Recent questions tagged past papers

The radical axis of circles $x^2 + y^2 + 5x + 4y-5=0$ and $x^2 + y^2 - 3x+ 5y-6=0$ is

asked Dec 11, 2018 by pady_1

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The limiting points of the co-axial system containing the two circles $x^2 +y^2+2x-2y+2=0$ and $25(x^2+y^2) -10x -80 y +65 =0$ are:

asked Dec 11, 2018 by pady_1

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The equation of the normal to the circle $x^2 + y^2 + 6 x + 4y -3=0$ at $(1,-2)$ is:

asked Dec 11, 2018 by pady_1

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A variable plane is at a constant distance $h$ from the origin and meets the co-ordinate axes in A, B, C. Locus of centroid of $\Delta ABC$ is :

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If $P = (0, 1, 2), \; Q = (4, -2,1), O = (0, 0, 0 )$, then $\angle{POQ}$ is equal to :

asked Dec 11, 2018 by pady_1

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If the foot of the perpendicular from $(0, 0, 0)$ to the plane is $(1,2,2)$, then the equation of the plane is :

asked Dec 11, 2018 by pady_1

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If a line makes angle $\frac{\pi}{3}$ and $\frac{\pi}{4}$ with the $x$-axis and $y$-axis respectively, then the angle made by the line with the $z$-axis is :

asked Dec 11, 2018 by pady_1

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The foot of the perpendicular from $(0, 2, 3)$ to the line $\frac{x+3}{5} = \frac{y-1}{2} = \frac{z+4}{3}$ is :

asked Dec 11, 2018 by pady_1

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If the extremities of diagonal of a square $(1, -2, 3), \; (2, -3, 5)$ then the length of its side, is:

asked Dec 11, 2018 by pady_1

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If the slope of one line is twice the slope of other in the pair of straight lines $ax^2 + 2hxy + by^2=0$, then $8h^2$ is equal to :

asked Dec 11, 2018 by pady_1

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If one of the lines of pair of straight lines $ax^2 + 2hxy + by^2 =0$ bisects the angle between the co-ordinates axes, then :

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The orthocentre of triangle formed by the lines $x + 3y = 10$ and $6x^2 + xy - y^2 = 0$ is :

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The incentre of triangle formed by the lines $x+y = 1, \; x=1, \;y=1$ is :

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The number of circles that touch all the straight lines $x+y=4$, $x-y=-2$ and $y=2$ is :

asked Dec 11, 2018 by pady_1

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The lines $2x + 3y = 6, \; 2x + 3y = 8$ cut the $x$-axis at $A$ and $B$ respectively. A line L drawn through the point $(2,2)$ meets the $x$-axis as $C$ in such a way that abscissae of A, B and C are in arithmetic progression. Then the equation of the line L is :

asked Dec 11, 2018 by pady_1

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For all values of $a$ and $b$ the line $(a + 2b) x + (a-b)y + (a+5b) = 0$ passes through the point :

asked Dec 11, 2018 by pady_1

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For a binomial variate $X$, if $n=4$ and $P(X = 4) =6 \; P(X =2)$, then the value of $p$ is

asked Dec 11, 2018 by pady_1

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Find the binomial probability distribution whose mean is 3 and variance is 2.

asked Dec 11, 2018 by pady_1

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Two dice are rolled simultaneously. The probability that the sum of the two numbers on the dice is a prime number, is :

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The events A and B have probabilities 0.25 and 0.50 respectively. The probability that both A and B occur simultaneously is 0.14, then the probability that neither A nor B occurs, is :

asked Dec 11, 2018 by pady_1

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The probabiliy that a number selected at random from the set of numbers $(1, 2, 3, ...., 100)$ is a cube, is :

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In a competition A, B, C are participating the probability that A wins is twice that of B, the probability that B wins is twice that of C, then probability that A loses is :

asked Dec 11, 2018 by pady_1

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$\overrightarrow{a} , \; \overrightarrow{b}, \; \overrightarrow{c}, \; \overrightarrow{d}$ are co-planar vectors, then $(\overrightarrow{a} \times \overrightarrow{b}) \times (\overrightarrow{c} \times \overrightarrow{d})$ is equal to :

asked Dec 11, 2018 by pady_1

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$[ \hat{i}-\hat{j}, \; \hat{j} - \hat{k}, \; \hat{k} - \hat{i} ]$ is equal to :

asked Dec 11, 2018 by pady_1

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If $\theta$ is the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ and $|\overrightarrow{a} \times \overrightarrow{b} | = |\overrightarrow{a}. \overrightarrow{b}|$, then $\theta$ is equal to :

asked Dec 11, 2018 by pady_1

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If $\overrightarrow{a}= \hat{i} + \hat{j} + t \hat{k}$, $\overrightarrow{b} = \hat{i} + 2 \hat{j} +3 \hat{k}$, then the values of $'t'$ for which $(\overrightarrow{a} + \overrightarrow{b})$ and $(\overrightarrow{a} - \overrightarrow{b})$ are perpendicular, are :

asked Dec 11, 2018 by pady_1

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ABCD is a parallelogram, with AC, BD as diagonals, then $\overrightarrow{AC} - \overrightarrow{BD}$ is equal to :

asked Dec 11, 2018 by pady_1

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If $\overrightarrow{a} = \hat{i} + 4 \hat{j}, \; \overrightarrow{b} = 2 \hat{i} - 3 \hat{j}, \; \overrightarrow{c} = 5 \hat{i} + 9 \hat{j}$, then $\overrightarrow{c}$ is equal to :

asked Dec 11, 2018 by pady_1

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How many litres of oxygen (at STP) are required for complete ccombustion of 39 g of liquid benzene ? (Atomic weights : C = 12, O = 16, H = 1 )

asked Dec 11, 2018 by pady_1

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Consider the following reaction : $A \to products$ This reaction is completed in 100 minutes. The rate constant of this reaction at $t_1 =10\; min$, is $10^{-2} \;min^{-1}$. What is the rate constant (in $min^{-1}$) at $t_2 = 20 $ minutes ?

asked Dec 11, 2018 by pady_1

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Equilibrium constant for the reaction $H_2O(g) + CO (g) \leftrightharpoons H_2(g) + CO_2 (g)$ is 81. If the velocity constant of the forward reaction is $162\; L\; mol^{-1} s^{-1}$. What is the velocity constant (in $L\;mol^{-1} s^{-1}$) for the backward reaction ?

asked Dec 11, 2018 by pady_1

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Molten $CuCl_2$ is electrolysed using platinum electrodes. The reaction occuring at anode is :

asked Dec 11, 2018 by pady_1

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One ampere of current is passed for 9650 seconds through molten $AlCl_3$. What is the weight in grams of $Al$ deosited at cathode ? (atomic weight of Al = 27)

asked Dec 11, 2018 by pady_1

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Which of the following would produce a buffer solution when mixed in equal volumes ?

asked Dec 11, 2018 by pady_1

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The $pK_a$ of a weak acid is $4.8$. What should be the ratio of $\frac{[acid]}{[salt]}$, if a buffer of $pH = 5.8$ is required ?

asked Dec 11, 2018 by pady_1

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250 mL of a sodium carbonate solution contains 2.65 g of $Na_2CO_3$. If 10 mL of this solution is diluted to one litre, what is the concentration of the resultant solution ?

asked Dec 11, 2018 by pady_1

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$n$ moles of an ideal gas at temperature $T$ (in kelvin) occupy $V\; L$ of volume, exerting a pressure of $P$ atmospheres. What is the concentration (in $mol/L$) ?

asked Dec 11, 2018 by pady_1

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The r.m.s velocity of $CO_2$ at a temperature $T$ (in kelvin) is $x\; cm\;sec^{-1}$. At what temperature (in kelvin), the r.m.s. velocity of nitrous oxide would be $4x\;cm\;sec^{-1}$ ? (Atomic weights of $C, \; N$ and $O$ are respectively $12, \; 14$ and $16$) :

asked Dec 11, 2018 by pady_1

1 answer

What are the oxidation numbers of nitrogen in $NH_4NO_3$ ?

asked Dec 11, 2018 by pady_1

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What is the volume (in litres) of oxygen at STP required for complete combustion of 32 g of $CH_4$ ? (Molecular weight of $CH_4$ is 16)

asked Dec 11, 2018 by pady_1

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Bond dissociation energies of $HF, \; HCl,\; HBr$ follow the order .....

asked Dec 11, 2018 by pady_1

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Which of the following statements is true ?

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The element with atomic number 12 belongs to .......... group and ............. period :

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Let electronegativity, ionisation energy and electron affinity be represented as EN, IP and EA respectively. Which one of the following equation is correct according to Mulliken ?

asked Dec 11, 2018 by pady_1

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What is X in the following reaction $_{12}Mg^{26} + _1H^2 \to _{12}Mg^{27}$ + X$ :

asked Dec 11, 2018 by pady_1

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In a nuclide, one a.m.u of mass is dissipated into energy to bind its nucleons. The energy equivalent of this mass is :

asked Dec 11, 2018 by pady_1

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In the ground state, an element has 13 electrons in M shell. The element is :

asked Dec 11, 2018 by pady_1

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The energy of an electron present in Bohr's second orbit of hydrogen atom is :

asked Dec 11, 2018 by pady_1

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The metal ion present in vitamin $B_{12}$ is :

asked Dec 11, 2018 by pady_1

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Consider the following reaction : $C_6H_5NO_2 \xrightarrow{Sn/HCl} X \xrightarrow{C_6H_5COCl} Y + HCl$ What is $Y$?

asked Dec 11, 2018 by pady_1

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