Recent questions tagged past papers

If $u = \log_e (x^2+y^2) + \tan^{-1} (y/x)$, then $\frac{\partial^2u}{dx^2} + \frac{\partial^2u}{\partial y^2}$ is equal to:

asked Dec 19, 2018 by pady_1

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$\frac{d^n}{dx^n} (e^x \sin x)$ is equal to :

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Area of the triangle formed by the normal to the curve $x = e^{\sin v} $ at $(1, 0)$ with the co-ordinate axes is :

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The minimum value of $x^x$ is :

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If $l^2 + m^2 = 1$, then the maximum value of $l+m$ is :

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The angle between the curves $y^2=4x, \; x^2 = 4y$ at $(4,4)$, is :

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The distance moved by the particle in time $t$ is given by $s = t^3 - 12t^2 + 6t +8$. At the instant when its acceleration is zero, the velocity is :

asked Dec 19, 2018 by pady_1

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If $xy=(x+y)^n$ and $\frac{dy}{dx} = \frac{y}{x}$, then $n$ is equal to :

asked Dec 19, 2018 by pady_1

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$\frac{d}{dx} \{ \cos^{-1} (\frac{4x^3}{27} - x ) \}$ is equal to :

asked Dec 19, 2018 by pady_1

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If $y=2^{2x}$, then $\frac{dy}{dx} $ is equal to :

asked Dec 19, 2018 by pady_1

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If the function $f(x) = \begin{cases} \frac{\sin 3x}{x}, & \quad x \neq 0\\ \frac{k}{2} & \quad x=0 \end{cases}$ continuous at $x=0$, then $k$ is equal to :

asked Dec 19, 2018 by pady_1

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$\displaystyle\lim_{x \to 0} \frac{\log_e (1+x)}{3^x-1}$ is equal to :

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$\displaystyle\lim_{\theta \to \pi/2} \frac{1-\sin \theta}{\cos (\frac{\pi}{2} - \theta)}$ is equal to :

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The radius of the circle $r^2 - 2\sqrt{2}r (\cos \theta + \sin \theta) -5 = 0$ is :

asked Dec 19, 2018 by pady_1

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The curve represented by $x=2 (\cos t + \sin t), \;y = 5(\cos t - \sin t)$ is :

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The prouct of the length of perpendiculars from the foci on any tangent to the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ is :

asked Dec 19, 2018 by pady_1

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The eccentricity of the ellipse $5x^2 + 9y^2 = 1$ is :

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The line $4x +6y+9=0$, touches the parabola $y^2 =4x$ at the point :

asked Dec 19, 2018 by pady_1

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The vertex of the parabola $x^2+ 8x + 12y+4=0$ is :

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If $(m_v \frac{1}{m_i}), \; i = 1, 2,3,4$ are noncyclic points, then the value of $m_1m_2m_3m_4$ is :

asked Dec 19, 2018 by pady_1

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If $(1,2)$ is a limiting point of a co-axial system of circles containing the circle $x^2 + y^2 + x - 5y + 9 =0$, then the equation of radical axis is :

asked Dec 19, 2018 by pady_1

1 answer

The number of common tangents that can be drawn to the circles $x^2 + y^2=1$ and $x^2 + y^2 -2x - 6y + 6 =0$, is :

asked Dec 19, 2018 by pady_1

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Two circles of equal radii cut orthogonally, if their centres are (2, 3) and (5, 6), then r is equal to:

asked Dec 19, 2018 by pady_1

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The slope $m$ of a tangent through the point $(7,1)$ to the circle $x^2+y^2=25$, satisfy the equation :

asked Dec 19, 2018 by pady_1

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The centre of circle which touch the y-axis at $(0,3)$ and making an intercept of $2$ units on the positive $x$-axis is :

asked Dec 19, 2018 by pady_1

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If the equation $\lambda x^2 - 5xy + 6y^2 + x - 3y =0$, represents a pair of straight lines, then their point of intersection is :

asked Dec 19, 2018 by pady_1

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The equaion of pair of lines through the point $(a,b)$ parallel to co-ordinate axes is :

asked Dec 19, 2018 by pady_1

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Two consecutive sides of a parallelogram are $4x+5y=0$ and $7x+2y=0$. If the equation of one diagonal is $11x + 7y =9$, then the equation of the other diagonal is :

asked Dec 19, 2018 by pady_1

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Which of the following is a tertiary alcohol ?

asked Dec 19, 2018 by pady_1

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Which of the following is Lucas reagent ?

asked Dec 19, 2018 by pady_1

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Chloroethane reacts with Y to form NaCl and Z. One mole of Z reacts with two moles of Hi to form water and iodo ethane. Which of the following is Y ?

asked Dec 19, 2018 by pady_1

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Which of the following is a secondary amine ?

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Which of the following converts acetone to acetone oxime ?

asked Dec 19, 2018 by pady_1

1 answer

Nitrobenzene on reduction with $Sn/HCl$ gives $A$, which on reaction with acetyl chloride form $B$. Which of the following is $B$ ?

asked Dec 19, 2018 by pady_1

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Which of the following converts acetic acid into acetyl chloride?

asked Dec 19, 2018 by pady_1

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What is X in the following reaction ? <br> $2CH_3CHO \xrightarrow{NaOH} X$ :

asked Dec 19, 2018 by pady_1

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What is the crystal structure of caesium chloride ?

asked Dec 19, 2018 by pady_1

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Which of the following is the correct pair ?

asked Dec 19, 2018 by pady_1

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Which of the following has the highest first IP ?

asked Dec 19, 2018 by pady_1

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The electronic configuration of group III elements is :

asked Dec 19, 2018 by pady_1

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The pH of an aqueous solution of a salt is 10. The salt is :

asked Dec 19, 2018 by pady_1

1 answer

Which of the following is correct for acid buffer ? [ salt = S, acid = A ] :

asked Dec 19, 2018 by pady_1

1 answer

What is the value (in litres) of $CO_2$ liberated at $STP$ when $2.12 \;g$ of sodium carbonate (mol. wt. 106) is treated with excess dilute $HCl$ ?

asked Dec 19, 2018 by pady_1

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Which of the following reactions does not involve change in the oxidation state of the metal ?

asked Dec 19, 2018 by pady_1

1 answer

I low many electrons are present in the $M$ shell of an atom of an element with atomic number 24 (Z = 24) ?

asked Dec 19, 2018 by pady_1

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The half-life of a radioactive element is 100 years. What is its disintegration contant (in years$^{-1}$) ?

asked Dec 19, 2018 by pady_1

1 answer

Which one of the $VI$ group element has the highest catenation power ?

asked Dec 19, 2018 by pady_1

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Brass is an alloy of :

asked Dec 19, 2018 by pady_1

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In which of the following reactions $H_2O_2$ acts as a reducing agent ?

asked Dec 19, 2018 by pady_1

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In the Castner's process of extraction of sodium, cathode is :

asked Dec 19, 2018 by pady_1

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