Recent questions in 2003

The upper $3/4th$ portion of a vertical pole subtends an angle $\tan^{-1} 3/5$ at a point in the horizontal plane through its foot and a distance $40\;m$ from the foot. A possible height of the vertical pole is :

asked Dec 11, 2018 by pady_1

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The trigonometric equation $\sin^{-1}x = 2 \sin^{-1} a$ , has a solution for :

asked Dec 11, 2018 by pady_1

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In a triangle ABC, medians AD and BE are drawn. If $AD=4$ , $\angle{DAB} = \frac{\pi}{6}$ and $\angle{ABE} = \frac{\pi}{3}$ , then the area of the $\Delta ABC$ is :

asked Dec 11, 2018 by pady_1

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If in a triangle $ABC$ $a \cos^2(\frac{C}{2} ) + c \cos^2(\frac{A}{2} ) = \frac{3b}{2}$ , then the sides $a,\;b$ and $c$ :

asked Dec 11, 2018 by pady_1

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The sum of the radii of inscribed and circumscribed circles for an $n$ sided regular polygon of side $a$ is :

asked Dec 11, 2018 by pady_1

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If $x_1, \; x_2, \; x_3$ and $y_1, \; y_2, \; y_3$ are both in GP with the same common ratio, then the points $(x_1, y_1), \; (x_2, \; y_2)$ and $(x_3, y_3)$ :

asked Dec 11, 2018 by pady_1

0 answers

Let $f(x)$ be a polynomial function of second degree. If $f(1) = f(-1)$ and $a, \; b, \; c$ are in AP, then $f'(a), \; f'(b)$ and $f'(c)$ are in :

asked Dec 11, 2018 by pady_1

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The sum of the series $\frac{1}{1.2} - \frac{1}{2.3} + \frac{1}{3.4} - ...$ upto $\infty$ is equal to :

asked Dec 11, 2018 by pady_1

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If $x$ is positive, the first negative term in the expansion of $(1+x)^{27/5}$ is :

asked Dec 11, 2018 by pady_1

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The number of integral terms in the expansion of $(\sqrt{3} + 8\sqrt{5})^{256}$ is :

asked Dec 11, 2018 by pady_1

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If $^nC_r$ denotes the number of combinations of $n$ things taken $r$ at a time, then the expression $^nC_{r+1} + ^nC_{r-1} + 2 \times ^nC_r$ equals :

asked Dec 11, 2018 by pady_1

0 answers

If $1, \omega, \omega^2$ are the cube roots of unity, then : $\Delta = \begin{vmatrix} 1 & \omega^n & \omega^{2n} \\ \omega^n & \omega^{2n} & 1 \\ \omega^{2n} & 1& \omega^n \end{vmatrix}$ is equal to :

asked Dec 11, 2018 by pady_1

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The number of ways in which 6 men and 5 women can dine at a round table, if no two women are to sit together, is given by :

asked Dec 11, 2018 by pady_1

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A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is :

asked Dec 11, 2018 by pady_1

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If $A = \begin{bmatrix} a & b \\ b & a \end{bmatrix}$ and $A^2 = \begin{bmatrix} \alpha & \beta \\ \beta & \alpha \end{bmatrix}$ , then :

asked Dec 11, 2018 by pady_1

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The value of 'a' for which one root of the quadratic equation $(a^2 -5a +3) x^2 + (3a - 1)x+2 =0$ is twice as large as the other, is :

asked Dec 11, 2018 by pady_1

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The number of the real solutions of the equation $x^2 - 3|x| + 2 =0$ is :

asked Dec 11, 2018 by pady_1

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If the sum of the roots of the quadratic equation $ax^2 + bx + c =0$ is equal to the sum of the square of their reciprocals, then $\frac{a}{c}, \frac{b}{a}$ and $\frac{c}{b}$ are in :

asked Dec 11, 2018 by pady_1

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If the system of linear equations $\; \; \; \; x +2 ay + az = 0$ $\; \; \; \; x + 3by + bz=0$ $\; \; \; \; x +4cy +cz = 0$ has a non-zero solution, then $a, \; b,\; c$ :

asked Dec 11, 2018 by pady_1

0 answers

If $\begin{vmatrix} a & a^2 & 1+a^3 \\ b & b^2 & 1+b^3 \\ c & c^2 & 1+c^3 \end{vmatrix} = 0$ and vectors $(1, a, a^2), \; (1, b, b^2)$ and $(1, c, c^2)$ are non-coplanar, then the product $abc$ equals :

asked Dec 11, 2018 by pady_1

0 answers

If $\begin{pmatrix} \frac{1+i}{1-i} \end{pmatrix}^x=1$ , then:

asked Dec 11, 2018 by pady_1

0 answers

If $z$ and $\omega$ are two non-zero complex numbers such that $|z \; \omega| = 1$ , and $arg (z) - arg(\omega) = \frac{\pi}{2}$ , then $\overline{z} \omega$ is equal to :

asked Dec 11, 2018 by pady_1

0 answers

Let $z_1$ and $z_2$ be two roots of the equation $z^2 + az + b = 0 , \; z$ being complex. Further, assume that the origin, $z_1$ and $z_2$ form an equilateral triangle. Then :

asked Dec 11, 2018 by pady_1

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A function $f$ from the set of natural numbers of integers defined by $f(n) = \begin{cases} \frac{n-1}{2}, & \quad \text{when } n \text{ is odd}\\ -\frac{n}{2 } & \quad \text{when } n \text{ is even} \end{cases}$ is :

asked Dec 11, 2018 by pady_1

0 answers

Which of the following could act as a propellant for rockets ?

asked Dec 11, 2018 by pady_1

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On mixing a certian alkane with chlorine and irradiating it with ultraviolet light, it forms only one monochloroalkane. This alkane could be :

asked Dec 11, 2018 by pady_1

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Nylon threads are made of :

asked Dec 11, 2018 by pady_1

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The reaction of chloroform with alcoholic KOH and p-toluidine form :

asked Dec 11, 2018 by pady_1

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The internal energy change when a system goes from state A and B is $40\; k\; J/mol$ . If the system goes from A to B by a reversible path and returns to state A by an irreversible path, what would be the net change in internal energy ?

asked Dec 11, 2018 by pady_1

0 answers

Ethyl isocyanide on hydrolysis in acidic medium generates :

asked Dec 11, 2018 by pady_1

0 answers

Bottles containing $C_6H_5I$ and $C_6H_5CH_2I$ lost their original labels. They were labelled A and B for testing. A and B were separately taken in a test tube and boiled with NaOH solution. The end solution in each tube was made acidic with dilute $HNO_3$ and then some $AgNO_3$ solution was added. Substance B gave a yellow precipitate. Which one of the following statements is true for this experiment ?

asked Dec 11, 2018 by pady_1

0 answers

The reason for double helical structure of DNA is operation of :

asked Dec 11, 2018 by pady_1

1 answer

The substance not likely to contain $CaCO_3$ is :

asked Dec 11, 2018 by pady_1

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For making good quality mirrors, plates of float glass are used. These are obtained by floating molten glass over a liquid metal which does not solidify before glass. The metal used can be :

asked Dec 11, 2018 by pady_1

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Complete hydrolysis of cellulose gives :

asked Dec 11, 2018 by pady_1

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When rain is accompanied by a thunderstorm, the collected rain water will have a pH value :

asked Dec 11, 2018 by pady_1

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Which one of the following nitrates will leave behind a metal on strong heating ?

asked Dec 11, 2018 by pady_1

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During dehydration of alcohols to alkenes by heating with concentration $H_2SO_4$ the initiation step is :

asked Dec 11, 2018 by pady_1

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The solubilities of carbonates decrease down the magnesium group due to a decrease in :

asked Dec 11, 2018 by pady_1

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Butene - 1 may be converted to butane by reaction with :

asked Dec 11, 2018 by pady_1

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The correct order of increasing basic nature for the bases $NH_3, \; CH_3NH_2$ and $(CH_3)_2NH$ is :

asked Dec 11, 2018 by pady_1

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Which one of the following statements is not true ?

asked Dec 11, 2018 by pady_1

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In curing cement plasters water is sprinkled from time to time. This helps in :

asked Dec 11, 2018 by pady_1

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Several blocks of magnesium are fixed to the bottom of a ship to :

asked Dec 11, 2018 by pady_1

1 answer

The half-life of a radioactive isotope is 3 h. If the initial mass of the isotope were 256 g, the mass of it remaining undecayed after 18 h would be :

asked Dec 11, 2018 by pady_1

0 answers

The radionuclide $_{90}^{234} Th$ undergoes two successive $\beta$ -decays followed by one- $\alpha$ -decay. The atomic number and the mass number respectively of the resulting radionuclide are :

asked Dec 11, 2018 by pady_1

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The radius of $La^{3+}$ (Atomic number of La = 57) is $1.06 \mathring{A}$ . Which one of the following given values will be closest to the radius of $Lu^{3+}$ (Atomic number of Lu = 71) ?

asked Dec 11, 2018 by pady_1

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One mole of the complex compound $Co(NH_3)_5Cl_3$ , gives 3 moles of ions on dissolution in water. One mole of the same complex reacts with two moles of $AgNO_3$ solution to yield two moles of $AgCl(s)$ . The structure of the complex is :

asked Dec 11, 2018 by pady_1

0 answers

Ammonia forms the complex ion $[Cu(NH_3)_4]^{2+}$ with copper ions in the alkaline solutions but not in acidic solutions. What is the reason for it ?

asked Dec 11, 2018 by pady_1

0 answers

In the co-ordination compound, $K_4[Ni(CN)_4]$ , the oxidation state of nickel is :

asked Dec 11, 2018 by pady_1

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