Recent questions tagged 09042016

If the tangent at a point on the ellipse $\large\frac{x^2}{27} +\frac{y^2}{3}$$=1$ meets the coordinate axes at A and B, and O is the origin, then the minimum area (in sq. units) of the triangle $OAB$ is :

asked May 29, 2017 by meena.p

1 answer

Consider the following two statements : <br> P : If 7 is an odd number, then 7 is divisible by 2. <br> Q : If 7 is a prime number, then 7 is an odd number. <br> If $V_1$ is the truth value of the contrapositive of $P$ and $V_2$ is the truth value of contrapositive of Q, then the ordered pair $(V_1, V_2)$ equals :

asked May 29, 2017 by meena.p

1 answer

If $m$ and $M$ are the minimum and the maximum values of $4 +\large\frac{1}{2} $$\sin ^2 2x - 2 \cos ^4 x , x \in R$ then $M−m$ is equal to :

asked May 29, 2017 by meena.p

1 answer

The number of $x \in [0, 2 \pi]$ for which $| \sqrt{2 \sin ^4 x +18 \cos ^2 x} - \sqrt {2 \cos ^4 x +18 \sin ^2 x}|=1$ is :

asked May 29, 2017 by meena.p

1 answer

If $A$ and $B$ are any two events such that $P(A)= \large\frac{2}{5}$ and $P(A \cap B)=\large\frac{3}{20}$,then the conditional probability, $P(A |(A' \cup B')),$ where $A'$ denotes the complement of A, is equal to :

asked May 29, 2017 by meena.p

1 answer

If the mean deviation of the numbers $1, 1+ d, ..., 1+100d$ from their mean is $255$, then a value of $d$ is :

asked May 29, 2017 by meena.p

1 answer

In a triangle $ABC$, right angled at the vertex $A$, if the position vectors of A, B and C are respectively $3 \hat i + \hat j - \hat k , \hat i+3 \hat j +p \hat k $ and $5 \hat i+q \hat j -4 \hat k$ then the point $(p, q)$ lies on a line :

asked May 29, 2017 by meena.p

1 answer

The distance of the point $(1, −2, 4)$ from the plane passing through the point $(1, 2, 2)$ and perpendicular to the planes $x−y+2z=3$ and $2x−2y+z+12=0,$ is :

asked May 29, 2017 by meena.p

1 answer

The shortest distance between the lines $\large\frac{x}{2}=\frac{y}{2}=\frac{z}{1}$ and $\large\frac{x+2}{-1} = \frac{y-4}{8} =\frac{z-5}{4}$ lies in the interval

asked May 29, 2017 by meena.p

1 answer

Let a and b respectively be the semitransverse and semi-conjugate axes of a hyperbola whose eccentricity satisfies the equation $9e^2−18e+5=0$. If $S(5, 0)$ is a focus and $5x=9$ is the corresponding directrix of this hyperbola, then $a^2−b^2$ is equal to

asked May 29, 2017 by meena.p

1 answer

A circle passes through $(−2, 4)$ and touches the y-axis at $(0, 2)$. Which one of the following equations can represent a diameter of this circle ?

asked May 26, 2017 by meena.p

1 answer

The point $(2, 1)$ is translated parallel to the line $L : x−y=4$ by $2 \sqrt 3$ units. If the new point Q lies in the third quadrant, then the equation of the line passing through Q and perpendicular to L is :

asked May 26, 2017 by meena.p

1 answer

If a variable line drawn through the intersection of the lines $\large\frac{x}{3}+\frac{y}{4}$$=1$ and $\large\frac{x}{4}+\frac{y}{3}$$=1$ , meets the coordinate axes at $A$ and $B,(A \neq B),$ then the locus of the midpoint of AB is :

asked May 26, 2017 by meena.p

1 answer

If $f(x)$ is a differentiable function in the interval $(0, \infty)$ such that $f(1)=1$ and $\lim \limits_{t \to x} \large\frac{t^2f(x)-x^2f(t)}{t-x} $$=1$ fopr each $x >0$ then $f( \large\frac{3}{2})$ is equal to :

asked May 26, 2017 by meena.p

1 answer

The area (in sq. units) of the region described by $A=\{(x, y)|y ≥ x2−5x+4, x+y ≥ 1, y ≤ 0\}$ is :

asked May 26, 2017 by meena.p

1 answer

If $2 \int \limits_0^1 \tan ^{-1} x dx = \int \limits _0^1 \cot ^{-1} (1-x+x^2)dx$ then $\int \limits_0^1 \tan ^{-1} (1-x+x^2)dx$ is equal to :

asked May 26, 2017 by meena.p

1 answer

If $\int \Large\frac{dx}{\cos ^3 x \sqrt {2 \sin 2x}}$$=(\tan x)^A+C(\tan x)^B +k$ where k is a constant of integration, then $A+B+C$ equals :

asked May 26, 2017 by meena.p

1 answer

The minimum distance of a point on the curve $y=x^2−4$ from the origin is :

asked May 26, 2017 by meena.p

1 answer

If the tangent at a point $P,$ with parameter $t$, on the curve $x=4t^2+3, y=8t^3−1, t \in R,$ meets the curve again at a point Q, then the coordinates of Q are :

asked May 26, 2017 by meena.p

1 answer

If the function $f(x) = \left\{ \begin{array}{l l} -x, & \quad x < 1 \\ a+\cos ^{-1} (x+b), & \quad 1 \leq x \leq 2 \end{array} \right.$ is differentiable at $x=1$, then $\large\frac{a}{b}$ is equal to :

asked May 26, 2017 by meena.p

1 answer

If $\lim \limits_{x \to \infty}$ \bigg( 1+ \large\frac{a}{x}-\frac{4]{x^2} \bigg)^{2x} =e^3$, then 'a' is equal to :

asked May 26, 2017 by meena.p

1 answer

The value of $\sum \limits_{r=1}^{15} r^2 \bigg( \large\frac{^{15} C_r}{^{15}C_{r-1}}\bigg)$ is equal to :

asked May 26, 2017 by meena.p

1 answer

Let $x, y, z$ be positive real numbers such that $x+y+z=12$ and $x^3y^4z^5=(0.1) (600)^3$. Then $x^3+y^3+z^3$ is equal to :

asked May 26, 2017 by meena.p

1 answer

For $x \in R,x \neq -1$, if $(1+x)^{2016} +x(1=x)^{2015} +x^2(1+x)^{2014}+.......+x^{2016}=\sum \limits_{i=0} ^{2016} a_i x^i $, then $a_{17}$ is equal to :

asked May 25, 2017 by meena.p

1 answer

If the four letter words (need not be meaningful ) are to be formed using the letters from the word “MEDITERRANEAN” such that the first letter is R and the fourth letter is E, then the total number of all such words is :

asked May 25, 2017 by meena.p

1 answer

The number of distinct real roots of the equation $P=\begin{vmatrix} \cos x & \sin x & \sin x \\ \sin x & \cos x & \sin x \\ \sin x & \sin x & \cos x \end{vmatrix} = 0 $ in the interval $\bigg[ \large\frac{-\pi}{4} ,\frac{\pi}{4} \bigg]$ is :

asked May 25, 2017 by meena.p

1 answer

If $P=\begin{bmatrix} \large\frac{\sqrt 3}{2} & \frac{1}{2} \\ \large\frac{-1}{2} & \large\frac{\sqrt 3}{2} \end{bmatrix} $ , $A=\begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix} $ and $Q= PAP^{T}$, then $P^Tq^{2015}P$ is :

asked May 25, 2017 by meena.p

1 answer

If the equations $x^2+bx−1=0$ and $x^2+x+b=0$ have a common root different from $−1$, then $|b|$ is equal to :

asked May 25, 2017 by meena.p

1 answer

The point represented by $2+i$ in the Argand plane moves $1 \;unit $ eastwards, then $2 \;units$ northwards and finally from there $2 \sqrt 2$ units in the south-westwards direction. Then its new position in the Argand plane is at the point represented by :

asked May 25, 2017 by meena.p

1 answer

For $ x \in R, x \neq 0,x \neq 1 ,$ let $f_0(x) =\large\frac{1}{1-x} $ and $f_{n+1}(x) =f_0 (f_n(x)),n =0,1,2$.... Then the value of $f_{100} (3)+f_1\bigg( \large\frac{2}{3}\bigg) +f_2 \bigg( \large\frac{3}{2}\bigg)$ is equal to :

asked May 25, 2017 by meena.p

1 answer

The most appropriate method of making egg-albumin sol is :

asked May 25, 2017 by meena.p

1 answer

The artificial sweetener that has the highest sweetness value in comparison to cane sugar is :

asked May 25, 2017 by meena.p

1 answer

Consider the following sequence for aspartic acid :

asked May 25, 2017 by meena.p

1 answer

The test to distinguish primary, secondary and tertiary amines is :

asked May 25, 2017 by meena.p

1 answer

Bouveault-Blanc reduction reaction involves :

asked May 25, 2017 by meena.p

1 answer

The gas evolved on heating $CH_3MgBr$ in methanol is

asked May 25, 2017 by meena.p

1 answer

$5\; L$ of an alkane requires $25\; L$ of oxygen for its complete combustion. If all volumes are measured at constant temperature and pressure, the alkane is :

asked May 25, 2017 by meena.p

1 answer

The hydrocarbon with seven carbon atoms containing a neopentyl and a vinyl group is :

asked May 25, 2017 by meena.p

1 answer

An organic compound contains C, H and S. The minimum molecular weight of the compound containing $8\%$ sulphur is : (atomic weight of $S=32 amu$)

asked May 25, 2017 by meena.p

1 answer

BOD stands for :

asked May 24, 2017 by meena.p

1 answer

Identify the correct trend given below : (Atomic No.= $Ti : 22, Cr : 24$ and $Mo : 42$)

asked May 24, 2017 by meena.p

1 answer

Which one of the following complexes will consume more equivalents of aqueous solution of $Ag(NO_3)$ ?

asked May 24, 2017 by meena.p

1 answer

Which one of the following species is stable in aqueous solution?

asked May 24, 2017 by meena.p

1 answer

The group of molecules having identical shape is :

asked May 24, 2017 by meena.p

1 answer

Match the items in Column I with its main use listed in Column II :

asked May 24, 2017 by meena.p

1 answer

The correct order of the solubility of alkaline-earth metal sulphates in water is :

asked May 24, 2017 by meena.p

1 answer

Identify the incorrect statement regarding heavy water :

asked May 24, 2017 by meena.p

1 answer

The plot shows the variation of −ln Kp versus temperature for the two reactions.

asked May 24, 2017 by meena.p

1 answer

The non-metal that does not exhibit positive oxidation state is :

asked May 24, 2017 by meena.p

1 answer

A particular adsorption process has the following characteristics : (i) It arises due to van der Waals forces and (ii) it is reversible. Identify the correct statement that describes the above adsorption process :

asked May 24, 2017 by meena.p

1 answer

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