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Recent questions tagged medium
Questions
Show that the point $(x,y)$ given by $x=\large\frac{2at}{1+t^2}$ and $y=\large\frac{a(1-t^2)}{1+t^2}$ lies on a circle for all real values of $t$ such that $-1\leq t \leq 1$ where $a$ is any given real numbers.
cbse
class11
math
conic-sections
circle
exemplar
sec-b
medium
q2
asked
Oct 17, 2014
by
sreemathi.v
1
answer
The equation of the ellipse whose focus is $(1,-1)$,the directrix the line $x-y-3=0$ and eccentricity $\large\frac{1}{2}$ is
cbse
class11
math
conic-sections
ellipse
exemplar
sec-a
medium
q54
asked
Oct 16, 2014
by
sreemathi.v
2
answers
Equation of the circle with centre on the $y$-axis and passing through the origin and the point $(2,3)$ is
cbse
class11
math
conic-sections
circle
exemplar
sec-a
medium
q49
asked
Oct 16, 2014
by
sreemathi.v
1
answer
Equation of a circle which passes through $(3,6)$ and touches the axes is
cbse
class11
math
conic-sections
circle
exemplar
sec-a
medium
q48
asked
Oct 16, 2014
by
sreemathi.v
1
answer
The equation of the hyperbola with vertices at $(0,\pm 6)$ and eccentricity $\large\frac{5}{3}$ is _________ and its foci are ___________
cbse
class11
math
conic-sections
hyperbola
exemplar
sec-a
medium
q46
asked
Oct 16, 2014
by
sreemathi.v
1
answer
The equation of the parabola having focus at $(-1,-2)$ and the directrix $x-2y+3=0$ is _________
cbse
class11
math
conic-sections
parabola
exemplar
sec-a
medium
q45
asked
Oct 16, 2014
by
sreemathi.v
1
answer
The equation of the ellipse having foci $(0,1),(0,-1)$ and minor axis of length $\sqrt 5$ is ____________
cbse
class11
math
conic-sections
ellipse
exemplar
sec-a
medium
q44
asked
Oct 16, 2014
by
sreemathi.v
1
answer
An ellipse is described by using an endless string which is passed over two pins.If the axes are 6 cm and 4 cm,the length of the string and distance between the pins are ____________
cbse
class11
math
conic-sections
ellipse
exemplar
sec-a
medium
q43
asked
Oct 16, 2014
by
sreemathi.v
1
answer
The equation of the circle circumscribing the triangle whose sides are the lines $y=x+2,3y=4x,2y=3x$ is _____________
cbse
class11
math
conic-sections
circle
exemplar
sec-c
medium
q42
asked
Oct 15, 2014
by
sreemathi.v
1
answer
The equation of the circle having centre at $(3,-4)$ and touching the line $5x+12y-12=0$ is __________
cbse
class11
math
conic-sections
circle
exemplar
sec-a
medium
q41
asked
Oct 15, 2014
by
sreemathi.v
1
answer
State whether the following statement is True or False : The locus of the point of intersection of lines $\sqrt 3x-y-4\sqrt 3k=0$ and $\sqrt 3kx+ky-4\sqrt 3=0$ for different value of $k$ is a hyperbola whose eccentricity is 2.
cbse
class11
math
conic-sections
hyperbola
exemplar
sec-a
medium
q40
asked
Oct 15, 2014
by
sreemathi.v
1
answer
State whether the following statement is True or False : The line $2x+3y=12$ touches the ellipse $\large\frac{x^2}{9}+\frac{y^2}{4}$$=2$ at the point $(3,2)$
cbse
class11
math
conic-sections
ellipse
exemplar
sec-a
medium
q39
asked
Oct 15, 2014
by
sreemathi.v
1
answer
State whether the following statement is True or False : The line $lx+my+n=0$ will touch the parabola $y^2=4ax$ if $ln=am^2$
cbse
class11
math
conic-sections
parabola
exemplar
sec-a
medium
q37
asked
Oct 15, 2014
by
sreemathi.v
1
answer
State whether the following statement is True or False: If the line $lx+my=1$ is a tangent to the circle $x^2+y^2=a^2$,then the point $(l,m)$ lies on a circle.
cbse
class11
math
conic-sections
circle
exemplar
sec-a
medium
q35
asked
Oct 15, 2014
by
sreemathi.v
1
answer
State whether the following statement is True or False:The shortest distance from the point $(2,-7)$ to the circle $x^2+y^2-14x-10y-151=0$ is equal to $5$.
cbse
class11
math
conic-sections
circle
exemplar
sec-a
medium
q34
asked
Oct 15, 2014
by
sreemathi.v
1
answer
Find the equation of the hyperbola with foci $(0,\pm\sqrt{10})$,passing through $(2,3)$.
cbse
class11
math
conic-sections
hyperbola
exemplar
sec-b
medium
q32-c
asked
Oct 15, 2014
by
sreemathi.v
1
answer
Show that the set of all points such that the difference of their distances from $(4, 0)$ and $(-4, 0)$ is always equal to $2$ represent a hyperbola.
cbse
class11
math
conic-sections
hyperbola
exemplar
sec-b
medium
q31
asked
Oct 14, 2014
by
sreemathi.v
1
answer
Find the equation of the set of all points the sum of whose distances from the points $(3, 0)$ and $(9, 0)$ is 12.
cbse
class11
math
conic-sections
exemplar
sec-b
medium
q29
asked
Oct 14, 2014
by
sreemathi.v
1
answer
Find the equation of a circle passing through the point $(7,3)$ having radius $3$ units and whose centre lies on the line $y=x-1$.
cbse
class11
math
conic-sections
circle
exemplar
sec-c
medium
q27
asked
Oct 14, 2014
by
sreemathi.v
1
answer
Find the equation of a circle of radius 5 which is touching another circle $x^2+y^2-2x-4y-20=0$ at $(5,5)$.
cbse
class11
math
conic-sections
circle
exemplar
sec-b
medium
q26
asked
Oct 14, 2014
by
sreemathi.v
1
answer
Find the equation of a circle whose centre $(3,-1)$ and which cuts off a chord of length $6$ units on the line $2x-5y+18=0$.
cbse
class11
math
conic-sections
circle
exemplar
sec-b
medium
q25
asked
Oct 13, 2014
by
sreemathi.v
1
answer
Find the equation of the circle which passes through the points $(2,3)$ and $(4,5)$ and the centre lies on the straight line $y-4x+3=0$.
cbse
class11
math
conic-sections
circle
exemplar
sec-c
medium
q24
asked
Oct 13, 2014
by
sreemathi.v
1
answer
If the lines $2x-3y=5$ and $3x-4y=7$ are the diameters of a circle of area 154 square units,then obtain the equation of the circle.
cbse
class11
math
conic-sections
circle
exemplar
sec-c
medium
q23
asked
Oct 13, 2014
by
sreemathi.v
1
answer
Find the equation of the hyperbola with eccentricity $\large\frac{3}{2}$ and foci at $(\pm 2,0)$.
cbse
class11
math
conic-sections
hyperbola
exemplar
sec-a
medium
q22
asked
Oct 10, 2014
by
sreemathi.v
1
answer
If the distance between the foci of a hyperbola is $16$ and its eccentricity is $\sqrt 2$,then obtain equation of the hyperbola.
cbse
class11
math
conic-sections
hyperbola
exemplar
sec-b
medium
q20
asked
Oct 10, 2014
by
sreemathi.v
1
answer
If the line $y=mx+1$ is tangent to the parabola $y^2=4x$ then find the value of $m$.
cbse
class11
math
conic-sections
parabola
exemplar
sec-a
medium
q19
asked
Oct 10, 2014
by
sreemathi.v
1
answer
If the points $(0,4)$ and $(0,2)$ are respectively the vertex and focus of a parabola,then find the equation of the parabola.
cbse
class11
math
conic-sections
parabola
exemplar
sec-a
medium
q18
asked
Oct 10, 2014
by
sreemathi.v
1
answer
Find the coordinates of a point on the parabola $y^2 = 8x$ whose focal distance is 4.
cbse
class11
math
conic-sections
parabola
exemplar
sec-a
medium
q16
asked
Oct 10, 2014
by
sreemathi.v
1
answer
Find the equation of ellipse whose eccentricity is $\large\frac{2}{3}$ , latus rectum is 5 and the centre is (0, 0).
cbse
class11
math
conic-sections
ellipse
exemplar
sec-b
medium
q14
asked
Oct 9, 2014
by
sreemathi.v
1
answer
If the eccentricity of an ellipse is $\large\frac{5}{8}$ and the distance between its foci is 10, then find latus rectum of the ellipse.
cbse
class11
math
conic-sections
ellipse
exemplar
sec-b
medium
q13
asked
Oct 9, 2014
by
sreemathi.v
1
answer
If the latus rectum of an ellipse is equal to half of minor axis,then find its eccentricity.
cbse
class11
math
conic-sections
ellipse
exemplar
sec-b
medium
q11
asked
Oct 9, 2014
by
sreemathi.v
1
answer
Find the equation of the circle having $(1,-2)$ as its centre and passing through $3x+y=14,2x+5y=18$.
cbse
class11
math
conic-sections
circle
exemplar
sec-b
medium
q8
asked
Oct 8, 2014
by
sreemathi.v
1
answer
If one end of a diameter of the circle $x^2+y^2-4x-6y+11=0$ is $(3,4)$,then find the coordinate of the other end of the diameter.
cbse
class11
math
conic-sections
circle
exemplar
sec-b
medium
q7
asked
Oct 8, 2014
by
sreemathi.v
1
answer
Find the equation of a circle which touches both the axes and the line $3x-4y+8=0$ and lies in the third quadrant.
cbse
class11
math
conic-sections
circle
exemplar
sec-b
medium
q6
asked
Oct 8, 2014
by
sreemathi.v
1
answer
Suppose 2 J of work is needed to stretch a spring from its natural length of 30 cm to a length of 42 cm.Then how far beyond its natural length will a force of 30 N keep the spring stretched?
jeemain
physics
class11
work-power-energy
ch6
work-done-by-a-spring
hookes-law
medium
asked
Sep 2, 2014
by
sreemathi.v
1
answer
Suppose 2 J of work is needed to stretch a spring from its natural length of 30 cm to a length of 42 cm.Then how much work is needed to stretch it from 30 cm to 40 cm.
jeemain
physics
class11
work-power-energy
ch6
work-done-by-a-spring
hookes-law
medium
asked
Sep 2, 2014
by
sreemathi.v
1
answer
A spring has a length of 15.4 cm and is hanging vertically from a support point above it.A weight with a mass of 0.200 kg is attached to the spring,causing it to extend to a length of 28.6cm.What is the value of the spring constant?
jeemain
physics
class11
work-power-energy
ch6
work-done-by-a-spring
hookes-law
medium
asked
Sep 1, 2014
by
sreemathi.v
1
answer
A spring has a natural length of 18 inches and a force of 20 lbs is required to stretch and hold the spring to a length of 24 inches. What is the work required in ft-lbs to stretch the spring from a length of 21 inches to a length of 26 inches?
jeemain
physics
class11
work-power-energy
ch6
work-done-by-a-spring
hookes-law
medium
asked
Sep 1, 2014
by
sreemathi.v
1
answer
A spring has a natural length of 1 meter.A force of 25 Newtons stretches the spring by $\large\frac{1}{4}$ of a meter.Determine how much work is done by stretching the spring from a length of 1.5 meters to 2.5 meters.
jeemain
physics
class11
work-power-energy
ch6
work-done-by-a-spring
hookes-law
medium
asked
Sep 1, 2014
by
sreemathi.v
1
answer
A spring has natural length 30 cm,and a force of 50 Newtons(N) is required to extend it to 35 cm.How much work is required to extend it from 32 to 36 cm?
jeemain
physics
class11
work-power-energy
ch6
work-done-by-a-spring
hookes-law
medium
asked
Sep 1, 2014
by
sreemathi.v
1
answer
A spring has a natural length of 20 cm. A 40 N force is required to stretch (and hold the spring) to a length of 30 cm. How much work is done in stretching the spring from 35 cm to 38 cm?
jeemain
physics
class11
work-power-energy
ch6
work-done-by-a-spring
hookes-law
medium
asked
Sep 1, 2014
by
sreemathi.v
1
answer
A block whose mass $m$ is $15\; kg$ slides on a horizontal frictionless surface with a constant speed $v$ of $3.7m/s$.It is brought momentarily to rest as it compresses a spring in its path.By what distance $d$ is the spring compressed?The spring constant $k$ is $1500\;N/m$
jeemain
physics
class11
work-power-energy
ch6
work-done-by-a-spring
medium
asked
Sep 1, 2014
by
sreemathi.v
1
answer
We have a cable that weighs 2lbs/ft attached to a bucket filled with coal that weighs 800lbs.The bucket is initially at the bottom of a 500 ft mine shaft.Determine the amount of work required to lift the bucket to the midpoint of the shaft.
jeemain
physics
class11
work-power-energy
ch6
work-done-by-a-variable-force
medium
asked
Sep 1, 2014
by
sreemathi.v
1
answer
A particle of mass 0.5 kg moves on the positive $x$-axis under the action of a variable force $\large\frac{40}{x^2}$ newtons,directed away from origin..The particle passes through a point 2 metres from origin,with velocity $8ms^{-1}$ away from origin. Its experiences a constant resistance force of 6 newtons. Find the speed of the particle when it is 5 metres from origin.
jeemain
physics
class11
work-power-energy
ch6
work-done-by-a-variable-force
medium
asked
Sep 1, 2014
by
sreemathi.v
1
answer
A body is sliding down a rough inclined plane of angle of inclination $\theta$ for which the coefficient of friction varies with distance x as $\mu (x)=kx$, where k is a constant . Here x is the distance moved by the body down the plane . The net force on the body will be zero at a distance $x_0$ given by :
jeemain
physics
class11
ch5
laws-of-motion
inclined-plane-with-effect-of-friction
newtons-second-law
medium
asked
Aug 29, 2014
by
meena.p
1
answer
Two blocks of masses $m_1=5 \;kg$ and $m_2= 6\;kg$ are connected by a light string passing over a light friction less pulley as shown in fig. The mass $m_1$ is at rest on the inclined plane and mass $m_2$ hangs vertically . If the angle of incline $\theta =30^{\circ}$, What is the magnitude and direction of the force of friction on the $5\;kg$ block . Take $g= 10 ms^{-2}$
jeemain
physics
class11
ch5
laws-of-motion
inclined-plane-with-effect-of-friction
newtons-second-law
medium
asked
Aug 29, 2014
by
meena.p
1
answer
A block of mass m = 2kg is raised vertically upwards by means of a massless string through a distance of S=4m with a constant acceleration a=2.2ms$^{-2}$.Find the net work done on the block.
jeemain
physics
class11
work-power-energy
ch6
work-done-by-a-
constant-force
medium
asked
Aug 28, 2014
by
sreemathi.v
1
answer
Two blocks of masses $m_1=m$ and $m_2=2m$ are connected by a light string passing over a frictionless pulley.The mass $m_1$ is placed on a smooth inclined plane of inclination $\theta=30^{\large\circ}$ and mass $m_2$ hangs vertically as shown in figure below.If the system is released the tension in the string is
jeemain
physics
class11
ch5
laws-of-motion
inclined- plane
frictionless-surface
newtons-second-law
medium
asked
Aug 28, 2014
by
sreemathi.v
1
answer
Two blocks of masses $m_1=m$ and $m_2=2m$ are connected by a light string passing over a frictionless pulley.The mass $m_1$ is placed on a smooth inclined plane of inclination $\theta=30^{\large\circ}$ and mass $m_2$ hangs vertically as shown in figure below.If the system is released,the blocks move with an acceleration equal to
jeemain
physics
class11
ch5
laws-of-motion
inclined- plane
frictionless-surface
newtons-second-law
medium
asked
Aug 28, 2014
by
sreemathi.v
1
answer
A block of mass M is resting on an inclined plane as shown in figure below.The inclination of the plane to the horizontal is gradually increased.It is found that when the angle of inclination is $\theta$ the block just begins to the slide down the plane.What is the minimum force F applied parallel to the plane that would just make the block move up the plane?
jeemain
physics
class11
ch5
laws-of-motion
inclined- plane
frictionless-surface
newtons-second-law
medium
asked
Aug 27, 2014
by
sreemathi.v
1
answer
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