List of practice Questions

Let \( L \) be the line passing through the points \( i\hat{i} - 9\hat{k} \) and \( 7j\hat{k} \), and \( \pi \) be the plane passing through the point \( 6i + j \) and perpendicular to the vector \( i + j + k \). If \( \theta \) is the angle between \( L \) and \( \pi \), then \( \sin \theta = \):

If \( \vec{OA} = 2i - j + k \), \( \vec{OB} = -3i - k \), and \( \vec{OC} = -2i + 2j - 3k \), then a unit vector perpendicular to the plane containing \( A, B, C \) is:

Let \( \vec{b} = 3i - 2j + k \) and \( \vec{c} = i - j - k \) be two vectors. If \( \vec{a} \) is a vector such that \( \vec{a} + \vec{b} + \vec{c} = 0 \), then \( | \vec{a} \times \vec{b} + \vec{b} \times \vec{c} + \vec{c} \times \vec{a} | \) is:

If each of the observations \( x_1, x_2, \dots, x_n \) is increased or decreased by \( k \), where \( k \) is a positive number, then the variance of the data thus obtained:

Assertion (A): The function \( f(x) = \begin{cases} 1 - \cos x, & x<0 \\ \sin x, & x \geq 0 \end{cases} \) is continuous at \(x = 0\). Reason (R): \(\lim_{x \to 0} \sin x = 0\)

Match the following

List I (Method)	List II (Metal refined)
A) Zone refining	I) Sn
B) Liquation	II) In
C) Vapour phase refining	III) Zn
D) Distillation	IV) Zr
	V) Al

Match the following:

List – I
A. Broad spectrum
B. Typhoid
C. Bactericidal
D. Bacteriostatic

List – II
I. Amoxycillin
II. Vancomycin
III. Erythromycin
IV. Chloramphenicol
V. Ofloxacin

Match the following:

List I	List II
A. Broad spectrum	I. Amoxycillin
B. Typhoid	II. Vancomycin
C. Bactericidal	III. Erythromycin
D. Bacteriostatic	IV. Chloramphenicol
	V. Ofloxacin

The molar conductivity of 0.027 M methanoic acid is 40.42 S cm2 mol–1. The value of dissociation constant of this acid is (Given: \(\lambda^0_{H^+} = 349.6~\text{S cm}^2 \text{mol}^{-1},~\lambda^0_{HCOO^-} = 54.6~\text{S cm}^2 \text{mol}^{-1}\))

Identify the therapy where the client is taught to recognize the bodily process and the emotions that are being blocked out from awareness. It focuses on increasing the client's self-awareness and self-acceptance and is known as:

1-Chloro-4-nitrobenzene, 1-Chloro-2,4-dinitrobenzene and 1-Chloro-2,4,6-trinitrobenzene are transformed to corresponding phenols with the reagents X, Y, Z respectively. What are X, Y, Z?

Which is the correct order of the following alkyl halides for an SN2 reaction?