Which of the following statements is/are correct?
(A) \(|x|\) is continuous everywhere in its domain.
\((B)|x|\) is differentiable everywhere in its domain.
(C) \([x]\) is continuous at every integral point.
\((D)[x]\) is discontinuous at every integral point.
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Kavya takes a personal loan of ₹ 10,00,000 at the rate of 12% per annum for 5 years, then the EMI by using flat rate method is:

For \(x \in R\), if \(f(x)=-(x-1)^2+2\), then
(A) f is an increasing function on \((-\infty, 1)\)
(B) ƒ has no critical points
(C) ƒ has a maximum value at x = 1
(D) ƒ has a minimum value at x = 1
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The inverse of the matrix \(\left[\begin{array}{lll}4 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 6\end{array}\right]\) is

The value of \(\int_0^3|2 x-6| d x\) is :

The window of the house is in the form of a rectangle surmounted by a semi-circular portion, having a perimeter of 10 m as shown in figure.

If \(x\) and \(y\) represent the length and breadth of rectangular region, then the area A of the window in terms of \(x\) is :

A box contains 2 black and 4 red balls and another box contains 4 black and 3 red balls. If a ball is drawn at random from one of the two boxes, then the probability of getting a black ball is

The unit vector in the direction of sum of vectors \(\vec{a}=2 \hat{i}-\hat{j}+\hat{k}\) and \(\vec{b}=2 \hat{j}+\hat{k}\) is:

The \(\Lambda_m^{\circ}\) for \(CaSO _4\) at 298 K , if \(\lambda_{ Ca ^{+2}}^{\circ}=119.0 Scm ^2 mol^{-1}\) and \(\lambda_{ SO _4^{2-}}^{\circ}=160.0 Scm ^2 mol^{-1}\) will be:

In a radioactive decay, neither the atomic number nor the mass number changes. Which of the following is emitted in the decay?

The solids that are electrical conductors, malleable and ductile are:

The magnification (m) and focal length (f) of a plane mirror are:

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.
Arrange the following in the increasing order of their pK_a values:
(A) CF₃-COOH
(B) O₂N-CH₂-COOH
(C) NC-CH₂-COOH
(D) H-COOH
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