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If $P=\begin{bmatrix} 1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{bmatrix} = 0$ is the adjoint of $3 \times 3$ matrix $A$ and $|A|=4$ , then $\alpha$ is equal to :

asked Apr 18, 2017 by meena.p

1 answer

$ABCD$ is a trapezium such that $AB$ and $CD$ are parallel and $BC \perp CD$ . If $\angle ADB = \theta, BC = p$ and $CD = q,$ then $AB$ is equal to :

asked Apr 18, 2017 by meena.p

1 answer

If z is a complex number of unit modulus and argument $\theta$ , then $arg\bigg(\large\frac{1+z}{1+\bar{z}}\bigg)$ equals

asked Apr 18, 2017 by meena.p

1 answer

Let $T_n$ be the number of all possible triangles formed by joining vertices of a n−sided regular polygon. If $T_{n+1} − T_{n} = 1$ then the value of n is :

asked Apr 18, 2017 by meena.p

1 answer

The area (in square units) bounded by the curves $y=\sqrt x, 2y−x+3= 0$ , x−axis, and lying in the first quadrant is :

asked Apr 18, 2017 by meena.p

1 answer

The term independent of x in expansion of $\bigg( \large\frac{x+1}{x^{2/3}-x^{1/3}+1} -\frac{x-1}{x-x^{1/2}} \bigg)^{10}$ is :

asked Apr 18, 2017 by meena.p

1 answer

The x−coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as $(0, 1) (1, 1)$ and $(1, 0)$ is :

asked Apr 18, 2017 by meena.p

1 answer

A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is :

asked Apr 18, 2017 by meena.p

1 answer

The equation of the circle passing through the foci of the ellipse $\large\frac{x^2}{16}+\frac{y^2}{9}$ $=1$ and having center at $(0,3)$ is :

asked Apr 17, 2017 by meena.p

1 answer

Statement − I : The value of the integral $\int\limits_{\pi/6} ^{\pi/3} \large\frac{dx}{1+\sqrt{\tan x}}$ is equal to $\large\frac{\pi}{6}$ . Statement − II : $\int\limits_{a}^{b} f(x)dx =\int \limits_a^b f(a+b-x)dx$

asked Apr 17, 2017 by meena.p

1 answer

$\lim\limits_{x \to 0} \large\frac{(1-cos 2x )(3+\cos x)}{x \tan 4x}$ is equal to

asked Apr 17, 2017 by meena.p

1 answer

If $\int f(x)=dx= \psi(x)$ , then $\int x^5 f(x^3)dx$ is equal to :

asked Apr 17, 2017 by meena.p

1 answer

Consider : Statement − I : $(p \wedge \sim q) \wedge p ( \sim p \wedge q)$ is fallacy. Statement - II : $(p \to q) \longleftrightarrow ( \sim q \to \sim p)$ is a tautology

asked Apr 13, 2017 by meena.p

1 answer

If x, y, z are in A.P. and $\tan^{-1}x,\tan^{-1}y$ and $\tan^{-1}z$ are also in A.P then :

asked Apr 12, 2017 by meena.p

1 answer

The circle passing through $(1, −2)$ and touching the axis of $x$ at $(3, 0)$ also passes through the point :

asked Apr 12, 2017 by meena.p

1 answer

If the equations $x^2 + 2x + 3 = 0$ and $ax^2+ bx + c = 0, a, b, c \in R,$ have a common root, then $a : b : c$ is

asked Apr 12, 2017 by meena.p

1 answer

The number of values of k, for which the system of equations : $(k + 1)x + 8y = 4k\\ kx + (k + 3)y = 3k − 1$ has no solution, is :

asked Apr 12, 2017 by meena.p

1 answer

A ray of light along $x+ \sqrt{3}y =\sqrt 3$ gets reflected upon reaching x−axis, the equation of the reflected ray is :

asked Apr 12, 2017 by meena.p

1 answer

The sum of first $20$ terms of the sequence $0.7, 0.77, 0.777, ……,$ is :

asked Apr 11, 2017 by meena.p

1 answer

The real number k for which the equation, $2x^3+3x+ k = 0$ has two distinct real roots in $[0, 1]$

asked Apr 11, 2017 by meena.p

1 answer

If the vector $\overrightarrow{AB} = 3 \hat i +4 \hat k$ and $\overrightarrow{AC} = 5 \hat i - 2 \hat j +4 \hat k$ are the sides of a triangle ABC, then the length of the median through A is :

asked Apr 11, 2017 by meena.p

1 answer

If the lines $\large\frac{x-2}{1} =\frac{y-3}{1} =\frac{z-4}{-k}$ and $\large\frac{x-1}{k} =\frac{y-4}{2} =\frac{z-5}{1}$ are coplanar, then k can have :

asked Apr 11, 2017 by meena.p

1 answer

Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of $A \times B$ having 3 or more elements is :

asked Apr 10, 2017 by meena.p

1 answer

At present,a firm is manufacturing $2000 \;items$ . It is estimated that the rate of change of production P w.r.t. additional number of workers x is given by $\large\frac{dp}{dx}$ $=100 12 \sqrt {x}$ . If the firm employs 25 more workers, then the new level of production of items is :

asked Apr 10, 2017 by meena.p

1 answer

Distance between two parallel planes $2x + y +2z = 8$ and $4x + 2y + 4z + 5 = 0$ is :

asked Apr 10, 2017 by meena.p

1 answer

Experimentally it was found that a metal oxide has formula $M_{0.98}O$ . Metal M, is present as $M^{2+}$ and $M^{3+}$ in its oxide. Fraction of the metal which exists as $M^{3+}$ would be :

asked Apr 7, 2017 by meena.p

1 answer

The gas leaked from a storage tank of the Union Carbide plant in Bhopal gas tragedy was :

asked Apr 7, 2017 by meena.p

1 answer

An unknown alcohol is treated with the “Lucas reagent” to determine whether the alcohol is primary, secondary or tertiary. Which alcohol reacts fastest and by what mechanism :

asked Apr 7, 2017 by meena.p

1 answer

Stability of the species $Li_2 , Li^{-}_2$ and $Li^{+}_{2}$ increases in the order of

asked Apr 7, 2017 by meena.p

1 answer

An organic compound A upon reacting with $NH_3$ gives $B$ .On heating, B gives $C$ . $C$ in presence of $KOH$ reacts with $Br_2$ to give $CH_3CH_2NH_2.A$ is :

asked Apr 7, 2017 by meena.p

1 answer

The first ionisation potential of $Na$ is $5.1\;eV$ . The value of electron gain enthalpy of $Na^+$ will be :

asked Apr 7, 2017 by meena.p

1 answer

How many litres of water must be added to 1 litre of an aqueous solution of HCl with a pH of 1 to create an aqueous solution with $pH$ of $2$ ?

asked Apr 6, 2017 by meena.p

1 answer

Four successive members of the first row transition elements are listed below with atomic numbers. Which one of them is expected to have the highest $E^0_{M^{3+} /m^{2+}}$ value ?

asked Apr 6, 2017 by meena.p

1 answer

Compound (A), $C_8H_9Br$ , gives a white precipitate when warmed with alcoholic $AgNO_3$ .Oxidation of (A) gives an acid (B) , $C_8H_6O_4$ . (B) easily forms anhydride on heating. Identify the compound (A) .

asked Apr 6, 2017 by meena.p

1 answer

Energy of an electron is given by $E= -2.178 \times 10^{18} J \bigg(\large\frac{Z^2}{n^2}\bigg)$ . Wavelength of light required to excite an electron in an hydrogen atom from level $n = 1$ to $n = 2$ will be

asked Apr 6, 2017 by meena.p

1 answer

Which of the following represents the correct order of increasing first ionization enthalpy for $Ca, Ba, S, Se \;and\; Ar ?$

asked Apr 6, 2017 by meena.p

1 answer

The coagulating power of electrolytes having ions $Na^{+} ,Al^{3+}$ and $Ba^{2+}$ for arsenic sulphide sol increases in the order :

asked Apr 6, 2017 by meena.p

1 answer

Synthesis of each molecule of glucose in photosynthesis involves :

asked Apr 6, 2017 by meena.p

1 answer

Which of the following exists as covalent crystals in the solid state ?

asked Apr 5, 2017 by meena.p

1 answer

In which of the following pairs of molecules / ions , both the species are not likely to exist ?

asked Apr 5, 2017 by meena.p

1 answer

A gaseous hydrocarbon gives upon combustion $0.72\; g$ . of water and $3.08\;g$ of $CO_2$ . The empirical formula of the hydrocarbon is :

asked Apr 5, 2017 by meena.p

1 answer

Which of the following is the wrong statement ?

asked Apr 5, 2017 by meena.p

1 answer

Consider the following reaction : $xMnO_4^{-} +yC_2O_4^{2-} +zH^{+} \to xMn^{2+} +2yCO_2 +\large\frac{z}{2}$ $H_2O$ The values of x, y and z in the reaction are, respectively :

asked Apr 5, 2017 by meena.p

1 answer

The order of stability of the following carbocations is:

asked Apr 5, 2017 by meena.p

1 answer

Which of the following arrangements does not represent the correct order of the property stated against it ?

asked Apr 4, 2017 by meena.p

1 answer

A compound with molecular mass $180$ is acylated with $CH_3COCl$ to get a compound with molecular mass 390. The number of amino groups present per molecule of the former compound is :

asked Apr 4, 2017 by meena.p

1 answer

The rate of a reaction doubles when its temperature changes from $300 \;K$ to $310\; K$ . Activation of such a reaction will be :

asked Apr 4, 2017 by meena.p

1 answer

For a gaseous state, if most probable speed is denoted by $C^{*}$ , average speed by C and mean square speed by C, then for a large number of molecules the ratios of these speeds are :

asked Apr 4, 2017 by meena.p

1 answer

Arrange the following compounds in order of decreasing acidity :

asked Apr 4, 2017 by meena.p

1 answer

The molarity of a solution obtained by mixing $750\; mL$ of $0.5\;(M)HCl$ with $250\; mL$ of $2(M)HCl$ will be :

asked Apr 4, 2017 by meena.p

1 answer

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