Maths-
General
Easy
Question
The line among the following that touches the
is
Hint:
The equation of tangent to parabola is given as
with slope = m.
Similarly find the equation of tangent to parabola with slope =
and simplify.
The correct answer is: 
Condition 1
The line with slope 'm' is a tangent to parabola 
The equation of tangent to parabola is given as
(slope = m)
Condition 2
If slope =
, then equation of tangent

Thus, equation of lines touching parabola with slope
is
.
Related Questions to study
Maths-
The number of necklaces which can be formed by selecting 4 beads out of 6 beads of different coloured glasses and 4 beads out of 5 beads of different metal, is-
The number of necklaces which can be formed by selecting 4 beads out of 6 beads of different coloured glasses and 4 beads out of 5 beads of different metal, is-
Maths-General
Maths-
The number of ways in which 20 persons can sit on 8 chairs round a circular table is-
The number of ways in which 20 persons can sit on 8 chairs round a circular table is-
Maths-General
Maths-
The number of numbers can be formed by taking any 2 digits from digits 6,7,8,9 and 3 digits from 1, 2, 3, 4, 5 is -
The number of numbers can be formed by taking any 2 digits from digits 6,7,8,9 and 3 digits from 1, 2, 3, 4, 5 is -
Maths-General
Maths-
How many numbers consisting of 5 digits can be formed in which the digits 3,4 and 7 are used only once and the digit 5 is used twice-
How many numbers consisting of 5 digits can be formed in which the digits 3,4 and 7 are used only once and the digit 5 is used twice-
Maths-General
Maths-
The number of ways of distributing n prizes among n boys when any of the student does not get all the prizes is-
The number of ways of distributing n prizes among n boys when any of the student does not get all the prizes is-
Maths-General
Maths-
If the line
is a tangent to the parabola
then k=
If the line
is a tangent to the parabola
then k=
Maths-General
Maths-
The number of ways in which n prizes can be distributed among n students when each student is eligible to get any number of prizes is-
The number of ways in which n prizes can be distributed among n students when each student is eligible to get any number of prizes is-
Maths-General
Maths-
In how many ways can six different rings be wear in four fingers?
Detailed Solution
Now, we have been given that there are 6 rings of different types and we have to find the ways in which they can be worn in 4 fingers.
Now, we know that the number of options each ring has is 4, that is each ring has 4 fingers as their possible way as it can be worn in any one of 4 fingers.
Now, similarly the other rings will have four options as it has not been mentioned in the options that there has to be at least a ring in a finger. So, each ring has four options i.e. four fingers.
Now, we know that by the fundamental principle of counting there can be = 4 x 4× 4× 4× 4× 4 ways of wearing 6 rings.
So, we have
= 4096 ways to wear 6 different types of rings.
Now, we have been given that there are 6 rings of different types and we have to find the ways in which they can be worn in 4 fingers.
Now, we know that the number of options each ring has is 4, that is each ring has 4 fingers as their possible way as it can be worn in any one of 4 fingers.
Now, similarly the other rings will have four options as it has not been mentioned in the options that there has to be at least a ring in a finger. So, each ring has four options i.e. four fingers.
Now, we know that by the fundamental principle of counting there can be = 4 x 4× 4× 4× 4× 4 ways of wearing 6 rings.
So, we have
In how many ways can six different rings be wear in four fingers?
Maths-General
Detailed Solution
Now, we have been given that there are 6 rings of different types and we have to find the ways in which they can be worn in 4 fingers.
Now, we know that the number of options each ring has is 4, that is each ring has 4 fingers as their possible way as it can be worn in any one of 4 fingers.
Now, similarly the other rings will have four options as it has not been mentioned in the options that there has to be at least a ring in a finger. So, each ring has four options i.e. four fingers.
Now, we know that by the fundamental principle of counting there can be = 4 x 4× 4× 4× 4× 4 ways of wearing 6 rings.
So, we have
= 4096 ways to wear 6 different types of rings.
Now, we have been given that there are 6 rings of different types and we have to find the ways in which they can be worn in 4 fingers.
Now, we know that the number of options each ring has is 4, that is each ring has 4 fingers as their possible way as it can be worn in any one of 4 fingers.
Now, similarly the other rings will have four options as it has not been mentioned in the options that there has to be at least a ring in a finger. So, each ring has four options i.e. four fingers.
Now, we know that by the fundamental principle of counting there can be = 4 x 4× 4× 4× 4× 4 ways of wearing 6 rings.
So, we have
Maths-
How many signals can be given by means of 10 different flags when at a time 4 flags are used, one above the other?
How many signals can be given by means of 10 different flags when at a time 4 flags are used, one above the other?
Maths-General
Maths-
The number of ways in which three persons can dress themselves when they have 4 shirts. 5 pants and 6 hats between them, is-
The number of ways in which three persons can dress themselves when they have 4 shirts. 5 pants and 6 hats between them, is-
Maths-General
Maths-
Eleven animals of a circus have to be placed in eleven cages, one in each cage. If four of the cages are too small for six of the animals, the number of ways of caging the animals is-
Eleven animals of a circus have to be placed in eleven cages, one in each cage. If four of the cages are too small for six of the animals, the number of ways of caging the animals is-
Maths-General
Maths-
Eight chairs are numbered from 1 to 8. Two women and three men wish to occupy one chair each. First women choose the chairs from amongst the chairs marked 1 to 4; and then the men select the chairs from the remaining. The number of possible arrangements is-
Eight chairs are numbered from 1 to 8. Two women and three men wish to occupy one chair each. First women choose the chairs from amongst the chairs marked 1 to 4; and then the men select the chairs from the remaining. The number of possible arrangements is-
Maths-General
Maths-
A tea party is arranged of 16 persons along two sides of a long table with 8 chairs on each side. 4 men wish to sit on one particular side and 2 on the other side. In how many ways can they be seated ?</span
DETAILED SOLUTION:
There are 16 people for the tea party.
People sit along a long table with 8 chairs on each side.
Out of 16, 4 people sit on a particular side and 2 sit on the other side.
Therefore first we will make sitting arrangements for those 6 persons who want to sit on some specific side.
Now we have remaining (16 - 6) =10 persons to arrange and out of 10, six people can sit on one side as only 6 seats will be reaming after making 2 people sit on one side on special demand and 4 people on other side as 4 people are already being seated on one side on special demand. (Take into consideration that one side has only 8 seats).
The number of ways of choosing 6 people out of 10 are
,
Now there are 4 people remaining and they will automatically place in those 4 seats available on the other side therefore total arrangement for those four people are
And now all the 16 people are placed in their seats according to the constraints.
Now we have to arrange them.
So, the number of ways of arranging 8 people out of 16 on one side and the rest 8 people on other side is(8!×8!).
So, a possible number of arrangements will be

Now as we know

So total number of arrangements is
= 210×(8! × 8!)
There are 16 people for the tea party.
People sit along a long table with 8 chairs on each side.
Out of 16, 4 people sit on a particular side and 2 sit on the other side.
Therefore first we will make sitting arrangements for those 6 persons who want to sit on some specific side.
Now we have remaining (16 - 6) =10 persons to arrange and out of 10, six people can sit on one side as only 6 seats will be reaming after making 2 people sit on one side on special demand and 4 people on other side as 4 people are already being seated on one side on special demand. (Take into consideration that one side has only 8 seats).
The number of ways of choosing 6 people out of 10 are
Now there are 4 people remaining and they will automatically place in those 4 seats available on the other side therefore total arrangement for those four people are
And now all the 16 people are placed in their seats according to the constraints.
Now we have to arrange them.
So, the number of ways of arranging 8 people out of 16 on one side and the rest 8 people on other side is(8!×8!).
So, a possible number of arrangements will be
Now as we know
So total number of arrangements is
= 210×(8! × 8!)
A tea party is arranged of 16 persons along two sides of a long table with 8 chairs on each side. 4 men wish to sit on one particular side and 2 on the other side. In how many ways can they be seated ?</span
Maths-General
DETAILED SOLUTION:
There are 16 people for the tea party.
People sit along a long table with 8 chairs on each side.
Out of 16, 4 people sit on a particular side and 2 sit on the other side.
Therefore first we will make sitting arrangements for those 6 persons who want to sit on some specific side.
Now we have remaining (16 - 6) =10 persons to arrange and out of 10, six people can sit on one side as only 6 seats will be reaming after making 2 people sit on one side on special demand and 4 people on other side as 4 people are already being seated on one side on special demand. (Take into consideration that one side has only 8 seats).
The number of ways of choosing 6 people out of 10 are
,
Now there are 4 people remaining and they will automatically place in those 4 seats available on the other side therefore total arrangement for those four people are
And now all the 16 people are placed in their seats according to the constraints.
Now we have to arrange them.
So, the number of ways of arranging 8 people out of 16 on one side and the rest 8 people on other side is(8!×8!).
So, a possible number of arrangements will be

Now as we know

So total number of arrangements is
= 210×(8! × 8!)
There are 16 people for the tea party.
People sit along a long table with 8 chairs on each side.
Out of 16, 4 people sit on a particular side and 2 sit on the other side.
Therefore first we will make sitting arrangements for those 6 persons who want to sit on some specific side.
Now we have remaining (16 - 6) =10 persons to arrange and out of 10, six people can sit on one side as only 6 seats will be reaming after making 2 people sit on one side on special demand and 4 people on other side as 4 people are already being seated on one side on special demand. (Take into consideration that one side has only 8 seats).
The number of ways of choosing 6 people out of 10 are
Now there are 4 people remaining and they will automatically place in those 4 seats available on the other side therefore total arrangement for those four people are
And now all the 16 people are placed in their seats according to the constraints.
Now we have to arrange them.
So, the number of ways of arranging 8 people out of 16 on one side and the rest 8 people on other side is(8!×8!).
So, a possible number of arrangements will be
Now as we know
So total number of arrangements is
= 210×(8! × 8!)
Maths-
If (m+n) P2 = 56 and m–nP2 = 12 then (m, n) equals-
If (m+n) P2 = 56 and m–nP2 = 12 then (m, n) equals-
Maths-General
physics-
A thin uniform annular disc (see figure) of mass
has outer radius
and inner radius
. The work required to take a unit mass from point
on its axis to infinity is

Potential at point

A thin uniform annular disc (see figure) of mass
has outer radius
and inner radius
. The work required to take a unit mass from point
on its axis to infinity is

physics-General
Potential at point
