If n(A x B) = 6 and A = {1,3} then n(B) is

If g = {(1,1), (2,3), (3,5), (4,7)} is a function given by g(x) = αx + β then the values of α and β are

The function t which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined Fahrenheit degree is 95, then the value of  C \(t(C)=\frac { 9c }{ 5 } +32\) is ___________

If \(f(x)=\frac { 1 }{ x } \), and \(g(x)=\frac { 1 }{ { x }^{ 3 } } \) then f o g o(y), is ________

If f(x) + f(1 - x) = 2 then \(f\left( \frac { 1 }{ 2 } \right) \) is ___________

If \(f(x)=\frac { x+1 }{ x-2 } ,g(x)=\frac { 1+2x }{ x-1 } \) then fog(x) is ___________

An A.P. consists of 31 terms. If its 16^th term is m, then the sum of all the terms of this A.P. is

In an A.P., the first term is 1 and the common difference is 4. How many terms of the A.P. must be taken for their sum to be equal to 120?

If m and n are the two positive integers then m² and n² are ____________

A boy saves Rs. 1 on the first day Rs. 2 on the second day, Rs. 4 on the third day and so on. How much did the boy will save upto 20 days?

A system of three linear equations in three variables is inconsistent if their planes

The values of a and b if 4x⁴ - 24x³ + 76x² + ax + b is a perfect square are

Consider the following statements:
(i) The HCF of x+y and x⁸-y⁸ is x+y
(ii) The HCF of x+y and x⁸+y⁸ is x+y
(iii) The HCF of x-y nd x⁸+y⁸ is x-y
(iv) The HCF of x-y and x⁸-y⁸ is x-y

The real roots of the quadratic equation x²-x-1 are ___________

If \(2A+3B=\left[ \begin{matrix} 2 & -1 & 4 \\ 3 & 2 & 5 \end{matrix} \right] \) and \(A+2B=\left[ \begin{matrix} 5 & 0 & 3 \\ 1 & 6 & 2 \end{matrix} \right] \) then B = [hint: B = (A+2B)-(2+3B)]

The perimeters of two similar triangles ∆ABC and ∆PQR are 36 cm and 24 cm respectively. If PQ = 10 cm, then the length of AB is

In the given figure, PR = 26 cm, QR = 24 cm, \(\angle PAQ\) = 90^o, PA = 6 cm and QA = 8 cm. Find \(\angle\)PQR

I the given figure DE||AC which of the following is true.

In the given figure DE||BC:BD = x - 3, BA = 2x,CE = x- 2, and AC = 2x + 3, Find the value of x.

If the angle between two radio of a circle is ^o, the angle between the tangents at the end of the radii is ____________

A man walks near a wall, such that the distance between him and the wall is 10 units. Consider the wall to be the Y axis. The path travelled by the man is

If A is a point on the Y axis whose ordinate is 8 and B is a point on the X axis whose abscissae is 5 then the equation of the line AB is

The area of triangle formed by the points (a, b+c), (b, c+a) and (c, a+b) is ____________

A line passing through the point (2, 2) and the axes enclose an area ∝. The intercept on the axes made by the line are given by the roots of ____________

a cot \(\theta \) + b cosec\(\theta \) = p and b cot \(\theta \) + a cosec\(\theta \) = q then p²- q² is equal to 

The electric pole subtends an angle of 30° at a point on the same level as its foot. At a second point ‘b’ metres above the first, the depression of the foot of the pole is 60°. The height of the pole (in metres) is equal to

If x = r sin θ cos φ y = r sin θ. Then x² + y² + z²___________

If m cos θ + n sin θ = a and m sin θ - n cos θ = b then a² + b² is equal to ___________

The top of two poles of height 18.5m and 7m are connected by a wire. If the wire makes an angle of measures 360^o with horizontal, then the length of the wire is ____________

The curved surface area of a right circular cone of height 15 cm and base diameter 16 cm is

A shuttle cock used for playing badminton has the shape of the combination of

A cylinder 10 cone and have there are of a equal base and have the same height. what is the ratio of there volumes?

How many balls, each of radius 1 cm, can be made from a solid sphere of lead of radius cm?

The height of a cone is 60 cm. A small cone is cut off at the top by plane parallel to the base and its volume is \(\left[ \frac { 1 }{ 64 } \right] ^{ th }\) the volume of the original cone. Then the height of the smaller cone is ___________

A floating boat having a length 3m and breadth 2m is floating on a lake. The boat sinks by 1 cm when a man gets into it. The mass of the man is (density of water is 10000 kg/m³)

Which of the following is not a measure of dispersion?

A purse contains 10 notes of Rs. 2000, 15 notes of Rs. 500, and 25 notes of Rs. 200. One note is drawn at random. What is the probability that the note is either a Rs. 500 note or Rs. 200 note?

If the smallest value and co-efficient of range a data are 25 and 0.5 respectively. Then the largest value is ___________

If the observations 1, 2, 3, ... 50 have the variance V₁ and the observations 51, 52, 53, ... 100 have the variance V₂ then \(\frac { { V }_{ 1 } }{ { V }_{ 2 } } \) is ___________

A number x is chosen at random from -4, -3, -2, -1, 0, 1, 2, 3, 4. The probability that \(\left| x \right| \le 3\) is ___________

Let f = {(-1, 3), (0, -1), (2, -9)}. be a linear function from Z into Z. Find f(x).

Let A =  {1,2, 3, 4} and B = {-1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} Let R = {(1, 3), (2, 6), (3, 10), (4, 9)} \(\subseteq \) A x B be a relation. Show that R is a function and find its domain, co-domain and the range of R.

Let A = {0, 1, 2, 3} and B = {1, 3, 5, 7, 9} be two sets. Let f: A \(\rightarrow\)B be a function given by  f(x) = 2x + 1. Represent this function as  a table.

Let A = {0, 1, 2, 3} and B = {1, 3, 5, 7, 9} be two sets. Let f: A \(\rightarrow\)B be a function given by  f(x) = 2x + 1. Represent this function as a graph.

Let A = {1,2,3,7} and B = {3,0,–1,7}, which of the following are relation from A to B ?
R₄ = {(7,–1), (0, 3), (3, 3), (0, 7)

Find the sum of first 28 terms of an A.P. whose n^th term is 4n - 3.

Find the sum of the following
6 + 13 + 20 + ...+ 97

Solve 2m²+ 19m + 30 = 0

Write down the quadratic equation in general form for which sum and product of the roots are given below.
\(-\frac { 7 }{ 2 } ,\frac { 5 }{ 2 } \)

If \(\triangle\)ABC is similar to \(\triangle\)DEF such that BC = 3 cm, EF = 4 cm and area of \(\triangle\)ABC = 54 cm². Find the area of \(\triangle\)DEF.

PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter of the circle such that \(\angle\)PQR = 120^o. Find \(\angle\)OPQ.

Find the area of the triangle formed by the points :(–10, –4), (–8, –1) and (–3, –5)

Find the equation of a line through the given pair of points (2, 3) and (-7, -1)

Find the slope of the following straight lines \(7x-\frac { 3 }{ 17 } \) = 0

prove that 1+\(\frac { co{ t }^{ 2 }\theta }{ 1+cosec\theta } \) = cosec\(\theta \) 

prove the following identities.\(\frac { 1-ta{ n }^{ 2 }\theta }{ co{ t }^{ 2 }\theta -1 } =ta{ n }^{ 2 }\theta \)

A conical flask is full of water. The flask has base radius r units and height h units, the water poured into a cylindrical flask of base radius xr units. Find the height of water in the cylindrical flask.

The barrel of a fountain-pen cylindrical in shape, is 7 cm long and 5 mm in diameter. A full barrel of ink in the pen will be used for writing 330 words on an average. How many words can be written using a bottle of ink containing one fifth of a litre?

What is the probability that a leap year selected at random will contain 53 saturdays. (Hint: 366 = 52 x 7 + 2)

A and B are two events such that, P(A) = 0.42, P(B) = 0.48, P(A ∩ B) = 0.16. Find (i) P(not A) (ii) P(not B) (iii) P(A or B)

A function f: [-7,6) \(\rightarrow\) R is defined as follows.

find 2f(-4) + 3f(2)

A function f: [-7,6) \(\rightarrow\) R is defined as follows.

\(\cfrac { 4f(-3)+2f(4) }{ f(-6)-3f(1) } \)

Which of the following list of numbers form an AP ? If they form an AP, write the next two terms:
1, 1, 1, 2, 2, 2, 3, 3,  3

Simplify
\(\frac { 2{ a }^{ 2 }+5a+3 }{ 2{ a }^{ 2 }+7a+6 } \div \frac { { a }^{ 2 }+6a+5 }{ -5{ a }^{ 2 }-35a-50 } \)

Find the values of a and b if the following polynomials are perfect squares
4x⁴ - 12x³ + 37x² + bx + a

Find
\(\frac { 16{ x }^{ 2 }-2x-3 }{ 3{ x }^{ 2 }-2x-1 } \div \frac { 8{ x }^{ 2 }+11x+3 }{ 3{ x }^{ 2 }-11x-4 } \)

The sum of two numbers is 15. If the sum of their reciprocals is \(\frac{3}{10}\), find the numbers.

5 m long ladder is placed leaning towards a vertical wall such that it reaches the wall at a point 4m high. If the foot of the ladder is moved 1.6 m towards the wall, then find the distance by which the top of the ladder would slide upwards on the wall

In the given figure AB || CD || EF. If AB = 6cm, CD = x cm, EF = 4 cm, BD = 5 cm and DE = y can. Final x and y

The graph relates temperatures y (in Fahrenheit degree) to temperatures x (in Celsius degree) Find the slope and y intercept

From the top of a lighthouse, the angle of depression of two ships on the opposite sides of it are observed to be 30° and 60°. If the height of the lighthouse is h meters and the line joining the ships passes through the foot of the lighthouse, show that the distance between the ships is \(\frac { 4h }{ \sqrt { 3 } } \)m.

A man is standing on the deck of a ship, which is 40 m above water level. He observes the angle of elevation of the top of a hill as 60° and the angle of depression of the base of the hill as 30° . Calculate the distance of the hill from the ship and the height of the hill. (\(\sqrt { 3 } \) = 1.732)

The angles of elevation and depression of the top and bottom of a lamp post from the top of a 66 m high apartment are 60° and 30° respectively. Find
The height of the lamp post.

If 15tan² θ+4 sec² θ=23 then find the value of (secθ+cosecθ)² -sin² θ

The volume of a cylindrical water tank is 1.078 x 10⁶ litres. If the diameter of the tank is 7m, find its height.

A solid sphere and a solid hemisphere have equal total surface area. Prove that the ratio of their volume is 3\(\sqrt{3}\) : 4.

The volume of a cone is 1005\(\frac{5}{7}\)cu. cm. The area of its base is 201\(\frac{1}{7}\)sq. cm. Find the slant height of the cone.

At a fete, cards bearing numbers 1 to 1000, one number on one card are put in a box. Each player selects one card at random and that card is not replaced. If the selected card has a perfect square number greater than 500, the player wins a prize. What is the probability that (i) the first player wins a prize (ii) the second player wins a prize, if the first has won?

A bag contains 5 red balls, 6 white balls, 7 green balls, 8 black balls. One ball is drawn at random from the bag. Find the probability that the ball drawn is
(i) white
(ii) black or red
(iii) not white
(iv) neither white nor black

The King, Queen and Jack of the suit spade are removed from a deck of 52 cards. One card is selected from the remaining cards. Find the probability of getting
(i) a diamond
(ii) a queen
(iii) a spade
(iv) a heart card bearing the number 5.

If f(x) = \(\frac { x-1 }{ x+1 } \), x ≠ 1 show that f(f(x)) = -\(\frac{1}{x}\), provided x ≠ 0.

How many terms of the AP: 24, 21, 18, ... must be taken so that their sum is 78?

Find two consecutive natural numbers whose product is 20.

Construct a triangle similar to a given triangle PQR with its sides equal to \(\frac{3}{5}\) of the corresponding sides of the triangle PQR (scale factor \(\frac { 3 }{ 5 } <1\)) 

Draw a triangle ABC of base BC = 8 cm, \(\angle\)A = 60^o and the bisector of \(\angle\)A meets BC at D such that BD = 6 cm.

Find the equation of a straight line Passing through (1, -4) and has intercepts which are in the ratio 2:5

Find the value of k if the points A(2, 3), B(4, k) and (6, -3) are collinear.

From a point on a bridge across a river, the angles of depression of the banks on opposite sides at the river are 30° and 45°, respectively. If the bridge is at a height at 3 m from the banks, find the width at the river.

A spherical ball of iron has been melted and made into small balls. If the radius of each smaller ball is one-fourth of the radius of the original one, how many such balls can be made?

Which team is more consistent?