Recent questions tagged 2008

Which one of the following constitutes a group of the isoelectronic species?

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Four species are listed below: i. $HCO_3^{-}$ ii. $H_3O^+$ iii. $HSO_4^{-}$ iv. $HSO_3F$ Which one of the following is the correct sequence of their acid strength?

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Standard entropy of $X_2, Y_2$ and $XY_3$ are 60, 40 and 50 $JK^{-1}mol^{-1}$, respectively. For the reaction,$\frac{1}{2}X_2+\frac{3}{2}Y_2\rightarrow XY_3,\Delta H=-30KJ$, to be at equilibrium, the temperature will be

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$\alpha$-D-(+)-glucose and $\beta$-D-(+)-glucose are

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The electrophile, $E^\oplus$ attacks the benzene ring to generate the intermediate $\sigma$-complex. Of the following, which $\sigma$-complex is of lowest energy?

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The absolute configuration of

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For the following three reactions a, b and c, equilibrium constants are given a. $CO(g)+ H_2O(g) =CO_2 (g) + H_2 (g); K_1$ b . $CH_4 (g) + H_2O(g) =CO(g) + 3H_2 (g); K_2$ c. $CH_4 (g) + 2H_2O(g) = CO_2 (g) + 4H_2(g); K_3$ Which of the following relations is correct?

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Bakelite is obtained from phenol by reacting with

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Which of the following factors is of no significance for roasting sulphide ores to the oxides and not subjecting the sulphide ores to carbon reduction directly?

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Oxidising power of chlorine in aqueous solution can be determined by the parameters indicated below: $\large\frac{1}{2}$$ Cl_2(g) \underrightarrow{\qquad \frac{1}{2} \Delta {diss} H^{-} \qquad } Cl(g) \underrightarrow{\qquad \Delta {eg} H^{-}\qquad} Cl^{-}(g) \underrightarrow{\qquad \Delta _{hyd} H^{-}\qquad } Cl^{-}(aq)$ The energy involved in the conversion of $\frac{1}{2}Cl_2(g) to Cl^{-}(g)$ (using the data , $\Delta_{diss}H^{\Theta}_{Cl_2}=240 KJmol^{-1}$ ,$\Delta_{eg}H^{\Theta}_{Cl}=-349 KJmol^{-1}$ , $\Delta_{hyd}H^{\Theta}_{Cl}=-381 KJmol^{-1}$)

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The equilibrium constants $K_{p_{1}}$ and $K_{p_{2}}$ for the reactions X = 2Y and Z = P + Q, respectively are in the ratio of 1 : 9. If the degree of dissociation of X and Z be equal then the ratio of total pressure at these equilibria is

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For a reaction $\frac{1}{2}\rightarrow 2B$ rate of disappearance of ‘A’ is related to the rate of appearance of ‘B’ by the expression

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At 80oC, the vapour pressure of pure liquid ‘A’ is 520 mm Hg and that of pure liquid ‘B’ is 1000 mm Hg. If a mixture solution of ‘A’ and ‘B’ boils at 80oC and 1 atm pressure, the amount of ‘A’ in the mixture is (1 atm = 760 mm Hg)

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In which of the following octahedral complexes of Co (at. no. 27), will the magnitude of $\triangle_o$ be the highest?

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Larger number of oxidation states are exhibited by the actinoids than those by the lanthanoids, the main reason being

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Phenol, when it first reacts with concentrated sulphuric acid and then with concentrated nitric acid, gives

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Identify the wrong statements in the following:

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The coordination number and the oxidation state of the element ‘E’ in the complex $[E(en)_2(C_2O_4)]NO_2$ (where (en) is ethylene diamine) are, respectively,

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Toluene is nitrated and the resulting product is reduced with tin and hydrochloric acid. The product so obtained is diazotised and then heated with cuprous bromide. The reaction mixture so formed contains

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The organic chloro compound, which shows complete stereochemical inversion during a $S_N2$ reaction is

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The quadratic equations $x^2 – 6x + a = 0$ and $x^2 – cx + 6 = 0$ have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then the common root is

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27. Let A be a square matrix all of whose entries are integers. Then which one of the following is true?

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27. Let a, b, c be any real numbers. Suppose that there are real numbers x, y, z not all zero such that x = cy + bz, y = az + cx and z = bx + ay. Then $a^2 + b^2 + c^2 + 2abc$ is equal to

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27. How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?

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The value of $\sqrt{2}\displaystyle\int\frac {sin\;{x}{dx}}{sin(x-\frac{\pi}{4})}$ is

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The area of the plane region bounded by the curves $x + 2y^2 = 0$ and $x + 3y^2 = 1$ is equal to

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$Let I ={\displaystyle\int^1_0\frac{sin{x}}{\sqrt{x}}dx}$ and $ J={\displaystyle\int^1_0\frac{cos{x}}{\sqrt{x}}dx}$. Then which one of the following is true?

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The differential equation of the family of circles with fixed radius 5 units and centre on the line y = 2 is

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The value of cot $\bigg(cosec^{-1}{\frac{5}{3}}+tan^{-1}{\frac{2}{3}}\bigg)$ is

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The statement $p \rightarrow(q \rightarrow p)$ is equivalent to

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How many real solutions does the equation $X^7+14X^5+16X^3+30X-560=0$ have?

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Suppose the cube $x^3 - px + q$ has three distinct real roots where p > 0 and q > 0. Then which one of the following holds?

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23. The first two terms of a geometric progression add up to 12. The sum of the third and the fourth terms is 48. If the terms of the geometric progression are alternately positive and negative, then the first term is

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Let $f(x) = \left\{ \begin{array} {1 1} (x-1) \sin \bigg(\large\frac{ 1 }{x-1}\bigg),\normalsize & \quad\text{ if x $\neq$ 1 }\\ 0 ,& \quad \text{if x =1}\\ \end{array} \right. $.Then which one of the following is true?

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In a shop there are five types of ice-creams available. A child buys six ice-creams. Statement -1: The number of different ways the child can buy the six ice-creams is $^{10}C_5$ Statement -2: The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging 6 A’s and 4 B’s in a row.

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Let p be the statement “x is an irrational number”, q be the statement “y is a transcendental number”, and r be the statement “x is a rational number iff y is a transcendental number”. Statement –1: r is equivalent to either q or p Statement –2: r is equivalent to $\sim (p\leftrightarrow \sim q)$.

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Statement -1: $\sum^{n}_{r=0}(r+1)^nC_r=(n+2)2^{n-1}$ Statement -2: $\sum^{n}_{r=0}(r+1)^nC_rX^r=(1+X)^n+nX(1+X)^{n-1}$

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Let A be a $2 \times 2$ matrix with real entries. Let I be the $2 \times 2$ identity matrix. Denote by tr (A), the sum of diagonal entries of A. Assume that $A^2 = I$. Statement -1: If $A \neq I$ and $A \neq - I$, then det A = - 1. , Statement -2: If $A \neq I$ and $A \neq - I$, then $tr (A) \neq 0$.

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Statement - 1: For every natural number $n\geq 2$ ,$\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+$........$+\frac{1}{\sqrt{n}}>\sqrt{n}$ Statement -2: For every natural number $n\geq 2$ $\sqrt{{n}({n+1})}$

asked Nov 29, 2018 by pady_1

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If the straight lines $\frac{x-1}{k}=\frac{y-2}{2}=\frac{z-3}{3}$ and $\frac{x-2}{3}=\frac{y-3}{k}=\frac{z-1}{2}$ intersect at a point, then the integer k is equal to

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The line passing through the points (5, 1, a) and (3, b, 1) crosses the yz-plane at the point $\bigg[0,\frac{17}{2},\frac{-13}{2}\bigg]$. Then

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The non-zero verctors $\overrightarrow{a}$ , $\overrightarrow{b}$ and $\overrightarrow{c}$ are related by $\overrightarrow{a} =8\overrightarrow{b} and \overrightarrow{c} = -7 \overrightarrow{b}$ .Then the angle between $\overrightarrow{a}$ and $\overrightarrow{c}$ is

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The vector $\overrightarrow{a}=\alpha \hat{i}+2\hat{j}+\beta \hat{k}$ lies in the plane of the vectors $\overrightarrow{b}=\hat{i}+\hat{j}\; and \overrightarrow{c}=\hat{j}+\hat{k}$ and bisects the angle between $\overrightarrow{b}$ and $\overrightarrow{c}$.Then which one of the following gives possible values of $\alpha$ and $\beta$ ?

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The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the following gives possible values of a and b?

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The solution of the differential equation $\frac{dy}{dx}=\frac{x+y}{x}$ satisfying the condition y (1) = 1 is

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The perpendicular bisector of the line segment joining P (1, 4) and Q (k, 3) has y-intercept - 4. Then a possible value of k is

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1. Let R be the real line. Consider the following subsets of the plane $R\times R.$ $S = {(x, y) : y = x + 1 \;and \;0 < x < 2}, T = {(x, y) : x - y\; is\; an\; integer}$. Which one of the following is true?

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The conjugate of a complex number is $\frac{1}{i-1}$.The conjugate of a complex number is

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Let $f : N\rightarrow Y$ be a function defined as $f (x) = 4x + 3$, where $Y = {y\; \epsilon \;N : y = 4x + 3 for \;some\; x \;\epsilon\; N}$. Show that f is invertible and its inverse is

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The point diametrically opposite to the point P (1, 0) on the circle $x^2 + y^2 + 2x + 4y - 3 = 0$ is

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