Recent questions tagged easy

The area of the region bounded by the curve $y=x+1$ and the lines $x=2$ and $x=3$ is \[(A)\frac{7}{2} sq.units\quad(B)\;\frac{9}{2}sq. units\quad(C)\frac{11} {2}sq.units\quad(D)\frac{13}{2} sq.units\]

asked Jan 16, 2013 by sreemathi.v

1 answer

The area of the region bounded by the circle $x^2+y^2=1$ is \[(A)\;2\pi sq.units\quad(B)\;\pi sq. units\quad(C)\;3\pi sq.units\quad(D)4\pi sq.units\]

asked Jan 16, 2013 by sreemathi.v

1 answer

The area of the region bounded by the curve $y=sin x$ between the ordinates $x=0$ and $x=\large\frac{\pi}{2}$ and the x-axis is

asked Jan 16, 2013 by sreemathi.v

1 answer

The area of the region bounded by the curve $y=\cos x$ between $x=0$ and $x=\pi$ is \begin{array}{1 1}(A)\;2 sq.units & (B)\;4 sq.units\\(C)\;3 sq.units & (D)\;1sq.units \end{array}

asked Jan 16, 2013 by sreemathi.v

1 answer

Evaluate [ 1 2 1 ] $ \begin{bmatrix} 2 \\ 4 \\ 2 \end{bmatrix}$

asked Jan 16, 2013 by thanvigandhi_1

1 answer

Let $ \begin{bmatrix} 3 & y \\ x & 1 \end{bmatrix} = \begin{bmatrix} 3 & 2 \\ 4 & 1 \end{bmatrix} $. Find the possible values of x and y, if x, y $ \in $ N.

asked Jan 16, 2013 by thanvigandhi_1

1 answer

The area of the region bounded by the curve $y=\sqrt {16-x^2}$ and x-axis is \begin{array}{1 1}(A)\;8\pi \;sq.units & (B)\;20\pi\; sq.units\\(C)\;16\pi\; sq.units & (D)\;256\pi\; sq.units \end{array}

asked Jan 16, 2013 by sreemathi.v

1 answer

Find the area bounded by the curve y=sinx between $x=0$ and $x=2\pi$.

asked Jan 16, 2013 by sreemathi.v

1 answer

Using integration,find the area of the region bounded by the line $2y=5x+7,x$-axis and the lines $x=2$ and $x=8.$

asked Jan 16, 2013 by sreemathi.v

1 answer

Calculate the area under the curve $y=2\sqrt x$ included between the lines $x=0$ and $x=1$.

asked Jan 16, 2013 by sreemathi.v

1 answer

Sketch the region $\{(x,0):y=\sqrt {4-x^2}$} and $x$-axis.Find the area of the region using integration.

asked Jan 16, 2013 by sreemathi.v

1 answer

Find the area of the region bounded by the line $x=2$ and the parabola $y^2=8x$.

asked Jan 16, 2013 by sreemathi.v

1 answer

The value of $\large\int\limits_{-\pi}^\pi$$\sin^3x\cos^2x dx$ is___________.

asked Jan 15, 2013 by sreemathi.v

1 answer

If $\Large \int\frac{1}{1+4x^2}$$dx=\large\frac{\pi}{8},$then a=____________.

asked Jan 15, 2013 by sreemathi.v

1 answer

$\int\Large{\frac{x+3}{(x+4)^2}}\normalsize e^xdx$=___________.

asked Jan 15, 2013 by sreemathi.v

1 answer

If $ \begin{bmatrix} 3a-b & -2b \\ 3 & 7 \end{bmatrix} = \begin{bmatrix} 5 & 3 \\ 3 & 7 \end{bmatrix}$ then find a.

asked Jan 15, 2013 by thanvigandhi_1

1 answer

If $A = \begin{bmatrix} 2 & 4 \\ 3 & 2 \end{bmatrix}$ and $ B = \begin{bmatrix} 1 & 3 \\ -2 & 5 \end{bmatrix}$, then find BA.

asked Jan 15, 2013 by thanvigandhi_1

1 answer

$\Large \int\limits_0^\frac{\pi}{2}\normalsize \sqrt {1-\sin2x}\;dx$ is equal to $(A)\;0\quad(B)\;2\quad(C)\;1\quad(D)\;-1$

asked Jan 15, 2013 by sreemathi.v

1 answer

$\Large \int\limits_\frac{-\pi}{4}^\frac{\pi}{4}\frac{dx}{1+\cos2x}$ is equal to $(A)\;1\quad(B)\;2\quad(C)\;3\quad(D)\;4$

asked Jan 15, 2013 by sreemathi.v

1 answer

If $\large \frac{x^3dx}{\sqrt{1-x^2}}=\normalsize a(1-x^2)^{\Large\frac{3}{2}}+b\sqrt{1-x^2}+C$,then

asked Jan 15, 2013 by sreemathi.v

1 answer

$\Large \int\frac{x^3}{x+1}$ is equal to\begin{array}{1 1}(A)\;x+\frac{x^2}{2}+\frac{x^3}{3}-log\mid1-x\mid+C & (B)\;x+\frac{x^2}{2}-\frac{x^3}{3}-log\mid1-x\mid+C\\(C)\;x-\frac{x^2}{2}-\frac{x^3}{3}-log\mid1+x \mid+C & (D)\;x-\frac{x^2}{2}+\frac{x^3}{3}-log\mid1+x \mid+C\end{array}

asked Jan 15, 2013 by sreemathi.v

1 answer

$\Large \int\frac{\cos 2x-\cos 2\theta}{\cos x-\cos\theta}\normalsize dx$ is equal to\begin{array}{1 1}(A)\;2(\sin x+x\cos\theta)+C & (B)\;2(\sin x-x\cos\theta)+C\\(C)\;2(\sin x+2x\cos\theta)+C & (D)\;2(\sin x-2x\cos\theta)+C\end{array}

asked Jan 15, 2013 by sreemathi.v

1 answer

Evaluate the following: $\int\limits_0^1\frac{xdx}{\sqrt{1+x^2}}$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following $\int\frac{x}{x^4-1}dx$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following $\displaystyle\int\frac{dx}{\sqrt {16-9x^2}}$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following $\int\sqrt{1+\sin x}\;dx$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following $\int\frac{(\sin x+\cos x)}{\sqrt {1+\sin 2x}}dx$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following$\int\frac{dx}{1+\cos x}$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following $\large\int\frac{(1+\cos x)}{x+\sin x}dx$

asked Jan 14, 2013 by sreemathi.v

1 answer

Verify the following $ \large\int\frac{2x+3}{x^2+3x}dx=log \mid x^2+3x\mid+C$

asked Jan 14, 2013 by sreemathi.v

1 answer

The equation of normal to the curve y=tan x at (0,0) is___________.

asked Jan 12, 2013 by sreemathi.v

1 answer

If x is real,the minimum value of $x^2-8x+17$ is

asked Jan 11, 2013 by sreemathi.v

1 answer

The function f(x)+tan x-x

asked Jan 11, 2013 by sreemathi.v

1 answer

Which of the following functions is decreasing on $\bigg(0,\frac{1}{2}\bigg)$

asked Jan 11, 2013 by sreemathi.v

1 answer

The function $f(x)=4\sin^3x-6\sin^2x+12sin x+100$ is strictly

asked Jan 11, 2013 by sreemathi.v

1 answer

$y=x(x-3)^2$ decreases for the values of x given by:

asked Jan 11, 2013 by sreemathi.v

1 answer

Let the $f:R\rightarrow R$ be defined by $f(x)=2x+\cos x,$then

asked Jan 11, 2013 by sreemathi.v

1 answer

Show that the matrix $ A = \begin{bmatrix} 0 & 1 & -1 \\ -1 & 0 & 1 \\ 1 & -1 & 0 \end{bmatrix} $ is a skew - symmetric matrix.

asked Jan 11, 2013 by thanvigandhi_1

1 answer

If A, B are symmetric matrices of the same order then AB-BA is a : \[ \begin{array} ((A)\: skew\: symmetric \: matrix \\ (B) \: symmetric\: matrix \\ (C)\: Zero \: matrix \\ (D)\: Identity \: matrix \end{array} \]

asked Jan 11, 2013 by thanvigandhi_1

1 answer

The tangent to the curve $y=e^{2x}$ at the point $(0,1)$ meets x-axis at:

asked Jan 11, 2013 by sreemathi.v

1 answer

The points at which the tangents to be curve $y=x^3-12x+18$ are parallel to x-axis are:

asked Jan 11, 2013 by sreemathi.v

1 answer

If $y=x^4-10$ and if x changes from $2$ to $1.99$,what is the change in y

asked Jan 11, 2013 by sreemathi.v

1 answer

If the curve $ay+x^2=7$ and $x^3=y,$ cut orthogonally at $(1,1)$ then the value of a is

asked Jan 11, 2013 by sreemathi.v

1 answer

The curve $y=x^\frac{1}{5}$ has at

asked Jan 11, 2013 by sreemathi.v

1 answer

The sides of an equilateral triangle are increasing at the rate of 2cm/sec.The rate at which the area increases ,when side is 10cm is

asked Jan 11, 2013 by sreemathi.v

1 answer

Prove that $f(x)=\sin x+\sqrt 3\cos x$ has maximum value at $x=\Large\frac{1}{6}$.

asked Jan 11, 2013 by sreemathi.v

1 answer

At what point,the slope of the curve $y=-x^3+3x^2+9x-27$ is maximum?Also find the maximum slope.

asked Jan 11, 2013 by sreemathi.v

1 answer

At what points on the curve $x^2+y^2-2x+4y+1=0$,the tangents are parallel to the y-axis?

asked Jan 11, 2013 by sreemathi.v

1 answer

x and y are the sides of two squares such that $y=x-x^2$.Find the rate of change of the area of second square with respect to the area of first square.

asked Jan 11, 2013 by sreemathi.v

1 answer

Find the approximate volume of metal in a hollow spherical shell whose internal and external radii are 3cm and 3.0005cm,respectively.

asked Jan 11, 2013 by sreemathi.v

1 answer

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