If f: A ⟶ B is a bijective function and if n(B) = 7, then n(A) is equal to

Let f and g be two functions given by
f = {(0,1), (2,0), (3,-4), (4,2), (5,7)}
g = {(0,2), (1,0), (2,4), (-4,2), (7,0)} then the  range of f o g is

7^4k \(\equiv \) ________ (mod 100)

The difference between the remainders when 6002 and 601 are divided by 6 is ____________

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

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

In figure CP and CQ are tangents to a circle with centre at O. ARB is another tangent touching the circle at R. If CP = 11 cm and BC = 7 cm, then the length of BR is

When proving that a quadrilateral is a trapezium, it is necessary to show

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

If (sin α + cosec α)² + (cos α + sec α)² = k + tan²α + cot²α, then the value of k is equal to

If sin θ - cos θ = 0, then the value of (sin⁴ θ + cos⁴ θ) is ___________

A solid sphere of radius x cm is melted and cast into a shape of a solid cone of same radius. The height of the cone is

Kamalam went to play a lucky draw contest. 135 tickets of the lucky draw were sold. If the probability of Kamalam winning is \(\frac{1}{9}\), then the number of tickets bought by Kamalam is

The standard deviation is the ____ of variance 

Find A x B, A x A and B x A
A = B = {p, q}

Find the sum of the following
3,7,11....up to 40 terms

Find the LCM and HCF of 6 and 20 by the prime factorisation method.

Reduce the rational expressions to its lowest form
\(\frac { { x }^{ 2 }-16 }{ { x }^{ 2 }+8x+16 } \)

Prove that the equation x²(a²+b²)+2x(ac+bd)+(c²+ d²) = 0 has no real root if ad≠bc.

Show that \(\triangle\) PST~\(\triangle\) PQR 

In figure the line segment XY is parallel to side AC of \(\Delta ABC\) and it divides the triangle into two parts of equal areas. Find the ratio \(\cfrac { AX }{ AB } \)

Find the equation of a straight line passing through the mid-point of a line segment joining the points (1, -5), (4, 2) and parallel to: Y axis

Show that the points (1, 7), (4, 2), (-1,-1) and (-4,4) are the vertices of a square.

calculate \(\angle \)BAC in the given triangles (tan 38.7° = 0.8011 )

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.

If the radii of the circular ends of a conical bucket which is 45 cm high are 28 cm and 7 cm, find the capacity of the bucket. (Use π = \(\frac{22}{7}\))

If the range and the smallest value of a set of data are 36.8 and 13.4 respectively, then find the largest value.

The marks scored by 5 students in a test for 50 marks are 20, 25, 30, 35, 40. Find the S.D for the marks. If the marks are converted for 100 marks, find the S.D. for newly obtained marks.

Let A = {1, 2} and B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}, Verify whether A x C is a subset of B x D?

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

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

Use Euclid’s Division Algorithm to find the Highest Common Factor (HCF) of
84, 90 and 120

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

If A = \(\frac { x }{ x+1 } \), B = \(\frac { 1 }{ x+1 } \), prove that  \(\frac { { \left( A+B \right) }^{ 2 }+{ \left( A-B \right) }^{ 2 } }{ A\div B } =\frac { 2\left( { x }^{ 2 }+1 \right) }{ x{ \left( x+1 \right) }^{ 2 } } \)

In \(AD\bot BC\) prove that AB² + CD² = BD² + AC². 

The owner of a milk store finds that, he can sell 980 litres of milk each week at Rs.14 / litre and 1220 litres of milk each week at Rs. 16 / litre. Assuming a linear relationship between selling price and demand, how many litres could he sell weekly at Rs. 17 / litre?

Find the area of the triangle formed by the points P(-1, 5, 3), Q(6, -2) and R(-3, 4).

From the top of the tower 60 m high the angles of depression of the top and bottom of a vertical lamp post are observed to be 38° and 60° respectively. Find the height of the lamp post (tan38° = 0.7813,\( \sqrt { 3 } \) = 1.732)

The angle of elevation of a tower at a point is 45^o, After going 20 meters towards the foot of the tower the angle of elevation of the tower becomes 60^o calculate the height of the tower.

An industrial metallic bucket is in the shape of the frustum of a right circular cone whose top and bottom diameters are 10 m and 4 m and whose height is 4 m. Find the curved and total surface area of the bucket.

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?

The time taken by 50 students to complete a 100 meter race are given below. Find its standard deviation.

Σx = 99, n = 9, Σ(x - 10)² = 79, then find,
(i) Σx²
(ii) Σ(x - \(\bar { x } \))²

Draw the graph of y = x² + 3x - 4 and hence use it to solve x² + 3x - 4 = 0

Discuss the nature of solutions of the following quadratic equations.
x² - 8x + 16 = 0

Draw a circle of diameter 6 cm from a point P, which is 8 cm away from its centre. Draw the two tangents PA and PB to the circle and measure their lengths.

Draw a tangent to the circle from the point P having radius 3.6 cm, and centre at O. Point P is at a distance 7.2 cm from the centre.