Recent questions tagged past papers

$A = (-9, 0)$ and $B = (-1, 0)$ are two points. If $P=(x,y)$ is a point such that $3PB = PA$, then the locus of $P$ is :

asked Dec 19, 2018 by pady_1

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If $1, \omega, \omega^2$ are the cube roots of unity, then $(1- \omega + \omega^2)^5 + (1 + \omega - \omega^2)^5$ is equal to

asked Dec 19, 2018 by pady_1

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The value of $\begin{pmatrix}\frac{1-\sqrt{3}i }{2}\end{pmatrix}^{36} + \begin{pmatrix}\frac{-1 -\sqrt{3} i }{2}\end{pmatrix}^{36} $ is equal to :

asked Dec 19, 2018 by pady_1

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If $1, \omega, \omega^2$ are the cube roots of unity and $a, b$ are real and $x = a + b$, $y = a \omega^2 + b \omega$, $z = a \omega + b \omega^2$, then $x^2 + y^2 + z^2 $ is equal to :

asked Dec 19, 2018 by pady_1

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If $P$ represent $z= x + iy$ in the argand plane and $|z-1|^2 + |z+1|^2 = 4$, then the locus of $P$ is :

asked Dec 19, 2018 by pady_1

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If the angles of depression of the upper and lower ends of a lamp post the top of a hill of height $h$ meters are $\alpha$ and $\beta$ respectively, then the height of the lamp post is equal to :

asked Dec 19, 2018 by pady_1

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If the area of the triangle ABC is $a^2 - (b-c)^2$, then $\tan \frac{A}{2}$ is equal to :

asked Dec 19, 2018 by pady_1

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In a triangle $ABC$, if $\angle{C} = 60^{\circ}$, then $\frac{a}{b+c} + \frac{b}{c+a}$ is equal to :

asked Dec 19, 2018 by pady_1

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A square, non-singular matrix A satisfies $A^2 - A + 2I=0$, then $A^{-1}$ is equal to :

asked Dec 19, 2018 by pady_1

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The matrix $\begin{bmatrix} 1 & 0 & 1 \\ 2 & 1 & 0 \\ 3 & 1 & 1 \end{bmatrix}$ is :

asked Dec 19, 2018 by pady_1

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$\begin{vmatrix} x & 1 & y+z \\ y & 1 & z+x \\ z & 1 & x+y \end{vmatrix}$ is equal to :

asked Dec 19, 2018 by pady_1

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If the sum of the squares of the roots of $x^2 + px - 3=0$ is $10$, then the value of $p$ is equal to :

asked Dec 19, 2018 by pady_1

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If $\tan^{-1}x + \tan^{-1}y + \tan^{-1}z = \frac{\pi}{2}$, then $1-xy-yz - zx$ is equal to :

asked Dec 19, 2018 by pady_1

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If $x = \tan^{-1}y$, then $\log_e(\frac{1+y}{1-y})$, then :

asked Dec 19, 2018 by pady_1

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If $\sqrt{\sin x} + \cos x = 0$, then $\sin x$ is equal to :

asked Dec 19, 2018 by pady_1

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If $A + B + C = 0$, then $\sin^2A + \sin^2B + \sin^2C$ is equal to :

asked Dec 19, 2018 by pady_1

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Maximum and minimum values of $\sin^2(120^{\circ} + \theta) + \sin^2(120^{\circ} - \theta)$ are respectively :

asked Dec 19, 2018 by pady_1

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The sum of the series $1 + 3x + 5x^2 + 7x^3+ ....+(2n-1)x^{n-1} + ...$ is:

asked Dec 19, 2018 by pady_1

0 answers

If $\frac{(x+1)^2}{x^3 + x} = \frac{A}{x} + \frac{Bx + C}{x^2 + 1}$, then $\sin^{-1} (A/C)$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

If $C_n$ is the coefficient of $x^n$ in the expansion of $(1+x)^n$, then $C_1 + 2C_2 + 3C_3 + ...+nC_n$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

The term independent of $x$ in the expansion of $(2x^2 - \frac{3}{x^3})^{15}$, is :

asked Dec 19, 2018 by pady_1

0 answers

If $a = 1 + \log_x yz, \; b = 1+ \log_y zx, \; c = 1 + \log_z xy$, then $ab + bc + ca$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

If $x = 2\sqrt{2} + \sqrt{7}$, then $x+\frac{1}{x}$ is equal to :

asked Dec 19, 2018 by pady_1

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A group consists of 6 men and 3 women. A committee is to be formed with 5 people choosing 3 men and 2 women. The number of different committees that can be formed, as :

asked Dec 19, 2018 by pady_1

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$\begin{vmatrix} a & b& c \\ b & c &a \\ c & a & b \end{vmatrix} = 0$ then :

asked Dec 19, 2018 by pady_1

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$\tan^{-1} x + \cot^{-1} (x+1)$ is equal to :

asked Dec 19, 2018 by pady_1

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Domain of $f(x) = \frac{1}{6} \sqrt{\log_{10} (5x-x^2) }$ is :

asked Dec 19, 2018 by pady_1

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If $f : R^+ \to R$, such that $f(x) = \log_3x$, then $f^{-1}(x)$ is equal to :

asked Dec 19, 2018 by pady_1

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Silica is soluble in :

asked Dec 19, 2018 by pady_1

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Which of the following does not participate in the Solvay's process for the manufacture of $Na_2CO_3$ ?

asked Dec 19, 2018 by pady_1

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Among the following compounds which have more than one type of hybridization for carbon atom :<br> 1. $CH_3.CH_2.CH_2.CH_3$ <br> 2.$CH_3.CH= CH.CH_3$ <br>3. $CH_2 = CH - CH = CH_2$ <br> 4.$H-C = C-H $

asked Dec 19, 2018 by pady_1

1 answer

$C_2H_5CHO$ and $(CH_3)_2CO$ can be distinguished by testing with :

asked Dec 19, 2018 by pady_1

0 answers

If the equilibrium constant for the reaction $2AB \rightleftharpoons A_2 + B_2$ is 49; what is the value of equilibrium constant for $AB \rightleftharpoons \frac{1}{2}A_2 +\frac{1}{2}B_2$ ?

asked Dec 19, 2018 by pady_1

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Acetaldehyde when treated with dilute $NaOH$ gives :

asked Dec 19, 2018 by pady_1

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The reagent used for converting ethanoic acid to ethanol is :

asked Dec 19, 2018 by pady_1

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When an alkyl halide reacts with an alkoxide the product is:

asked Dec 19, 2018 by pady_1

1 answer

Compound A reacts with $PCl_5$ to give B which on treatment with $KCN$ followed by hydrolysis gave propanoic acid. What is A and B respectively ?

asked Dec 19, 2018 by pady_1

0 answers

By which of the following reactions can one get N-methyl aniline from aniline ?

asked Dec 19, 2018 by pady_1

1 answer

In Wurtz reaction the reagent used is :

asked Dec 19, 2018 by pady_1

0 answers

The homologue of ethyne is :

asked Dec 19, 2018 by pady_1

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Hydrolysis of trichloromethane with aqueous KOH gives :

asked Dec 19, 2018 by pady_1

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Carbogen is :

asked Dec 19, 2018 by pady_1

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Which of the following sets of elements does not belong to transitional element set ?

asked Dec 19, 2018 by pady_1

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Silver containing lead as an impurity is removed by :

asked Dec 19, 2018 by pady_1

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Acetic acid reacts with $PCl_5$ to form :

asked Dec 19, 2018 by pady_1

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Which one of the following reactions is an example of calcination process ?

asked Dec 19, 2018 by pady_1

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Which of the following is the strongest Lewis acid ?

asked Dec 19, 2018 by pady_1

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A mixture contains four solid organic compounds A, B, C, D. On heating only C changes from solid to vapours state. C can be separated from the rest in the mixture by :

asked Dec 19, 2018 by pady_1

1 answer

Cassiterite is concentrated by :

asked Dec 19, 2018 by pady_1

0 answers

The number of moles of $AgCl$ precipitated when excess $AgNO_3$ is added to one mole of $[Cr(NH_3)_4Cl_2]Cl$ is :

asked Dec 19, 2018 by pady_1

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