The greatest integer function defined by \(f(x)=[2 x], 0 < x < 2\)

If \(e^y(x+1)=1\), then

The vector equation of the line passing through the point \((-1,5,4)\) and perpendicular to the plane \(z=0\) is :

Which of the following are correct?
(A) If \(A\) and \(B\) are symmetric matrices such that \(A B=B A\), then \(A B\) is symmetric.
(B) If \(A\) and \(B\) are symmetric matrices of the same order, then \((A+B)\) is a symmetric matrix.
(C) If \(A\) and \(B\) are symmetric matrices of the same order, then \((A B-B A)\) is a symmetric matrix.
(D) If \(A\) and \(B\) are symmetric matrices of the same order, then \((A B+B A)\) is a skew-symmetric matrix.
Choose the correct answer from the options given below :

The inverse of the matrix \(A=\left[\begin{array}{ccc}\frac{1}{2} & 0 & 0 \\ 0 & \frac{1}{4} & 0 \\ 0 & 0 & \frac{1}{8}\end{array}\right]\) is

Let \(A=\left[a_{i j}\right]_{n \times n}\) and \(B=\left[b_{i j}\right]_{n \times n}\).
Then which of the following is/are true?
(A) \(A B=B A\)
(B) \((A B)^{-1}=B^{-1} A^{-1}\)
(C) \((A B)^T=B^T A^T\)
(D) \(A B=0 \Rightarrow A=0\) or \(B=0\)
Choose the correct answer from the options given below :

The interval in which \(y=x^2 e^{-x}\) is strictly increasing is:

The 'hilum' represents the junction between:

When sodium chromate is acidified with sulfuric acid and
then further treated with potassium chloride, we obtain...

Which one of the followings represent a correct form of mature angiosperm embryo sac?

Out of following plants, which one is not browsed by cattle :

Identify the equations of lines through origin which intersect the line \(\frac{x-3}{2}=\frac{y-3}{2}=\frac{z}{1}\) at an angle \(\frac{\pi}{3}\).
(A) \(\frac{x}{1}=\frac{y}{2}=\frac{z}{-1}\)
(B) \(\frac{x}{1}=\frac{y}{-2}=\frac{z}{1}\)
(C) \(\frac{x}{-1}=\frac{y}{-1}=\frac{z}{-2}\)
(D) \(\frac{x}{-1}=\frac{y}{1}=\frac{z}{-2}\)
Choose the correct answer from the options given below:

Read the passage carefully and answer the questions
The carbonyl group of aldehydes and ketones is highly polar. The positively charged carbon is readily attacked by electron-rich nucleophile and the negatively charged oxygen atom is attacked by an electro-deficient electrophile. Aldehydes and ketones undergo nucleophilic addition reactions in the presence of acid or a base. The mechanism involves attack of a nucleophile on the electron deficient carbonyl carbon to form a tetrahedral intermediate. A new bond is formed between the carbon and oxygen. Protonation of the anion furnished by the reaction medium yields a neutral addition product. The addition product is same whether the reaction is catalyzed by acid or a base. For example in the presence of base aldehydes and ketones react with hydrogen cyanide to form cyanohydrin.
The source of nucleophile in the base catalyzed cyanohydrin formation is: