List of practice Questions

The variance of the following continuous frequency distribution is:

class intervalFrequency
0 -- 42
4 -- 83
8 -- 122
12 -- 161

 

P and Q are the extremities of a focal chord of the parabola \( y^2 = 4ax \). If \( P = (9,9) \) and \( Q = (p, q) \), then \( p - q \) is:
A, B, C are the vertices of a triangle ABC. If the bisector of \( \angle BAC \) intersects the side BC at D\((p,q,r)\), then \( \sqrt{2p+q+r} = ? \)
A plane \( (\pi) \) passing through the point \( (1,2,-3) \) is perpendicular to the planes \( x + y - z + 4 = 0 \) and \( 2x - y + z + 1 = 0 \). If the equation of the plane \( (\pi) \) is \( ax + by + cz + 1 = 0 \), then \( a^2 + b^2 + c^2 \) is equal to:
The vertical angle of a right circular cone is \( 60^\circ \). If water is being poured into the cone at the rate of \( \frac{1}{\sqrt{3}} \) m\(^3\)/min, then the rate (m/min) at which the radius of the water level is increasing when the height of the water level is 3m is:
Evaluate the integral: \[ I = \int_{\frac{-3\pi}{4}}^{\frac{\pi}{6}} \log(\sin(4x+3)) \,dx \]
Evaluate the integral: \[ \int_0^{16} \frac{\sqrt{x}}{1 + \sqrt{x}} dx. \]
Evaluate the integral: \[ I = \int_{0}^{32\pi} \sqrt{1 - \cos 4x} \,dx \]
Among the following four statements, the statement which is not true, for all \( n \in N \) is:
Bag \( P \) contains 3 white, 2 red, 5 blue balls and bag \( Q \) contains 2 white, 3 red, 5 blue balls. A ball is chosen at random from \( P \) and is placed in \( Q \). If a ball is chosen from bag \( Q \) at random, then the probability that it is a red ball is:
The mean of a binomial variate \( X \sim B(n, p) \) is 1. If \( n>2 \) and \( P(X = 2) = \frac{27}{128} \), then the variance of the distribution is:}
If the distance from a variable point \( P \) to the point \( (4,3) \) is equal to the perpendicular distance from \( P \) to the line \( x + 2y - 1 = 0 \), then the equation of the locus of the point \( P \) is:
If \( \beta \) is the angle made by the perpendicular drawn from origin to the line \( L = x + y - 2 = 0 \) with the positive X-axis in the anticlockwise direction. If \( a \) is the X-intercept of the line \( L = 0 \) and \( p \) is the perpendicular distance from the origin to the line \( L = 0 \), then \( \tan \beta + p^2 = \):
If \( (l, k) \) is a point on the circle passing through the points \( (-1, 1) \), \( (0, -1) \), and \( (1, 0) \), and if \( k \neq 0 \), then find \( k \).
Among the following, the incorrect statement about chloramphenicol is:
An alcohol X (C\(_5\)H\(_{12}\)O) when reacted with conc. HCl and anhydrous ZnCl\(_2\), produces turbidity instantly. The alcohol X can be prepared from which of the following reactions?
The reagents/ chemicals X and Y that convert cyanobenzene to Schiff's base are
The correct statements of the following are: A) Aniline forms a stable benzene diazonium chloride at 285K.
B) N - Phenylethanamide is less reactive towards nitration than aniline.
C) p - CH\(_3\)C\(_6\)H\(_4\)COCl is Hinsberg reagent.
Which of the following when subjected to thermal decomposition will liberate dinitrogen? (i) sodium nitrate (ii) ammonium dichromate (iii) barium azide
Observe the following reaction. This reaction represents: \[ 4HCl + O_2 \xrightarrow{CuCl_2, 723K} 2Cl_2 + 2H_2O \]
Identify the set which is not correctly matched in the following:
Identify the correct statements from the following: (i) Ti (IV) is more stable than Ti (III) and Ti (II)
(ii) Among 3d-series elements (from Z = 22 to 29) only copper has positive reduction potential (\( M^{2+}/M \)) (iii) Both Sc and Zn exhibit +1 oxidation state
The molecular formula of a coordinate complex is CoH\(_{12}\)O\(_6\)Cl\(_3\). When one mole of this aqueous solution of complex is reacted with excess of aqueous AgNO\(_3\) solution, three moles of AgCl were formed. What is the correct formula of the complex?
The molecular formula of a compound is \( AB_2O_4 \). Atoms of O form a ccp lattice. Atoms of A (cation) occupy \( \frac{1}{8} \) of tetrahedral voids. Atoms of B (cation) occupy a fraction of octahedral voids. What is the fraction of vacant octahedral voids?
Distilled water boils at 373.15 K and freezes at 273.15 K. A solution of glucose in distilled water boils at 373.202 K. What is the freezing point (in K) of the same solution? (For water, \( K_b = 0.52 \) kg mol\(^{-1}\), \( K_f = 1.86 \) kg mol\(^{-1}\))