Ten bulbs are drawn successively with replacement from a lot containing \(10 \%\) defective bulbs. The probability that there is at least one defective bulb is :

If \(e^x+e^y=e^{x+y}\), then \(\frac{d y}{d x}=\)

\(\int e^x\left(\frac{1-x}{1+x^2}\right)^2\) \(dx\) is equal to

If the points \(( a 1, b 1),( a 2, b 2)\) and \(( a 1+ a 2, b 1+ b 2)\) are collinear, then

If A is a square matrix of order 3 and \(A ^{\prime}\) is the transpose of A such that \(\left|A^{\prime}\right|=-5\), then \(\left|A A^{\prime}\right|=\)

The value of \(k\) for which the lines \(\frac{2 x-3}{4}=\frac{3-y}{k}=\frac{z-2}{-2}\) and \(\frac{x-2}{1}=\frac{y}{4}=\frac{5-z}{3}\) are perpendicular to each other is :

In reference to the Inferential Statistics, which of the following is NOT correct?

Match List-l with List-ll

List-l	List-II
(A) \(\lim _{x \rightarrow 0} \frac{1-\cos 2 x}{x}\)	(I) \(\frac{5}{2}\)
(B) \(\lim _{x \rightarrow 0} \frac{\sin 2 x}{x}\)	(II) 5
(C) \(\lim _{x \rightarrow 1} \frac{x^5-1}{x^2-1}\)	(III) 2
(D) \(\lim _{x \rightarrow 0} \frac{(x+1)^5-1}{x}\)	(IV) 0

Choose the correct answer from the options given below:

If in a pond there were 20 lotus plants last year and through reproduction 8 new plants are added, taking the current population to 28, the birth rate would be:

Werner was the first to describe the bonding features in coordination compounds. But his theory could not answer basic questions like :
(i) Why only certain elements possess the remarkable property of forming coordination compounds ?
(ii) Why the bonds in coordination compounds have directional properties ?
(iii) Why coordination compounds have characteristics magnetic and optical properties ?
Many approaches have been put forth to explain the nature of bonding in coordination compounds viz. Valence Bond Theory (VBT), Crystal Field Theory (CFT), Ligand Field Theory (LFT) and Molecular Orbital Theory (MOT).
We shall focus our attention on elementary treatment of the application of VBT and CFT to coordination compounds.
According to this theory, the metal atom or ion under the influence of ligands can use its ( \(n -1\) )d, ns np or ns, np, nd orbitals for hybridisation to yield a set of equivalent orbitals of definite geometry such as octahedral, tetrahedral, square planar and so on.
These hybridised orbitals are allowed to overlap with ligand orbitals that can donate electron pairs for bonding.
The formula which correctly represents Potassium tetra hydroxo zincate (II) is :

Match List - I with List - II.

List - I	List - II
(A) RNA	(I) Adenosine
(B) Nucleoside	(II) Adenosine monophosphate
(C) Nucleotide	(III) Deoxyribose
(D) Sugar	(IV) Uracil

Choose the correct answer from the options given below:

Read the passage carefully and answer the Questions
Aldehydes, carboxylic acids and ketones are widespread in the animal and plant kingdoms.
They play a pivotal role in various biochemical processes of life. Their presence in nature adds fragrance and flavor. These compounds are widely used in food products, pharmaceuticals, paints, resins and other important product industries. These compounds are prepared by various laboratory methods, which mainly include oxidation, formylation, acylation and reduction. Due to the polar nature of the carbonyl group in aldehydes and ketones, they can exhibit different reactions like nucleophilic addition. They do exhibit redox and various condensation reactions which lead to the formation of various important compounds. On the other hand, the carboxylic acids are mainly prepared by oxidation and hydrolysis of different compounds. The carboxylic acid consists of a carbonyl group and the hydroxy group (attached to the carbonyl carbon atom). This makes it possible for the carboxylic acid to participate in various chemical reactions which involve cleavage of the C-OH bond and the O_H bond along with the reactions involving the complete -COOH group.
The products formed when 2,2-Dimethylpropan-1-al is heated with concentrated KOH are :

Which of the following is not the use of a shunt?