If \(\vec{a}+\lambda \vec{b}\) is perpendicular to \(\vec{c}\), where
\(\vec{a}=-\hat{i}+2 \hat{j}+\hat{k}, \vec{b}=3 \hat{i}+2 \hat{j}+\hat{k}\), and \(\vec{c}=\hat{i}-\hat{j}\),
then :

The area bounded by \(y=3 x+1, x=0, y=0\) and \(x=a\) is 8 Sq.units. Then value of \(a\) (where \(a>0\) ) is

Let \(\vec{a}=\hat{i}+\hat{j}, \vec{b}=\hat{i}-\hat{j}\) and \(\vec{c}=\hat{i}+\hat{j}+\hat{k}\). If \(\hat{m}\) is a unit vector perpendicular to both \(\vec{a}\) and \(\vec{b}\), then \(|\vec{c} \cdot \hat{m}|\) is equal to :

If \(A\) and \(B\) are invertible matrices then which of the following statement is NOT correct?

A box contains 10 balls, each marked with one of the digits 0 to 9 .
If four balls are drawn successively with replacement from the box,
then the probability that none is marked with the digit \(0\) is :

If \(A=\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right]\), then the value of \((A+I)^3-4 A\) is:

If \(A=\left[\begin{array}{cc}x+4 & 2 \\ 3 & 1\end{array}\right] B =\left[\begin{array}{cc}x & 2 x-1 \\ 2 & 5\end{array}\right]\) and \(|A B|=12\), then the value(s) of \(x\) is/are :

Direction ratios of the line perpendicular to the lines \(\frac{x+2}{1}=\frac{y+3}{2}=\frac{z-5}{-2}\) and \(\frac{x-3}{2}=\frac{y+7}{-3}=\frac{z-2}{1}\) are:

Which among the following metals shows 6 secondary valencies ?
(A) 1 mole of \(PdCl _2 \cdot 4 NH _3\) reacts with excess of \(AgNO _3\) to give 2 moles of AgCl precipitated
(B) 1 mole of \(NiCl _2 \cdot 6 H _2 O\) reacts with excess of \(AgNO _3\) to give 2 moles of AgCl precipitated
(C) 1 mole of \(PtCl _4 \cdot 2 HCl\) does not give reaction with \(AgNO _3\)
(D) 1 mole of \(CoCl _3 \cdot 4 NH _3\) reacts with excess of \(AgNO _3\) to give 1 mole of AgCl precipitated
(E) 1 mole of \(PtCl _2 \cdot 2 NH _3\) does not give reaction with \(AgNO _3\)
Choose the correct answer from the options given below :

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Read the passage carefully and answer the Questions
Haloalkanes undergo nucelophilic substitution reactions owing to the polarity of C X bond. The nucleophile reacts with the haloalkane on the carbon possessing a partial positive charge holding the halogen atom. The halogen atom \(X\) is replaced by a nucleophile. Depending on the kinetics and mode of bond breaking, the mechanism can be either SN1 or SN2 reaction. The rate of SN1 reaction is governed by the stability of carbocation and in SN2 reaction, the rate of reaction is governed by steric factor. Chirality is the main factor in both SN1and SN2. In SN1 reaction, the chirality of alkyl halide is accompanied by racemization of the product, while in SN2 reaction, the product is characterized by inversion of configuration. The structure of alkyl halide and the nature of the solvent also governs the mechanism of the substitution.
What is chiral carbon ?

Which of the following is an example of vic-dihalide?

The output voltage of an ideal transformer connected to 240 V a.c. mains is 24 V. When this transformer is used to light a bulb with ratings 24 V, 24 W, the primary current would be-