acids. The reaction is known as Hell Volhard Zelinsky reaction. Besides these aromatic carboxylic acids undergo electrophilic substitution reactions. They are versatile and are employed in the manufacture of various useful compounds. For example, methanoic acid is used in rubber, textile, dyeing, leather and electroplating industries. Higher fatty acids are used in the manufacture of soaps and detergents. Esters of Benzoic acid are used in perfumery.
Identify the strongest acid

Following are the wavelength of some constituents of the electromagnetic spectrum. The wavelength range that are used in Radar system for Aircraft navigation is :
(A) 1 mm to 700 nm
(B) 0.1 m to 1 mm
(C) 400 nm to 1 nm
(D) < \(10^{-3} nm\)
(E) > 1 m
Choose the correct answer from the options given below :

A and B throw a die alternatively till one of them gets a number more than 4 and wins the game. Then the probability of winning the game by B , if A starts first :

In Young's double slit experiment, slits are illuminated by light of wavelength 650 nm. The slits are 0.13 cm apart and the screen is placed 1.2 m away. What will be the separation of the adjacent maxima?