Recent questions tagged set e

The contrapositive of the statement If it is raining, then I will not come, is :

asked Sep 30, 2015 by meena.p

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If $f(x)=2 \tan^{-1} x + \sin^{-1} \bigg(\large\frac{2x}{1+x^2}\bigg),$$x >1$ then $f(5) $ is equal to

asked Sep 30, 2015 by meena.p

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In a $\Delta ABC, \frac{a}{b}$$=2+\sqrt 3$ and $\angle C=60^{\circ}$. Then the ordered pair $\angle A, \angle B) $ is equal to :

asked Sep 30, 2015 by meena.p

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A factory is operating in two shifts, day and night, with 70 and 30 workers respectively. If per day mean wage of the day shift workers is Rs.54 and per day mean wage of all the workers is Rs.60, then per day mean wage of the night shift workers (in Rs) is :

asked Sep 30, 2015 by meena.p

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Let X be a set containing 10 elements and $P(X)$ be its power set. If A and B are picked up at random from $P(X)$, with replacement , then the probability that A and B have equal number of elements, is :

asked Sep 30, 2015 by meena.p

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Let $\overrightarrow{a}$ and $\overrightarrow{b}$ be two unit vectors such that $|\overrightarrow{a}+\overrightarrow{b}|=\sqrt 3 $. If $\overrightarrow{c}=\overrightarrow{a}+2 \overrightarrow{b}+3(\overrightarrow{a} \times \overrightarrow{b})$, then $2 |\overrightarrow{c}|$ is equal to :

asked Sep 30, 2015 by meena.p

1 answer

If the shortest distance between the lines $\large\frac{x-1}{\alpha } = \frac{y+1}{-1}= \frac{z}{1} $$, (\alpha \neq -1) $ and $x+y+z+1=0=2x-y+z+3 $ is $ \large\frac{1}{\sqrt 3} $, then a value of $\alpha $ is

asked Sep 30, 2015 by meena.p

1 answer

If the points $(1, 1, \lambda)$ and $(23, 0, 1)$ are equidistant from the plane, $3x+4y-12z+13=0,$ then $\lambda$ satisfies the equation :

asked Sep 30, 2015 by meena.p

1 answer

An ellipse passes through the foci of the hyperbola, $9x^2-4y^2=36$ and its major and minor axes lie along the transverse and conjugate axes of the hyperbola respectively. If the product of eccentricities of the two conics is $\large\frac{1}{2}$, then which of the following points does not lie on the ellipse ?

asked Sep 30, 2015 by meena.p

1 answer

If the tangent to the conic, $y-6=x^2$ at $(2, 10)$ touches the circle, $x^2+y^2+8x-2y=k$(for some fixed k) at a point $(\alpha, \beta)$ then $(\alpha, \beta)$ is :

asked Sep 30, 2015 by meena.p

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If $y+3x=0$ is the equation of a chord of the circle, $ x^2+y^2-30=0$, then the equation of the circle with this chord as diameter is :

asked Sep 30, 2015 by meena.p

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Let L be the line passing through the point $P(1, 2)$ such that its intercepted segment between the co-ordinate axes is bisected at P. If $L_1$ is the line perpendicular to L and passing through the point $(-2, 1),$ then the point of intersection of L and L1 is :

asked Sep 30, 2015 by meena.p

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The points $\bigg(0,\large\frac{8}{3}\bigg),$$(1,3)$ and $(82,30)$ :

asked Sep 30, 2015 by meena.p

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If y(x) is the solution of the differential equation $(x+2) \large\frac{dy}{dx}$$=x^2+4x-9, x \neq -2 $ and $y(0)=0,$ then $y(-4)$ is equal to :

asked Sep 30, 2015 by meena.p

1 answer

The area (in square units) of the region bounded by the curves $y+2x^2=0$ and $y+3x^2=1$, is equal to :

asked Sep 30, 2015 by meena.p

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For $x >0$ , let $f(x)= \int \limits_1^x \large\frac{log t}{1+t}$$dt$. Then $f(x)+f\bigg(\large\frac{1}{x}\bigg)$ is equal to:

asked Sep 30, 2015 by meena.p

1 answer

The integral $\int \large\frac{dx}{(x+1)^{3/4} (x-2)^{5/4}}$ is equal to

asked Sep 29, 2015 by meena.p

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Let the tangents drawn to the circle, $x^2+y^2=16$ from the point $P(0, h)$ meet the x-axis at points A and B. If the area of $DAPB$ is minimum, then h is equal to :

asked Sep 29, 2015 by meena.p

1 answer

If Rolles theorem holds for the function $f (x)=2x^3+bx^2+cx, x \in [-1, 1],$ at the point $x= \large\frac{1}{2}$, then $2b+c$ equals :

asked Sep 29, 2015 by meena.p

1 answer

The distance, from the origin, of the normal to the curve, $x= 2 \cos t +2 t \sin t; y=2 \sin t- 2t \cos t 2t $ at $t= \large\frac{\pi}{4}$ is :

asked Sep 29, 2015 by meena.p

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$\lim \limits _{x \to 0} \large\frac{e^{x^2}-\cos x}{\sin ^2 x}$ is equal to

asked Sep 29, 2015 by meena.p

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The value of $ \sum _{r=16} ^{30} (r+2)(r-3)$ s equal to

asked Sep 29, 2015 by meena.p

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If the coefficients of the three successive terms in the binomial expansion of $(1+x)^n$ are in the ratio $1 : 7 : 42$, then the first of these terms in the expansion is :

asked Sep 29, 2015 by meena.p

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Let the sum of the first three terms of an A.P. be 39 and the sum of its last four terms be 178. If the first term of this A.P. is 10, then the median of the A.P. is :

asked Sep 29, 2015 by meena.p

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The number of ways of selecting 15 teams from 15 men and 15 women, such that each team consists of a man and a woman, is :

asked Sep 29, 2015 by meena.p

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If $A=\begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$ then which one of the following statements is not correct ?

asked Sep 29, 2015 by meena.p

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The least value of the product xyz for which the determinant $\begin{bmatrix}x & 1 & 1\\1 & y & 1\\1 & 1 & z\end{bmatrix}$ is non-negative , is :

asked Sep 29, 2015 by meena.p

1 answer

If $2+3i$ is one of the roots of the equation $2x^3-9x2+kx-13=0,$ k \in R$, then the real root of this equation

asked Sep 29, 2015 by meena.p

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The largest value of r for which the region represented by the set $\{\omega \in C/| \omega -4-i| \geq r \}$ is contained in the region represented by the set $\{z \in C/|Z-1| \geq | z+i| \}$ is equal to :

asked Sep 29, 2015 by meena.p

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In a certain town, $25\%$ of the families own a phone and $15 \%$ own a car ; $65\%$ families own neither a phone nor a car and $2,000$ families own both a car and a phone.Consider the following three statements : (a) $5\%$ families own both a car and a phone. (b) $35\%$ families own either a car or a phone. (c) $40,000$ families live in the town. Then,

asked Sep 29, 2015 by meena.p

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The cation that will not be precipitated by $H_2S$ in the presence of dil $HCl$ is :

asked Sep 29, 2015 by meena.p

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Refer the following diagram :

asked Sep 29, 2015 by meena.p

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Match the polymers in column-A with their main uses in column-B and choose the correct answer :

asked Sep 29, 2015 by meena.p

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Arrange the following amines in the order of increasing basicity.

asked Sep 29, 2015 by meena.p

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In the presence of a small amount of phosphorous, aliphatic carboxylic acids react with chlorine or bromine to yield a compound in which a - hydrogen has been replaced by halogen. This reaction is known as :

asked Sep 29, 2015 by meena.p

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A compound A with molecular formula $C_{10}H_{13}Cl$ gives a white precipitate on adding silver nitrate solution. A on reacting with alcoholic $KOH$ gives compound $B$ as the main product. B on ozonolysis gives $C$ and $D$. $ C$ gives Cannizaro reaction but not aldol condensation. $D$ gives aldol condensation but not Cannizaro reaction. $A$ is :

asked Sep 29, 2015 by meena.p

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The optically inactive compound from the following is :

asked Sep 29, 2015 by meena.p

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$1.4\; g$ of an organic compound was digested according to Kjeldahls method and the ammonia evolved was absorbed in $60\; mL$ of $M/10\; H_2SO_4$ solution. The excess sulphuric acid required $20\;mL$ of $M/10\;NaOH$ solution for neutralization. The percentage of nitrogen in the compound is :

asked Sep 28, 2015 by meena.p

1 answer

Photochemical smog consists of excessive amount of X, in addition to aldehydes, ketones, peroxy acetyl nitrile (PAN), and so forth. X is :

asked Sep 28, 2015 by meena.p

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The correct statement on the isomerism associated with the following complex ions,$ (a) [Ni(H_2O)_5NH_3]^{2+},\\ (b) [Ni(H_2O)_4(NH_3)_2]^{2+} \;and\\ (c) [Ni(H_2O)_3(NH_3)_3]^{2+}\; is :$

asked Sep 28, 2015 by meena.p

1 answer

Which molecule/ion among the following cannot act as a ligand in complex compounds ?

asked Sep 28, 2015 by meena.p

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Which molecule/ion among the following cannot act as a ligand in complex compounds ?

asked Sep 28, 2015 by meena.p

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An aqueous solution of a salt X turns blood red on treatment with $SCN^{-}$ and blue on treatment with $K_4[Fe(CN)_6]$. $X$ also gives a positive chromyl chloride test. The salt X is :

asked Sep 28, 2015 by meena.p

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The geometry of $XeOF_4$ by $VSEPR$ theory is

asked Sep 28, 2015 by meena.p

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The least number of oxyacids are formed by :

asked Sep 28, 2015 by meena.p

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The correct order of thermal stability of hydroxides is :

asked Sep 28, 2015 by meena.p

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Permanent hardness in water cannot be cured by :

asked Sep 28, 2015 by meena.p

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In the isolation of metals, calcination process usually results in :

asked Sep 28, 2015 by meena.p

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In the long form of the periodic table, the valence shell electronic configuration of $5s^2, 5p^4$ corresponds to the element present in :

asked Sep 28, 2015 by meena.p

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The following statements relate to the adsorption of gases on a solid surface. Identify the incorrect statement among them :

asked Sep 28, 2015 by meena.p

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