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Number of ways in which 7 girls & 7 boys can be arranged such that no two boys and no two girls are together is?

Consider a parabola

and a hyperbola XY = 1. A tangent is drawn to parabola meets the hyperbola in A and B then the locus of midpoint of AB is

The total number of 1 word, 2 word, 3 word sentences that can be formed using the letters of the word SAMSUNG is?

For n => 3 circles, the value of n for which the number of the radical axis is equal to number of radical centres is?

Ram travels towards east covering 5 km. He takes a left turn and travels 10 km more. Then, he takes a right turn and travels another 5km and finally takes a right turn to cover 10 km. How far is he from his original position?

The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?

A particle moves in a straight line such that the distance covered by it in time t seconds measured t3 from a fixed point on the line is given by 

The acceleration when the velocity is zero is

If inside a big circle exactly 24 small circles, each of radius 2, can be drawn in such a way that each small circle touches the big circle and also touches both its adjacent small circles, then radius of the big circle is?

The differential equation of the system of circles touching the x-axis at origin is?

The number of permutations of the letters of the word HINDUSTAN such that neither the pattern ‘HIN’ nor ‘DUS’ nor ‘TAN’ appears, are

Number of ways in which 7 girls & 7 boys can be arranged such that no two boys and no two girls are together is?

The number of ways of selecting two numbers from the set {1, 2, ...,12} whose sum is divisible by 3 is?

Let a relation be defined on a set of functions defined on R  R such that R = {(f, g)|f – g is an even function} then, relation R is?

If a is square matrix of order 3 such that adja=64 find |a|

The normal at P to a hyperbola of eccentricity e, intersects its transverse and conjugate axes at L and M respectively. If locus of the mid-point of LM is hyperbola, then eccentricity of the hyperbola is?

The number of ordered pairs (x, y) of real numbers satisfying 

is equal to ?

If 9th term of AP is 12 and 10the term is 18.what will be 18the term?

Let a, b, c and d be non−zero numbers. If the point of intersection of the lines 4ax + 2ay + c = 0 and 5bx + 2by + d = lies in the fourth quadrant and is equidistant from the two axes then?

A bird is sitting on the top of a vertical pole 20 m high and its elevation from a point O on the ground is 45°. It flies off horizontally straight away from the point O. After one second, the elevation of the bird from O is reduced to 30°. Then the speed (in m/s) of the bird is?

The slope of the line touching both the parabolas

Three positive numbers form an increasing G.P. If the middle term in this G.P. is doubled, the new numbers are in A.P. Then the common ratio of the G.P. is?

Let PS be the median of the triangle with vertices P(2, 2), Q(6, −1) and R (7, 3). The equation of the line passing through (1, −1) and parallel to PS is ?

Let C be the circle with centre at (1, 1) and radius = 1. If T is the circle centred at (0, y), passing through origin and touching the circle C externally, then the radius of T is equal to ?

Let α and β be the roots of equation px2 + qx + r = 0, p ≠ 0. If p, q, r are in A.P. and 1/α +1/ β = 4, then the value of |α − β| is

A purse contains 4 copper and 3 silver coins and another purse contains 6 copper and 2 silver coins. One coin is drawn from any one of these two purses. The probability that it is a copper coin is ?

A bag contains 4 red and 4 blue balls. Four balls are drawn one by one from the bag, then find the probability that the drawn balls are in alternate colour?

A bag contains 3 red, 6 white and 7 blue balls. Two balls are drawn one by one. What is the probability that first ball is white and second ball is blue when first drawn ball is not replaced in the bag?

Find the equation of the hyperbola whose directrix is 2x + y = 1, focus (1, 2) and eccentricity 

A box contains 5 different red and 6 different white balls. In how many ways can 6 balls be drawn so that there are at least two balls of each colour ?

A college offers 6 courses in the morning and 4 in the evening. The number of ways a student can select exactly one course, either in the morning or in the evening?

Three vertices out of six vertices of a regular hexagon are chosen randomly. The probability of getting a equilateral triangle after joining three vertices is ?

If four cards are drawn at random from a pack of fifty-two playing cards, find the probability that at least one of them is an ace?

From a group of 10 persons consisting of 5 lawyers, 3 doctors and 2 engineers, four persons are selected at random. The probability that the selection contains at least one of each category is?

If the letters of INTERMEDIATE are arranged, then the odds in favour of the event that no two 'E's occur together, are ?

At a certain place, the horizontal component of earth's magnetic field is root  times of the vertical component. What the angle of dip at that place.

In a group of 1000 people, there are 750 who can speak Hindi and 400 who can speak English. How many can speak Hindi only ?How many can speak English ? How many can speak both Hindi and English?

A number consists of three digits which are in G.P. the sum of the right hand and left hand digits exceeds twice the middle digit by 1 and the sum of the left hand and middle digits is two third of the sum of the middle and right hand digits. Find the numbers?

Four numbers are in A.P. If their sum is 20 and the sum of their squares is 120, then the middle terms are ?

Four different integers form an increasing A.P. One of these numbers is equal to the sum of the squares of the other three numbers. Find the numbers?

Can anybody help me here. Thanks!! 

Given f(x) = e ^{(x 2 - x)}, find
a) the interval(s) of increase and decrease of f,
b) value(s) of x for which f has a local extremum,
c) the interval(s) of concavity and any inflection point(s).

What is the domain and range of the relation R given by

Let A = {1, 2, 3, 4} and B = {5, 7, 9}.

What is the value of

(i) A × B

(ii) B × A

(iii) Is A × B = B × A ?

(iv) Is n (A × B) = n (B × A) ?

In how ways can 6 coins be chosen from 20 one rupees coins, 10 fifty paise coins, 7 twenty paise coins.

A card is lost from a pack of 52 playing cards. From the remainder of the pack, one card is drawn and is found to be spade. The probability that the missing card is a spade is?

Write the set of all positive integers whose cube is odd.

A bag contains 50 tickets, numbered from 1 to 50. One ticket is drawn at random. What is the probability that

(i) number on the ticket is a perfect square or divisible by 3 ?

(ii) number on the ticket is prime number or greater than 40 ?

From a group of 8 boys and 5 girls a committee of 5 is to be formed. Find the probability that the committee contains 3 boys and 2 girls?

Find the differential equation of the family of all circles which pass through the origin and whose centre lie on y–axis?

A pair of dice is thrown 7 times. If getting a total of 7 is considered a success, what is the probability of

1.  no success ?
2.  6 successes ?
3.  at least 6 successes ?
4.  at most 6 successes ?

A problem in statistics is given to three students A, B and C. Their chances of solving the problem are 1/3, 1/4 and 1/5 respectively. If all of them try independently, what is the probability that?

1. (i)  problem is not solved ?
2. (ii)  problem is solved ?
3. (iii)  exactly two students solve the problems

A pair of dice is thrown. If sum of the numbers is an even number, what is the probability that it is a perfect square ?

An equation of the plane passing through the points (3, 2, –1), (3, 4, 2) and (7, 0, 6) is 5x + 3y – 2z = l, where l is

A drunken man takes a step forward with probability 0.4 and backwards with probability 0.6. Find the probability that at the end of eleven steps, he is one step away from the starting point?

A dice is tossed 5 times. Getting an odd number is considered a success. Then the variance of distribution of success is?

5 letters are to be posted in 5 post boxes. If any number of letters can be posted in 5 post boxes, what is the probability that each box contains only one letter?

 A stone is dropped into a quiet lake and waves move in a circle at a speed of 3.5 cm/sec. At the instant when the radius of the circular wave is 7.5 cm. How fast is the enclosed area increasing?

A dice is tossed 5 times. Getting an odd number is considere a success. Then the variance of distribution of success is?

A drunken man takes a step forward with probability 0.4 and backwards with probability 0.6. Find the probability that at the end of eleven steps, he is on e step away from the star ting point?

Let S be a finite set containing n elements. Then the total number of binary operations on S is:

Total number of possible matrices of order 3 × 3 with each entry 2 or 0 is?

Differentiate the following function w.r.t. x :

A doctor is called to see a sick child. The doctor has prior information that 80% of sick children in that area have the flu, while the other 20% are sick with measles. Assume that there is no other disease in that area. A well-known symptom of measles is a rash. From the past records it is known that, chances of having rashes given that sick child is suffering from measles is 0.95. However, occasionally children with flu also develop rash, whose chances are 0.08. Upon examining the child, the doctor finds a rash. What is the probability that the child has measles?

A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence are of same length x .The maximum area enclosed by the park is?

Coefficient of variation of two distributions are 60 and 70, and their standard deviations are 21 and 16, respectively. Their arithmetic means are?

An arch is in the form of semi-ellipse. It is 8m wide and 2m high at the centre. Then, the height of the arch at a point1.5m from one end is?

An arch is in the form of semi-ellipse. It is 8m wide and 2m high at the centre. Then, the height of the arch at a point1.5m from one end is?

Coefficient of variation of two distributions are 60 and 70,and their standard deviations are 21 and 16, respectively.Their arithmetic means are?

A school has four sections of chemistry in class XII having40, 35, 45 and 42 students. The mean marks obtained inChemistry test are 50, 60, 55 and 45 respectively for the four sections, the over all average of marks per students is?

Let f (x) be a polynomial function of second degree. If f (1) = f (–1) and a, b, c are in A.P., then f'(a),
f'(b) and f'(c) are in?

In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then the common ratio of this progression is equals

The first two terms of a geometric progression add up to 12. The sum of the third and the fourth terms is 48. If the terms of the geometric progression are alternately positive and negative, then the first term is?

A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is?

In a bag, there are 6 red balls and 9 green balls. Two balls are drawn at random, what is the probability that at least one of the balls drawn is red ?

There are 6 consecutive odd numbers. The difference between the square of the average of the first three numbers and the square of the average of the last three numbers is 288. What is the last odd number ?

A vessel contains a mixture of milk and water in the respective ratio of 10 : 3. Twenty-six litre of this mixture was taken out and replaced with 8 litre of water. If the resultant respective ratio of milk and water in the mixture was 5 : 2, what was the initial quantity of mixture in the vessel ? (in litre)

The cost price of item B is Rs. 150/- more than the cost price of item A. Item A was sold at a profit of 10% and item B was sold at a loss of 20%. If the respective ratio of selling prices of items A and B is 11 : 12, what is the cost price of item B?

If a, b, c are rational, show that the roots of the equation

are rational.

The following statement (p->q)->[(~p->q)->q] is? 1.a tautology 2.equivalent to ~p->q 3.equivalent to p->~q 4.a fallacy

Circle(s) touching x-axis at a distance 3 from the origin 

and having an intercept of length  on y-axis is (are)

Let PQ be a focal chord of the parabola  

The tangents to the parabola at P and Q meet at a point lying on the line y = 2x + a, a > 0.

1.Length of chord PQ is?

2.If chord PQ subtends an angle θ at the vertex of y2 = 4ax, then tanθ =

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The function has a local minimum or a local maximum at x =?

In an examination of a school having 60 students in XII A and 40 students in XII B, 15 and 20 students failed in XII A and XII B, respectively. A student is called by the principal at random, find the probability that he is from XII A if he passed in the examination.

A factory makes nuts and bolts. A nut takes 1.5 hrs of machine time and 3 hrs of worker’s time in its making while a bolt takes 3 hrs of machine time and 1 hr of worker’s time. In a day, the factory has the availability of not more than 42 hrs of machine time and 24 hrs of worker’s time. If the profit on a nut is Rs. 20 and on a bolt is Rs. 10, find the number of nuts and bolts the factory should manufacture to earn maximum profit.

Make it as L.P.P and solve it graphically.

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Find the equation of normal at point for the curve 

find 5 digit numbers  divisible by 3 which does not contain 3.

A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in this party, is?

Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in sq. m) of the flower-bed, is?

then value of cos 4x?

In a triangle PQR, P is the largest angle and cos P = 1/3. Further the incircle of the triangle touches the sides PQ, QR and RP at N, L and M respectively, such that the lengths of PN, QL and RM are consecutive even integers. Then possible length(s) of the side(s) of the triangle is (are) ?

Words of length 10 are formed using the letters, A, B, C, D, E, F, G, H, I, J. Let x be the number of such words where no letter is repeated ; and let y be the number of such words where exactly one letter is repeated twice and no other letter is repeated. Then, y/9x=?

Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.

For three events A, B and C, P(Exactly one of A or B occurs) = P(Exactly one of B or C occurs) = P (Exactly one of C or A occurs) = 1/ 4 and P(All the three events occur simultaneously) = 1 /16 . Then the probability that at least one of the events occurs, is?

If two different numbers are taken from the set {0, 1, 2, 3, …, 10}; then the probability that their sum as well as absolute difference are both multiple of 4, is:

For three events A, B and C, P(Exactly one of A or B occurs) = P(Exactly one of B or C occurs) = P (Exactly one of C or A occurs) = 1 /4 and P(All the three events occur simultaneously) = 1/ 16 . Then the probability that at least one of the events occurs, is:

Calculate y=|x| if the The radius of a circle, having minimum area, which touches the curve y = 4 – x*x?

If 2x - y + 1 = 0 is a tangent to the hyperbola (x/a)*(x/a)-(y/4)*(y/4)=1,then what is the sides of a right angled triangle?

Let a vertical tower AB have its end A on the level ground. Let C be the mid-point of AB and P be a point on the ground such that AP = 2AB. If angle BPC = β , then calculate value of tan β.

What will be the probability that at least one of the event occurs for three events A, B and C, P(Exactly one of A or B occurs) = P(Exactly one of B or C occurs) = P(Exactly one of C or A occurs) = 1/4 and P(All the three events occur simultaneously) = 1/16?

Let S = {1, 2, 3, ..... , 9}. For k = 1, 2, ....., 5, let NK be the number of subsets of S, each containing five elements out of which exactly k are odd. Then N1 + N2 + N3 + N4 + N5

Calculate the length of the other edges if Cuboid with edge a=14 cm and body diagonal u=42 cm has volume V=10976 cm3?

How many m^2 of cardboard are needed to make the cuboid with dimensions 40 cm 60 cm and 20 cm?

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What is the equation of the plane passing through the point (1, 1, 1) and perpendicular to the planes 2x + y -2z = 5 and 3x-6y -2z = 7?

I'm Student of class10

What will be the variance of the number of green balls drawn if A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one-by-one, with replacement?

What is cuboid? What will be the real time examples of the cuboid.

What will be the variance of the number of green balls drawn is if A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one by one, with replacement?

What will be maximum area (in sq. m) of the flower-bed if Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector?

The sides of a right angled triangle are in arithmetic progression. If the triangle has area 24, then what is the length of its smallest side ?

If a chord, which is not a tangent, of the parabola y2 = 16x has the equation 2x + y = p, and midpoint (h, k), then what is(are) possible value(s) of p, h and k ?

15. In a two digit number, the sum of the digits is 13. If the number is subtracted from the one obtained by inter changing the result is 45. Find the number.

Find the volume of a pyramid whose base is a square with side lengths of 10 m and height 9 m.

How many edges faces and vertices are on a cone?

What type of pyramid has four faces?

What is the edge of a cube?

What is a square based pyramid?

How many vertices are in a pyramid?

What is the number of vertices in a pyramid with 10 faces?

Mr. Sharma and Mr. Arora are family friends and they decided to go for a trip with family . For the trio they reserved their rail tickets . Mr. Arora has not taken a half ticket for his child who is 6 years old where as Mr, Sharma has taken half tickets for his two children who are 6 year and 8.5 year.A railway half ticket costs half of the full fare but the reservation charges are the same as on a FULL TICKET. MR AND MRS ARORA PAID 1700,WHILE MR AND MRS SHARMA PAID 2700. Find the full share of one ticket and reservation charges per ticket.

Can the number n ^6,n being a natural number ,end with the digit 5? Give reasons.

A man has certain note of denomination 20 and 5 which amount to 380 . If the number of notes of each kind are interchanged,they amount to 60 less than before . Find the number of notes of each denomination.

What is the matrix and what is the use of it? What are the types and how it works?

What is Distance and displacement calculation? What is the difference between both of you.