Recent questions and answers in 2012

If the lines $\frac{x-1}{2} = \frac{y+1}{3} = \frac{z-1}{4}$ and $ \frac{x-3}{1} = \frac{y-k}{2} = \frac{z}{1}$ intersect, then $k$ is equal to

answered May 15, 2020 by priyanka.clay6

1 answer

Let $x_1, x_2, ....., x_n$ be $n$ observations, and let $\overline{x}$ be their arithematic mean and $\sigma^2$ be their variance. Statement 1 : Variance of $2x_1, 2x_2, ....,2x_n$ is $4 \sigma^2$ Statement 2 : Arithmetic mean of $2x, 2x_2, .... , 2x_n$ is $4 \overline{x}$.

answered May 15, 2020 by priyanka.clay6

1 answer

If the line $2x + y = k$ passes through the point which divides the line segment joining the points (1, 1) and (2, 4) in the ratio $ 3 : 2$, then $k$ equals

answered May 15, 2020 by priyanka.clay6

1 answer

In a $\Delta PQR$, if $ 3 \sin P + 4 \cos Q = 6 $ and $4 \sin Q + 3 \cos P = 1$, then the angle R is equal to

answered May 15, 2020 by priyanka.clay6

1 answer

If 100 times the $100^{th}$ term of an AP with non zero common difference equal the 50 times its $50^{th} $ term, then the $150^{th}$ term of this AP is

answered May 2, 2020 by priyanka.clay6

1 answer

If $n$ is a positive integer, then $(\sqrt{3} + 1)^{2n} - (\sqrt{3} - 1)^{2n}$ is

answered May 2, 2020 by priyanka.clay6

1 answer

Let $A = \begin{pmatrix} 1 & 0 & 0 \\ 2 & 1 & 0 \\ 3 & 2 & 1 \end{pmatrix}$. If $u_1$ and $u_2$ are column matrices such that $Au_1 = \begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix} $ and $Au_2 = \begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix} $, then $u_1 + u_2$ is equal to

answered May 2, 2020 by priyanka.clay6

1 answer

Statement 1 : An equation of a common tangent to the parabola $y^2 = 16 \sqrt{3}x$ and the ellipse $2x^2 + y^2 = 4$ is $y = 2x + 2\sqrt{3}$. Statement 2 : If the line $y = mx + \frac{4 \sqrt{3}}{m}, (m \neq 0)$ is a common tangent to the parabola $y^2 = 16 \sqrt{3}x $ and the ellipse $2x^2 + y^2 = 4$, then $m$ satisfies $m^2 + 2m^2 = 24$.

answered May 2, 2020 by priyanka.clay6

1 answer

If the integral $\begin{align} \int \frac{5 \tan x}{\tan x - 2} dx = x + a \;In |\sin x - 2 \cos x | + k \end{align}$, then $a$ is equal to

answered May 2, 2020 by priyanka.clay6

1 answer

The negation of the statement "If I become a teacher, then I will open a school" is

answered May 2, 2020 by priyanka.clay6

1 answer

Statement 1 : The sum of the series $ 1 + ( 1 + 2+4) + (4+6+9) + (9+12+16) + .......+ (361 + 380+400)$ is $8000$. Statement 2 : $\displaystyle\sum_{k=1}^{n} (k^3 - ( k-1)^3 ) = n^3$ for any natural number $n$.

answered May 2, 2020 by priyanka.clay6

2 answers

A spherical balloon is filled with $4500 \pi$ cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate if $72 \pi$ cubic meters per minute, then the rate (in meters per minute) at which the radius of the ballon decreases 49 minutes after the leakage began is

answered May 2, 2020 by priyanka.clay6

1 answer

Let $\hat{a}$ and $\hat{b}$ be two unit vectors. If the vectors $\overrightarrow{c} = \hat{a} + 2 \hat{b}$ and $\overrightarrow{d} = 5 \hat{a} - 4 \hat{b}$ are perpendicular to each other, then the angle between $\hat{a}$ and $\hat{b}$ is

answered May 2, 2020 by priyanka.clay6

1 answer

The equation $e^{\sin x }- e^{- \sin x} - 4 = 0 $ has

answered May 2, 2020 by priyanka.clay6

1 answer

Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are 3% each, then error in the value of resistance of the wire is

answered Apr 15, 2020 by ranipushpa1209

1 answer

Helium gas goes through a cycle ABCDA (consisting of two isochoric and two isobaric lines) as shown in figure. Efficiency of this cycle is nearly : (Assume the gas to be close to ideal gas )

answered Mar 21, 2019 by skhazra869

1 answer

In the given transformation, which of the following is the most appropriate reagent ?

answered Dec 21, 2018 by pjmathurkar

1 answer

The population $p(t)$ at time $t$ of a certain mouse species satisfies the differential equation $\frac{dp(t)}{dt} = 0.5\; p(t) -450$. If $p(0) = 850$, then the time at which the population becomes zero is

asked Dec 11, 2018 by pady_1

0 answers

In which of the following pairs the two species are not isostructural ?

asked Dec 11, 2018 by pady_1

0 answers

Iodoform can be prepared from all except :

asked Dec 11, 2018 by pady_1

0 answers

2-Hexyne gives trans-2-Hexene on treatment with :

asked Dec 11, 2018 by pady_1

0 answers

The increasing order of he ionic radii of the given isoelectronic species is :

asked Dec 11, 2018 by pady_1

0 answers

What is DDT among the following :

asked Dec 11, 2018 by pady_1

0 answers

$K_f$ for water is $1.86 \;K\;mol^{-1}$. If your automobile radiator holds 1.0 kg of water, how many grams of ethylene glycol $(C_2H_6O_2)$ must you add to get the freezing point of the solution lowered to $-2.8^{\circ}C$ ?

asked Dec 11, 2018 by pady_1

0 answers

Which branched chain isomer of the hydrocarbon with molecular mass 72 u gives only one isomer of mono substituted alky halide ?

asked Dec 11, 2018 by pady_1

0 answers

The pH of a 0.1 molar solution of the acid HQ is 3. The value of the ionization constant, Ka of this acid is :

asked Dec 11, 2018 by pady_1

0 answers

Iron exhibits +2 and +3 oxidation states. Which of the following statements about iron is incorrect ?

asked Dec 11, 2018 by pady_1

0 answers

For a first order reaction, $(A) \to products$, the concentration of A changes from 0.1 M to 0.025 M in 40 minutes. The rate of reaction when the concentration of A is 0.01 M is :

asked Dec 11, 2018 by pady_1

0 answers

The electrons identified by quantum numbers n and I : (a) n = 4, I = 1 (b) n = 4, I = 0 (c) n = 3, I = 2 (d) n = 3, I = 1 Can be placced in order of increasing energy as :

asked Dec 11, 2018 by pady_1

0 answers

Very pure hydrogen (99.9%) can be made by which of the following processes ?

asked Dec 11, 2018 by pady_1

0 answers

How many chiral compounds are possible on monochlorination of 2-methyl butane ?

asked Dec 11, 2018 by pady_1

0 answers

Ortho-Nitrophenol is less soluble in water than p- and m- Nitrophenols because :

asked Dec 11, 2018 by pady_1

0 answers

Aspirin is known as :

asked Dec 11, 2018 by pady_1

0 answers

Which one of the following statements is correct ?

asked Dec 11, 2018 by pady_1

0 answers

The compressibility factor for a real gas at high pressure is :

asked Dec 11, 2018 by pady_1

0 answers

The equilibrium constant $(K_C)$ for the reaction $N_2(g) + O_2(g) \to 2NO (g)$ at temperature T is $ 4 \times 10^{-4}$. The value of $K_C$ for the reaction, $NO(g) \to 1/2 N_2 (g) + 1/2 O_2 (g)$ at the same temperature is :

asked Dec 11, 2018 by pady_1

0 answers

According toFreundiich adsorption isotherm, which of the following is correct ?

asked Dec 11, 2018 by pady_1

0 answers

The standard reduction potentials for $Zn^{2+}/Zn, Ni^{2+}/Ni$ and $Fe^{2+}/Fe$ are -0.76, -0.23 and -0.44V respectively. The reaction $X + Y^2 \to X^{2+} + Y$ will be spontaneous when :

asked Dec 11, 2018 by pady_1

0 answers

Which of the following on thermal decomposition yields a basic as well as an acidic oxide ?

asked Dec 11, 2018 by pady_1

0 answers

The species which can best serve as an initiator for the cationic polymerization is :

asked Dec 11, 2018 by pady_1

0 answers

The density of a solution prepared by dissolving 120 g of urea ( mol. Mass = 60 u) in 1000 g of water is 1.15 g/mL. The molarity of this solution is :

asked Dec 11, 2018 by pady_1

0 answers

The incorrect expression among the following is :

asked Dec 11, 2018 by pady_1

0 answers

Which of the following compounds can be detected by Molisch's test ?

asked Dec 11, 2018 by pady_1

0 answers

The molecule having smallest bond angle is :

asked Dec 11, 2018 by pady_1

0 answers

Lithium forms body centred cubic structure. The length of the side of its unit cell is 351 pm. Atomic radius of the lithium will be :

asked Dec 11, 2018 by pady_1

0 answers

Which method of purification is represented by the following equation : $Ti(s) + 2I_2 (g) \xrightarrow{523 K} TiI_4 (g) \xrightarrow{1700 K} Ti(s) + 2I_2 (g)$

asked Dec 11, 2018 by pady_1

0 answers

Which among he following will be named as dibromidobis (ethylene diamine) chrominum (III) bromide ?

asked Dec 11, 2018 by pady_1

0 answers

Proton, Deuteron and alpha particle of the same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton, deuteron and alpha particle are respecctively $r_p$, $r_d$ and $r_{\alpha}$. Which one of the following relations is correct ?

asked Dec 11, 2018 by pady_1

0 answers

This question has statement 1 and statement 2. Of the four choices given after the statements, choose the one that best describes the two statements. An insulating solid sphere of radius R has a uniformly positive charge density $\rho$. As a result of this uniform charge distribution there is a finite value of electric potential at the centre of the sphere, at the surface of the sphere and also at a point out side the sphere. The electric potential at infinity is zero. Statement 1 : When a charge q is taken from the centre to the surface of the sphere, its potential energy changes by $\frac{qp}{3 \varepsilon_0}$ Statement 2 : The electric field at a distance r (r < R) from the centre of the sphere is $\frac{\rho r}{ 3 \varepsilon_0}$

asked Dec 11, 2018 by pady_1

0 answers

A spectrometer gives the following reading when used to measure the angle of a prism. Main scale reading : 58.5 degree Vernier scale reading : 09 divisions Given that 1 division on main scale corresponds to 0.5 degree. Total divisions on the vernier scale is 30 and match with 29 divisions of the main scale. The angle of the prism from the above data

asked Dec 11, 2018 by pady_1

0 answers

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