Recent questions tagged class12

Find the equation of the tangent and normal to the curves.$\;y=x-\sin x\cos x, $at$\;x=\large\frac{\pi}{2}$

asked May 1, 2013 by poojasapani_1

1 answer

Find the equation of the tangent and normal to the curves. $y=x^{2}-4x-5$ at $\;x=-2$

asked May 1, 2013 by poojasapani_1

1 answer

Gravel is being dumped from a conveyor belt at a rate of $30\;ft^{3}/min$ and its coarsened such that it forms a pile in the shape of the cone whose base diameter and hight are always equal. How fast is the hight of the pile increasing when the pile is $10$ ft hight?

asked May 1, 2013 by poojasapani_1

1 answer

Two sides of a tringle have length $12$m and $15$m. The angle between them is increasing at a rate of $2^{\circ}/min.$ How fast is the length of third side increasing when the angle between the sides of fixe is $60^{\circ}$?

asked May 1, 2013 by poojasapani_1

1 answer

Two sides of a tringle are $4$m and $5$m in length and the angle between them is increasing at a rate of $0.06$ rad/sec. Find the rate at which the area of tringle is increasing when the angle between the sides of fixed length is $\pi/3$.

asked May 1, 2013 by poojasapani_1

1 answer

At noon, ship $A$ is $100$ km west of ship $B$. Ship $A$ is sailing east at $35$ km/hr and ship $B$ is sailing north at $25$km/hr. How fast is the distance between the ships changing at $4.00$pm.

asked May 1, 2013 by poojasapani_1

1 answer

The altitude of a triangle is increasing at a rate of $1\; cm/min$ while the area of the triangle is increasing at a rate of $2 \;cm^{2}/min$. At what rate is the base of the triangle changing when the altitude is $10$ cm and the area is $100\;cm^{2}$

asked May 1, 2013 by poojasapani_1

1 answer

Find the angle between the pairs of lines: $ \overrightarrow r = 3\hat i + \hat j - 2\hat k + \lambda (\hat i - \hat j - 2\hat k)\: and \: \overrightarrow r = 2\hat i - \hat j - 56\hat k + \mu (3\hat i - 5\hat j - 4\hat k) $

asked Apr 30, 2013 by rvidyagovindarajan_1

1 answer

Newton's law of cooling is given by $\theta=\theta_0^{\circ}e^{-kt},$ where the excess of temperature at zero time is $0^{\circ}_{\circ}C $ and at time $t$ seconds is $\theta ^{\circ}C $. Determine the rate of change of temperature after $40 s,$ given that $\theta_{\cdot}=16^{\circ}C $ and $k=-0.03.\qquad (e^{1.2}=3.3201)$

asked Apr 30, 2013 by poojasapani_1

1 answer

The distince $x$ meters traveled by a vehical in time $t$ seconds after the brakes are applied is given by:$\;x=20 t-\large\frac{5}{3}$$t^{2}$. Determine the distance the car travelled before it stops.

asked Apr 30, 2013 by poojasapani_1

1 answer

The distince $x$ meters traveled by a vehical in time $t$ seconds after the brakes are applied is given by:$\;x=20 t-\large\frac{5}{3}$$t^{2}$. Determine the speed of the vehicle (in km/hr) at the instant the brakes are applied

asked Apr 30, 2013 by poojasapani_1

1 answer

A particle of unit mass moves so that displacement after $t$ secs is given by $x=3\cos(2t-4).$ Find the acceleration and kinetic energy at the end of $2 \;secs.[ K.E =\large\frac{1}{2}$$mv^{2}\quad m $ is mass]

asked Apr 30, 2013 by poojasapani_1

1 answer

A missile fired from ground level rises $x$ metres vertically upwards in $t$ seconds and $x=100t-\large\frac{25}{2}t^{2}$ find the velocity with which the missile strikes the ground

asked Apr 30, 2013 by poojasapani_1

1 answer

A missile fired from ground level rises $x$ metres vertically upwards in $t$ seconds and $x=100t-\large\frac{25}{2}t^{2}$ find the maximum hight reached .

asked Apr 30, 2013 by poojasapani_1

1 answer

A missile fired from ground level rises $x$ metres vertically upwards in $t$ seconds and $x=100t-\large\frac{25}{2}t^{2}$ find the time when the height of the missile is a maximum

asked Apr 30, 2013 by poojasapani_1

1 answer

A missile fired from ground level rises $x$ metres vertically upwards in $t$ seconds and $x=100t-\large\frac{25}{2}t^{2}$ find the initial velocity of the missile.

asked Apr 30, 2013 by poojasapani_1

1 answer

Prove that the curved surface area of a sphere of radius $r$ intercepted between two parallel planes at a distance $a$ and $b$ from the centre of the sphere is $\;2\pi r(b-a)$ and hence deduct the surface area of the sphere,$(b>a)$

asked Apr 30, 2013 by poojasapani_1

1 answer

Find the surface area of the solid generated by revolving the arc of the parabola$\;y^{2}=4ax$, bounded by its latus rectum about $x$- axis.

asked Apr 30, 2013 by poojasapani_1

1 answer

Find the length of the curve $x=a(t-\sin t),y=a(1-\cos t)$ between $t=0$and $\pi$.

asked Apr 30, 2013 by poojasapani_1

1 answer

Find the perimeter of the circle with radius $a$.

asked Apr 30, 2013 by poojasapani_1

1 answer

The area of the region bounded by the curve $xy=1, x$-axis$\;x=1.$ Find the volume of the solid generated by revolving the area mentioned about $x$-axis.

asked Apr 30, 2013 by poojasapani_1

1 answer

Derive the formula for the volume of a right circular cone with radius $'r'$ and height $'h'$.

asked Apr 30, 2013 by poojasapani_1

1 answer

Find the volume of the solid that results when the region enclosed by the given curve: $(11$$to14)$$\large\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ is revolved about major axis $a>b>0.$

asked Apr 30, 2013 by poojasapani_1

1 answer

Find the volume of the solid that results when the region enclosed by the given curve: $\;y=x^{3},x=0,y=1$ is revolved about the $y$-axis.

asked Apr 30, 2013 by poojasapani_1

1 answer

Find the volume of the solid that results when the region enclosed by the given curve: $(11$$to14)$ $2ay2=x(x-a)2$ is revolved about $x$-axis ,$a>0$

asked Apr 28, 2013 by poojasapani_1

1 answer

If $A=\{1,2,3,4\}$ and $B=\{1,2\}$, then the number of onto functions from $A$ to $B$ is

asked Apr 28, 2013 by rvidyagovindarajan_1

1 answer

Find the volume of the solid that results when the region enclosed by the given curve: $(11$$to14)$$y=1+x^{2},x=1,x=2,y=0$ is revolved around the $x$- axis.

asked Apr 28, 2013 by poojasapani_1

1 answer

Find the area of the circle whose radius is $a$ .

asked Apr 28, 2013 by poojasapani_1

1 answer

Find the common area enclosed by the parabolas $4y^{2}=9x$ and $3x^{2}=16y$

asked Apr 28, 2013 by poojasapani_1

1 answer