Recent questions tagged past papers

Let $k$ be an integer such that the triangle with vertices $(k, -3k),\; (5, k)$ and $(-k, 2)$ has area 28 sq. units. Then the orthocentre of this triangle is at the point :

asked Dec 11, 2018 by pady_1

1 answer

Let $\omega$ be a complex number such that $2 \omega + 1 = z$ where $z = \sqrt{-3}$. If $\begin{vmatrix} 1 & 1& 1 \\ 1 & -\omega^2-1& \omega^2 \\ 1 & \omega^2 & \omega^7 \end{vmatrix} = 3k$, then $k$ is equal to :

asked Dec 11, 2018 by pady_1

1 answer

For three events A, B and C, P(Exactly one of A or B occurs) = P(Exactly one of B or C occurs) = P(Exactly one of C or A occurs) = $\frac{1}{4}$ and P (All the three events occur simultaneously) = $\frac{1}{6}$. Then the probability that at least one of the events occurs, is :

asked Dec 11, 2018 by pady_1

1 answer

If $5(\tan^2 x – \cos^2 x) = 2 \cos2x + 9$, then the value of $\cos 4 x$ is :

asked Dec 11, 2018 by pady_1

1 answer

The following statement $(p \to q)\; [(\sim p \to q) \to q]$ is :

asked Dec 11, 2018 by pady_1

1 answer

If S is the set of distinct values of 'b' for which of the following system of linear equations $x + y + z = 1$ $x + ay + z = 1$ $ax + by + z = 0$ has no solution, then S is :

asked Dec 11, 2018 by pady_1

1 answer

The Boolean Expression $(p \wedge \sim q) \vee q \vee(\sim p \wedge q)$ is equivalent to :

asked Dec 11, 2018 by pady_1

1 answer

A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pillar is $30^{\circ}$. After walking for 10 minutes from A in the same direction, at a point B, he observes that the angle of elevation of the top of the pillar is $60^{\circ}$. Then the time taken (in minutes) by him, from B to reach the pillar, is :

asked Dec 11, 2018 by pady_1

1 answer

If $0 \leq x \leq 2\pi$, then the number of real values of $x$, which satisfy the equation $\cos x+\cos 2x+\cos 3x+\cos 4x=0$, is :

asked Dec 11, 2018 by pady_1

1 answer

Let two fair six-faced dice $A$ and $B$ be thrown simultaneously. If $E_1$ is the event that die $A$ shows up four, $E_2$ is the event that die $B$ shows up two and $E_3$ is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true ?

asked Dec 11, 2018 by pady_1

1 answer

If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true ?

asked Dec 11, 2018 by pady_1

1 answer

Let $\overrightarrow{a}, \; \overrightarrow{b}$ and $\overrightarrow{c}$ be three unit vectors such that $ \overrightarrow{a} \times (\overrightarrow{b} \times \overrightarrow{c} ) = \frac{\sqrt 3}{2} (\overrightarrow{b} + \overrightarrow{c})$. If $\overrightarrow{b}$ is not parallel to $\overrightarrow{c}$, then the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is :

asked Dec 11, 2018 by pady_1

1 answer

If the line, $\frac{x-3}{2} = \frac{y+2}{-1} = \frac{z+4}{3}$ lies in the plane, $lx + my - z =9$, then $l^2 + m^2$ is equal to

asked Dec 11, 2018 by pady_1

1 answer

The distance of the point $(1, −5, 9)$ from the plane $x−y+z=5$ measured along the line $x=y=z$ is :

asked Dec 11, 2018 by pady_1

1 answer

The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal to half of the distance between its foci, is :

asked Dec 11, 2018 by pady_1

1 answer

Let P be the point on the parabola, $y^2=8x$ which is at a minimum distance from the centre C of the circle, $x^2+(y+6)^2=1$. Then the equation of the circle, passing through C and having its centre at P is :

asked Dec 11, 2018 by pady_1

1 answer

If one of the diameters of the circle, given by the equation, $x^2+y^2−4x+6y−12=0$, is a chord of a circle S, whose centre is at (−3, 2), then the radius of S is :

asked Dec 11, 2018 by pady_1

1 answer

The centres of those circles which touch the circle, $x^2+y^2−8x−8y−4=0$, externally and also touch the x-axis, lie on :

asked Dec 11, 2018 by pady_1

1 answer

Two sides of a rhombus are along the lines, $x−y+1=0$ and $7x−y−5=0$. If its diagonals intersect at $(−1, −2)$, then which one of the following is a vertex of this rhombus ?

asked Dec 11, 2018 by pady_1

1 answer

If a curve $y = f(x)$ passes through the point $(1, -1)$ and satifies the differential equation, $y(1+xy) dx = x ;dy$, then $f(-\frac{1}{2})$ is equal to :

asked Dec 11, 2018 by pady_1

1 answer

The area (in sq. units) of the region $\{ (x,y) : y^2 \geq 2x $ and $x^2 + y^2 \leq 4x, \; x \geq 0, \; y \geq 0 \}$ is :

asked Dec 11, 2018 by pady_1

1 answer

$\begin{align} \displaystyle{\lim_{n \to \infty} \begin{pmatrix} \frac{(n+1) (n+2) ...3n}{n^{2n}} \end{pmatrix} }^{1/n} \end{align}$ is equal to :

asked Dec 11, 2018 by pady_1

1 answer

The integral $\begin{align} \int \frac{2x^{12} + 5x^9}{(x^5 + x^3 + 1)^3} dx \end{align}$ is equal to : where C is an arbitrary constant.

asked Dec 11, 2018 by pady_1

1 answer

A wire of length 2 units is cut into two parts which are bent respectively to form a square of side $=x$ units and a circle of radius $=r$ units. If the sum of the areas of the square and the circle so formed is minimum, then :

asked Dec 11, 2018 by pady_1

1 answer

Consider $f(x) = \tan^{-1} \begin{pmatrix} \sqrt{\frac{1+\sin x}{1 - \sin x}} \end{pmatrix}, x \in (0, \frac{\pi}{2})$. A normal to $y = f(x)$ at $x = \frac{\pi}{6}$ also passes through the point :

asked Dec 11, 2018 by pady_1

2 answers

For $x \in R, \; f(x) = | \log 2 - \sin x | $ and $g(x) = f( f(x))$, then :

asked Dec 11, 2018 by pady_1

1 answer

Let $p = \displaystyle{\lim_{x \to 0^+} (1 + \tan^2 \sqrt{x} )^{1/2x} }$ then $\log p$ is equal to :

asked Dec 11, 2018 by pady_1

1 answer

If the sum of the first ten terms of the series $(1 + \frac{3}{5})^2 + ( 2 + \frac{2}{5})^2 + (3 + \frac{1}{5})^2 + 4^2 + (4 + \frac{4}{5})^2......,$ is $\frac{16}{5} m$, then $m$ is equal to :

asked Dec 11, 2018 by pady_1

1 answer

If the $2^{nd},\; 5^{th}$ and $9^{th}$ terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is :

asked Dec 11, 2018 by pady_1

1 answer

If the number of terms in the expansion of $\begin{pmatrix} 1 - \frac{2}{x} + \frac{4}{x^2} \end{pmatrix}^n, x \neq 0$ is 28, then the sum of the coefficients of all the terms in this expansion, is :

asked Dec 11, 2018 by pady_1

1 answer

If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary; then the position of the word SMALL is :

asked Dec 11, 2018 by pady_1

1 answer

The system of linear equations $ x + \lambda y - z = 0 $ $\lambda x - y - z =0$ $x + y - \lambda z = 0$ has a non-trivial solution for :

asked Dec 11, 2018 by pady_1

1 answer

If $A= \begin{bmatrix} 5a & -b \\ 3 & 2 \end{bmatrix}$ and $A \; adj \; A = A A^T$, then $5a + b$ is equal to :

asked Dec 11, 2018 by pady_1

1 answer

The sum of all real values of $x$ satisfying the equation $(x^2 - 5x + 5)^{x^2 + 4x - 60} = 1$ is :

asked Dec 11, 2018 by pady_1

1 answer

A value of $\theta$ for which $\frac{2 + 3 i \sin \theta}{1 - 2 i \sin \theta}$ is purely imaginary, is :

asked Dec 11, 2018 by pady_1

1 answer

If $f(x) + 2f (\frac{1}{x}) = 3x, \; x \neq 0$, and $S = \{ x \in R : f(x) = f(-x) \}$; then $S$ :

asked Dec 11, 2018 by pady_1

1 answer

The hottest region of Bunsen flame shown in the figure below is :

asked Dec 11, 2018 by pady_1

0 answers

Which of the following is an anionic detergent ?

asked Dec 11, 2018 by pady_1

1 answer

Thiol group is present in :

asked Dec 11, 2018 by pady_1

0 answers

Which of the following statements about low density polythene is FALSE ?

asked Dec 11, 2018 by pady_1

0 answers

In the Hofmann bromamide degradation reaction, the number of moles of $NaOH$ and $Br_2$ used per mole of amine produced are :

asked Dec 11, 2018 by pady_1

0 answers

The reaction of propene with $HOCl\; (Cl_2+H_2O)$ proceeds through the intermediate :

asked Dec 11, 2018 by pady_1

0 answers

2-chloro-2-methylpentane on reaction with sodium methoxide in methanol yields :

asked Dec 11, 2018 by pady_1

0 answers

The absolute configuration of is :

asked Dec 11, 2018 by pady_1

0 answers

The product of the reaction given below is :

asked Dec 11, 2018 by pady_1

0 answers

The distillation technique most suited for separating glycerol from spent-lye in the soap industry is :

asked Dec 11, 2018 by pady_1

0 answers

The concentration of fluoride, lead, nitrate and iron in a water sample from an underground lake was found to be 1000 ppb, 40 ppb, 100 ppm and 0.2 ppm, respectively. This water is unsuitable for drinking due to high concentration of :

asked Dec 11, 2018 by pady_1

1 answer

Which one of the following complexes shows optical isomerism ? (en=ethylenediamine)

asked Dec 11, 2018 by pady_1

0 answers

The pair having the same magnetic moment is : [At. No : Cr = 24, Mn = 25, Fe = 26, Co = 27]

asked Dec 11, 2018 by pady_1

0 answers

Which of the following compounds is metallic and ferromagnetic ?

asked Dec 11, 2018 by pady_1

0 answers

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