Recent questions tagged past papers

The inverse point of $(1, -1)$ with respect to the circle $x^2 + y^2 = 4$ is equal to :

asked Dec 19, 2018 by pady_1

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The parametric equaions $x= \frac{2a(1-t^2)}{1+t^2}$, and $y = \frac{4at}{1+'t^2}$ represents a circle of radius is equal to :

asked Dec 19, 2018 by pady_1

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If the equation $ax^2 + 5xy - 6y^2 - 10x + 11y + c = 0$ represents two perpendicular lines, then $c$ is equal to :

asked Dec 19, 2018 by pady_1

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The angle between the pair of straight lines $y^2 \cos^2 \theta - xy \cos^2 \theta + x^2 (\sin^2 \theta - 1)=0$, is :

asked Dec 19, 2018 by pady_1

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If $\lambda x^2 + 6xy + 9y^2 +4x + 12y+3=0$ represents a pair of straight lines, then $\lambda$ is equal to :

asked Dec 19, 2018 by pady_1

1 answer

The product of length of perpendiculars from $(-1,2)$ to the pair of lines $2x^2 -5xy + 2y^2 =0$, is :

asked Dec 19, 2018 by pady_1

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The reflection of a point $(6, 8)$ about the line $x=y$, is :

asked Dec 19, 2018 by pady_1

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The equation of lines passing through the intersection of lines $x - 2y + 5=0$ and $3x+2y+7=0$ and perpendicular to $x-y=0$ is :

asked Dec 19, 2018 by pady_1

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If the straight line $y=4-3x, \; ay = x + 10$ and $2y + bx + 9=0$ represents the three consecutive sides of rectangle, then $ab$ is equal to :

asked Dec 19, 2018 by pady_1

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Equation of a straight line making an intercept of 3 units on the $y$-axis and inclined at $45^{\circ}$ to the $x$-axis, is :

asked Dec 19, 2018 by pady_1

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The ratio in which the line $y=x$ divides the segment joining $(2,3)$ and $(8,6)$ is :

asked Dec 19, 2018 by pady_1

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If the axes are rotated through an angle $30^{\circ}$ about the origin, then the tranformed equation of $x^2 + 2 \sqrt{3} xy - y^2 = 2a^2$, is :

asked Dec 19, 2018 by pady_1

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The locus of the point whose distance from $x$ axis is twice its distance from $y$ axis is :

asked Dec 19, 2018 by pady_1

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If $\frac{3 + 2i \sin \theta}{1- 2i \sin \theta}$ is real, then $\theta$ is equal to :

asked Dec 19, 2018 by pady_1

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The least positive integer $n$ such that $\begin{pmatrix} \frac{1 - i}{1+i} \end{pmatrix}^{2n} = 1$ is :

asked Dec 19, 2018 by pady_1

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$P$ represents $z = x + iy$ in argand plane and $|3z - 1|=3|z-2|$; then locus of $P$ is :

asked Dec 19, 2018 by pady_1

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If $\alpha, \; \beta$ are the cube roots of unity, then $\alpha^5 + \beta^5 + \alpha \beta$ is equal to :

asked Dec 19, 2018 by pady_1

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In a triangle $A = \sqrt{15} - \sqrt{11}, \; B = \sqrt{17} - \sqrt{13}$ then :

asked Dec 19, 2018 by pady_1

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In a triangle $ABC, \; r_1 \cot \frac{A}{2} + r_2 \cot \frac{B}{2} + r_3 \cot \frac{C}{2}$ is equal to :

asked Dec 19, 2018 by pady_1

2 answers

In a $\Delta ABC, \; r \begin{bmatrix} \cot \frac{B}{2} + \cot \frac{C}{2} \end{bmatrix}$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

The general solution of $\tan^2 \theta = 3$ is :

asked Dec 19, 2018 by pady_1

1 answer

From the top of a building of height $h$ metres the angle of depression of an object on the ground is $\alpha$. The distance of the object from the foot of the building, is :

asked Dec 19, 2018 by pady_1

0 answers

If $|x| = x $, then $\frac{1}{2} \log \begin{pmatrix} \frac{1+x}{1-x} \end{pmatrix}$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

The period of $\sin^3x + \cos^3 x^2$ is :

asked Dec 19, 2018 by pady_1

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The maximum value of $1+8 \sin^2 x^2 \cos^2 x^2$ is :

asked Dec 19, 2018 by pady_1

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$\tan^{-1} (\frac{1}{2}) + \tan^{-1} (\frac{1}{3})$ is equal to :

asked Dec 19, 2018 by pady_1

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$\frac{\sin \theta + \sin 2 \theta}{1 + \cos \theta + 2 \cos \theta}$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

The oxidation number of Mn in potassium permanganate is :

asked Dec 19, 2018 by pady_1

0 answers

The electronic configuration of sodium is :

asked Dec 19, 2018 by pady_1

0 answers

Which of the following reagents converts nitrobenzene into N-phenyl hydroxylamine ?

asked Dec 19, 2018 by pady_1

0 answers

Acetic acid gives acetic anhydride when treated with :

asked Dec 19, 2018 by pady_1

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Which of the following compounds undergo aldol condensation ?

asked Dec 19, 2018 by pady_1

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$O^{2-}$ and $Si^{4+}$ are isoelectronic ions. If the ionic radius of $O^{2-}$ is $1.4 \mathring{A}$, the ionic radius of $Si^{4+}$ will be :

asked Dec 19, 2018 by pady_1

0 answers

The solvent used in the preparation of Grignard reagent is :

asked Dec 19, 2018 by pady_1

1 answer

In which of the following reactions heat liberated is known as standard heat of formation of $CO_2$ ?

asked Dec 19, 2018 by pady_1

0 answers

Tinstone is contaminated with Wolframite. Which one of the following methods can be employed to dress the tinstone ore ?

asked Dec 19, 2018 by pady_1

1 answer

How many moles of potassium chlorate should be decomposed completely to obtain $67.2\; L$ of oxygen at NTP ?

asked Dec 19, 2018 by pady_1

0 answers

A solid organic compound $X$ on heating is directly converted into the vapour phase which on cooling solidifies. The best method for purifying $X$ is :

asked Dec 19, 2018 by pady_1

1 answer

A mixture contains $16\;g$ of oxygen, $28\; g$ of nitrogen and $8\; g$ of $CH_4$. Total pressure of mixture is $740\;mm$. What is the partial pressure of nitrogen in $mm$?

asked Dec 19, 2018 by pady_1

0 answers

Which of the following covalent molecules is an exception to octet rule ?

asked Dec 19, 2018 by pady_1

0 answers

Among the first lines of Lyman, Balmer, Paschen and Brackett series in hydrogen atomic spectra, which has the highest energy?

asked Dec 19, 2018 by pady_1

1 answer

At $90^{\circ}C$ the concentration of $H_3O^+$ in pure water is $10^{-6}\; mol\;L^{-1}$. What is the value of $K_w$ at this temperature ?

asked Dec 19, 2018 by pady_1

0 answers

The unit of radio-activity is :

asked Dec 19, 2018 by pady_1

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The pH of a 1 litre solution is 2. It is diluted with water till its pH becomes 4. How many litres of water are added ?

asked Dec 19, 2018 by pady_1

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The activity of a radioactive element is $2 \times 10^{10}$ disintegration per second. After ten minutes the activity is reduced to $2 \times 10^9$ distintegrations per second. The disintegration constant of the radioactive element is :

asked Dec 19, 2018 by pady_1

0 answers

n-octane and n-nonane have :

asked Dec 19, 2018 by pady_1

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The oxidation number of nitrogen in $NH_3$ is:

asked Dec 19, 2018 by pady_1

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Which of the following alkane cannot be prepared by Wurtz reaction ?

asked Dec 19, 2018 by pady_1

0 answers

Which of the following is used as a rocket fuel ?

asked Dec 19, 2018 by pady_1

0 answers

Ethyne is treated with $30 \% \; H_2SO_4$ in the presence of $1\%$ mercuric sulphate at $70^{\circ}C$. What is the product formed ?

asked Dec 19, 2018 by pady_1

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