Recent questions and answers in 2001

......... process is used for the removal of hardness of water :

answered Mar 24, 2020 by sangethamadhu82

1 answer

The events A and B have probabilities 0.25 and 0.50 respectively. The probability that both A and B occur simultaneously is 0.14, then the probability that neither A nor B occurs, is :

answered Feb 4, 2020 by smitha.ds

1 answer

In a nuclide, one a.m.u of mass is dissipated into energy to bind its nucleons. The energy equivalent of this mass is :

answered Dec 20, 2019 by azharwahab950

1 answer

The energy of an electron present in Bohr's second orbit of hydrogen atom is :

answered Jul 15, 2019 by sharmaaparna1

1 answer

Find the binomial probability distribution whose mean is 3 and variance is 2.

answered Jul 15, 2019 by ritishgulati2018

1 answer

The r.m.s velocity of $CO_2$ at a temperature $T$ (in kelvin) is $x\; cm\;sec^{-1}$. At what temperature (in kelvin), the r.m.s. velocity of nitrous oxide would be $4x\;cm\;sec^{-1}$ ? (Atomic weights of $C, \; N$ and $O$ are respectively $12, \; 14$ and $16$) :

answered Jul 14, 2019 by vsimmi196

1 answer

If the normal to the parabola $y^2 = 4x$ at $P(1,2)$ meets the parabola again in $Q$, then co-ordinates of $Q$ are :

answered Jul 10, 2019 by dattawakde7507

1 answer

A magnet of length $10\; cm$ and magnetic moment $1\; Am^2$ is placed along side AB of an equilateral triangle ABC. If the length of the side AB is $10\; cm$. The magnetic induction at the point 'C' is : $(\mu_0 = 4 \pi \times 10^{-7} Hm^{-1})$

answered Jul 8, 2019 by syedataj761

1 answer

Absolute alcohol (100% alcohol) is prepared by distilled rectified spirit over :

answered Jul 7, 2019 by akbhavya67

1 answer

The equation $16x^2 + y^2 + 8xy - 74x -78 y +212 = 0$ represents :

answered Mar 9, 2019 by nsravni180

1 answer

In order to double the frequency of the fundamental note emitted by a stretched string, the length is reduced to $\frac{3}{4}^{th}$ of the original length and the tension is changed. The factor by which the tension is to be changed is :

answered Mar 5, 2019 by sangeethav838

1 answer

A steel meter scale is to be ruled so hat millimeter intervals are accurate within about $5 \times 10^{-5}m$ at a certain temperature. The maximum temperature variation allowable during the ruling is: (Coefficient of linear expansion of steel = $10 \times 10^{-6} K^{-1}$)

answered Feb 25, 2019 by upkarsingh2580

1 answer

The shadow of a tower standing on a level ground is found to be 60 metres longer when the sun's altitude is $30^{\circ}$ than when it is $45^{\circ}$. The height of the tower is :

asked Dec 11, 2018 by pady_1

0 answers

In a triangle $ABC, \;a^2 \sin 2C + c^2 \sin 2A $ is equal to :

asked Dec 11, 2018 by pady_1

0 answers

In a triangle $ABC, \; \frac{a}{b^2-c^2} + \frac{c}{b^2-a^2} = 0$, then $B$ is equal to :

asked Dec 11, 2018 by pady_1

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In a triangle $ABC$, $\frac{\cos C + \cos A}{c+a} + \frac{\cos B}{b}$ is equal to :

asked Dec 11, 2018 by pady_1

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$\sin^{-1} \begin{pmatrix}\frac{x}{\sqrt{1-x^2}} \end{pmatrix}$ is equal to :

asked Dec 11, 2018 by pady_1

0 answers

$\sec^2 (\tan^{-1}2) + \mathrm{cosec^2} (\cot^{-1} 3)$ is equal to :

asked Dec 11, 2018 by pady_1

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The equation $\sqrt{3}\sin x +\cos x = 4$, has:

asked Dec 11, 2018 by pady_1

0 answers

If $ A, B, C, D$ are angles of a cyclic quadrilateral, then $\cos A + \cos B + \cos C + \cos D$ is equal to :

asked Dec 11, 2018 by pady_1

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$\cos^2 ( \frac{\pi}{6} + \theta) - \sin^2 (\frac{\pi}{6} - \theta)$ is equal to :

asked Dec 11, 2018 by pady_1

0 answers

If $\mathrm{cosec} \theta = \frac{p+q}{p-q}$, then $\cot (\frac{\pi}{4} + \frac{\theta}{2} ) $ is equal to :

asked Dec 11, 2018 by pady_1

0 answers

$\frac{\sin 5 \theta}{\sin \theta}$ is equal to :

asked Dec 11, 2018 by pady_1

0 answers

If $\theta = \frac{\pi}{6}$, then the $10^{th}$ term of $1 + (\cos \theta + i \sin \theta) +(\cos \theta + i \sin \theta)^2+(\cos \theta + i \sin \theta)^3 + ... $ is equal to :

asked Dec 11, 2018 by pady_1

0 answers

If $\begin{vmatrix} 1-i & i \\ 1+2i & -i \end{vmatrix} = x + iy$, then $x$ is equal to :

asked Dec 11, 2018 by pady_1

0 answers

If $a$ is a complex number and $b$ is a real number, then the equation $\overline{a} + a + b =0$ represents a:

asked Dec 11, 2018 by pady_1

0 answers

If $A = \begin{bmatrix}0 & 2 \\ 3 & - 4 \end{bmatrix}, \; hA = \begin{bmatrix} 0 & 3a \\ 2b & 24 \end{bmatrix}$, then the value of $h, \;a,\;b$ are respectively :

asked Dec 11, 2018 by pady_1

0 answers

A square matrix $[a_{ij}]$ in which $a_{ij} =0$ for $i \neq j$ and $a_{ij}=k$ (constant) for $i=j$ is called a:

asked Dec 11, 2018 by pady_1

0 answers

If $A = \begin{bmatrix} -2 & 2 \\ -3 & 2 \end{bmatrix}, \; B = \begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$, then $(B^{-1}A^{-1})^{-1}$ is equal to :

asked Dec 11, 2018 by pady_1

0 answers

The bi-quadratic equation, two of whose roots are $1+i, \; 1-\sqrt{2}$, is :

asked Dec 11, 2018 by pady_1

0 answers

$\displaystyle\lim_{x \to 0} \frac{\sin x \sin^{-1} x}{x^2}$ is equal to :

asked Dec 11, 2018 by pady_1

0 answers

If $1$ is a multiple root of order 3 for the equation $x^4 - 2x^3 + 2x-1=0$, then the other root is :

asked Dec 11, 2018 by pady_1

0 answers

The roots of the equation $x^3 - 14 x^2 + 56x -64=0$ are in :

asked Dec 11, 2018 by pady_1

0 answers

Each of the roots of the equation $x^3 - 6x^2 + 6x-5 =0$ are increased by $h$. So that the new transformed equation does not contain $x^2$ term, then $h$ is equal to :

asked Dec 11, 2018 by pady_1

0 answers

$20^{2-3x^2} = (40\sqrt{5})^{3x^2-2}$, then $x$ is equal to :

asked Dec 11, 2018 by pady_1

0 answers

If $\alpha, \beta$ are the roots of the equation $x^2 + bx + c =0$ and $\alpha + h, \; \beta+h$ are the roots of the equation $x^2 + qx + r =0$, then $h$ is equal to :

asked Dec 11, 2018 by pady_1

0 answers

$|x| <1$, the coefficient of $x^3$ in the expansion of $\log (1+x+x^2)$ in ascending powers of $x$, is :

asked Dec 11, 2018 by pady_1

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$\frac{2}{2!} + \frac{2+4}{3!} + \frac{2+4+6}{4!}$ + ...$ is equal to:

asked Dec 11, 2018 by pady_1

0 answers

If $\frac{x-4}{x^2-5x-2k} = \frac{2}{x-2} - \frac{1}{x+k'}$ then $k$ is equal to :

asked Dec 11, 2018 by pady_1

0 answers

If $(1+x)^n = C_0 + C_1x + C_2x^2 + ....+ C_nx^n$, then $C_0+2C_1 + 3C_2 + ....+(n+1)C_n$ is equal to :

asked Dec 11, 2018 by pady_1

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The co-efficient of $x^4$ in the expansion of $\frac{(1-3x)^2}{(1-2x)}$ is equal to :

asked Dec 11, 2018 by pady_1

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$1+\frac{1}{4} + \frac{1.3}{4.8} + \frac{1.3.5}{4.8.12} + ...$ is equal to :

asked Dec 11, 2018 by pady_1

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Using the digits $0, 2, 4, 6, 8$ not more than once in any number, the number of 5 digited numbers that can be formed, is :

asked Dec 11, 2018 by pady_1

0 answers

The number of ways in which 5 boys and 4 girls sit around a circular tables. So that no two girls sit together is :

asked Dec 11, 2018 by pady_1

0 answers

If $y = A \cos nx + B \sin nx$, then $y_2 = n^2y$ is equal to :

asked Dec 11, 2018 by pady_1

0 answers

If $2^3 + 4^3 + 6^3 + ....+(2n)^3 = hn^2 (n+1)^2$, then $h$ is equal to :

asked Dec 11, 2018 by pady_1

0 answers

If $x =\log_{0.1} 0.001, \; y = \log_9 81 $, then $\sqrt{x -2\sqrt{y}}$ is equal to :

asked Dec 11, 2018 by pady_1

0 answers

$\frac{\sqrt{8 +\sqrt{28} } + \sqrt{8 - \sqrt{28}}}{\sqrt{8 +\sqrt{28} } - \sqrt{8 - \sqrt{28}}} $ is equal to :

asked Dec 11, 2018 by pady_1

0 answers

Two functions $f : R \to R, \; g: R \to R$ are defined as follows $ f(x) = \begin{cases} 0 , & \quad \text{x } \text{ is rational}\\ 1, & \quad \text{x} \text{ is irrational} \end{cases}$ $ g(x) = \begin{cases} -1 , & \quad \text{x } \text{ is rational}\\ 0, & \quad \text{x} \text{ is irrational} \end{cases}$ Then $(fog) (\pi) + (gof)(e)$ is equal to :

asked Dec 11, 2018 by pady_1

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Let $f : R \to R$ is defined by $ f(x) = \begin{cases} x+2, & x \leq -1 \\ x^2 , & -1 < x <1 \\ 2-x, & x \geq 1 \end{cases}$ Then the value of $f(-1.75) + f(0.5) + f(1.5)$ is :

asked Dec 11, 2018 by pady_1

0 answers

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