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

f(x) = (x + 1)³ - (x - 1)³ represents a function which is

\((x-\frac { 1 }{ x } )={ x }^{ 2 }+\frac { 1 }{ { x }^{ 2 } } \) then f(x) =

Let f(x) = x² - x, then f(x- 1) - (x + 1) is ___________

If function f : N⟶N, f(x) = 2x then the function is, then the function is ___________

If f is identify function, then the value of f(1) - 2f(2) + f(3) is: 

Using Euclid’s division lemma, if the cube of any positive integer is divided by 9 then the possible remainders are

If A = 2⁶⁵ and B = 2⁶⁴ + 2⁶³ + 2⁶² +...+ 2⁰ Which of the following is true?

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?

The solution of the system x + y − 3z = −6, −7y + 7z = 7, 3z = 9 is

If number of columns and rows are not equal in a matrix then it is said to be a

Which of the following are linear equation in three variables ___________

The square root of 4m² - 24m + 36 is ___________

Choose the correct answer
(i) Every scalar matrix is an identity matrix
(ii) Every identity matrix is a scalar matrix
(iii) Every diagonal matrix is an identity matrix
(iv) Every null matrix is a scalar matrix

In a given figure ST || QR, PS = 2 cm and SQ = 3 cm. Then the ratio of the area of \(\triangle\)PQR to the area \(\triangle\)PST is 

Two poles of heights 6 m and 11 m stand vertically on a plane ground. If the distance between their feet is 12 m, what is the distance between their tops?

The ratio of the areas of two similar triangles is equal to ____________

In a triangle, the internal bisector of an angle bisects the opposite side. Find the nature of the triangle.

In figure \(\angle OAB={ 60 }^{ o }\) and OA = 6cm then radius of the circle 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

(2, 1) is the point of intersection of two lines.

Find the value of P, given that the line  \(\frac { y }{ 2 } =x-p\) passes through the point (-4, 4) is ____________

Find the slope and the y-intercept of the line \(3y-\sqrt { 3x } +1=0\) is ____________

If sin \(\theta \) + cos\(\theta \) = a and sec \(\theta \) + cosec \(\theta \) = b, then the value of b(a² - 1) is equal to 

Two persons are standing ‘x’ metres apart from each other and the height of the first person is double that of the other. If from the middle point of the line joining their feet an observer finds the angular elevations of their tops to be complementary, then the height of the shorter person (in metres) is

If sin A + sin²A = 1, then the value of the expression (cos²A + cos⁴A) is ___________

If 4 tan θ = 3, then \(\left( \frac { 4sin\theta -cos\theta }{ 4sin\theta +cos\theta } \right) \) is equal to ___________

A ladder of length 14m just reaches the top of a wall. If the ladder makes an angle of 60^o with the horizontal, then the height of the wall is ____________

If two solid hemispheres of same base radius r units are joined together along their bases, then curved surface area of this new solid is

A frustum of a right circular cone is of height 16 cm with radii of its ends as 8 cm and 20 cm. Then, the volume of the frustum is

The radio of base of a one 5 cm and to height 12 cm. The slant height of the cone ___________

If S₁ denotes the total surface area at a sphere of radius ૪ and S₂ denotes the total surface area of a cylinder of base radius ૪ and height 2r, then ___________

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

The curved surface area of a cylinder is 264 cm² and its volume is 924 cm². The ratio of diameter to its height is ___________

The mean of 100 observations is 40 and their standard deviation is 3. The sum of squares of all observations is

A page is selected at random from a book. The probability that the digit at units place of the page number chosen is less than 7 is

If the data is multiplied by 4, then the corresponding variances is get multiplied by ___________

If the co-efficient of variation and standard deviation of a data are 35% and 7.7 respectively then the mean is ___________

A box contains some milk chocalates and some coco chocolates and there are 60 choolates in the box. If the probability of taking a milk chocolate is \(\frac { 2 }{ 3 } \) then the number of coco chocolates is ___________

The Cartesian product A x A has 9 elements among which (–1, 0) and (0, 1) are found. Find the set A and the remaining elements of A x A.

Write the domain of the following real functions
p(x) = \(\frac { -5 }{ 4x^{ 2 }+1 }\)

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 set of ordered pairs.

Let A = {0, 1, 2, 3} and B = {1, 3, 5, 7, 9} be two sets. Letf: 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 an arrow .

if a₁ = 1, a₂ = 1 and a_n = 2a_{n - 1} + a_{n - 2} n \(\ge\)3, n \(\in\) N, then find the first six terms of the sequence

First term a and common difference d are given below. Find the corresponding A
a = \(\frac { 3 }{ 4 } \), d = \(\frac { 1 }{ 2 } \)

If the difference between the roots of the equation x² - 13x + k = 0 is 17. find k

Simplify
\(\frac { 12{ t }^{ 2 }-22t+8 }{ 3t } \div \frac { 3{ t }^{ 2 }+2t-8 }{ 2{ t }^{ 2 }+4t } \)

D and E are respectively the points on the sides AB and AC of a \(\triangle\)ABC such that AB = 5.6 cm, AD = 1.4 cm, AC = 7.2 cm and AE = 1.8 cm, show that DE || BC

Two circles with centres O and O' of radii 3 cm and 4 cm, respectively intersect at two points P and Q, such that OP and O'P are tangents to the two circles. Find the length of the common chord PQ.

Find the equation of the straight line passing through (5, 7) and is Parallel to X axis

Find the equation of a line passing through the point (3, - 4) and having slope \(\frac { -5 }{ 7 } \)

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

prove that \(\frac { sec\theta }{ sin\theta } -\frac { sin\theta }{ cos\theta } =cot\theta \)

A road is flanked on either side by continuous rows of houses of height \( 4\sqrt { 3 } \)m with no space in between them. A pedestrian is standing on the median of the road facing a row house. The angle of elevation from the pedestrian to the top of the house is 30°. Find the width of the road.

The radius of a conical tent is 7 m and the height is 24 m. Calculate the length of the canvas used to make the tent if the width of the rectangular canvas is 4 m?

The volume of a solid right circular cone is 11088 cm³. If its height is 24 cm then find the radius of the cone.

If the standard deviation of a data is 4.5 and if each value of the data is decreased by 5, then find the new standard deviation.

If A and B are two mutually exclusive events of a random experiment and P(not A) = 0.45, P(A U B) = 0.65, then find P(B).

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

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

f(x) = (1+ x)
g(x) = (2x - 1)
Show that fo(g(x)) = gof(x)

Which of the following list of numbers form an AP? If they form an AP, write the next two terms:
4,10,16, 22, ...

A ball rolls down a slope and travels a distance d = t² - 0.75t feet in t seconds. Find the time when the distance travelled by the ball is 11.25 feet.

A flock of swans contained x² members. As the clouds gathered, 10x went to a lake and one-eighth of the members flew away to a garden. The remaining three pairs played about in the water. How many swans were there in total?

If α and β are the roots of the polynomial f(x) = x² - 2x + 3, find the polynomial whose roots are
\(\frac { \alpha -1 }{ \alpha +1 } ,\frac { \beta -1 }{ \beta +1 } \)

A chess board contains 64 equal squares and the area of each square is 6.25 cm², A border round the board is 2 cm wide.

In \(\triangle\) ABC, if DE||BC, AD = x, DB = x − 2, AE = x +2 and EC = x − 1 then find the lengths of the sides AB and AC.

An insect 8 m away initially from the foot of a lamp post which is 6 m tall, crawls towards it moving through a distance. If its distance from the top of the lamp post is equal to the distance it has moved, how far is the insect away from the foot of the lamp post?

Find the equation of a line passing through the point of intersection of the lines 4x + 7y − 3 = 0 and 2x − 3y + 1 = 0 that has equal intercepts on the axes.

if \(\frac { cos\theta }{ 1+sin\theta } =\frac { 1 }{ a } \),then prove that \(\frac { { a }^{ 2 }-1 }{ a^{ 2 }+1 } \) = sin\(\theta \)

As shown in the figure,Two trees are standing on the flat ground.the angel of elevation of the top of both the trees from a point x on the ground is 40° .if the horizontal distance between x and the smaller tree is 8m and the distance of the top of the trees is 20m, calculate, the distance between the point x and the top of the smaller tree.

From the top of a tree of height 13 m the angle of elevation and depression of the top and bottom of another tree are 45° and 30° respectively. Find the height of the second tree.(\(\sqrt { 3 } \) = 1.732)

\(P.T\left( \frac { 1+{ tan }^{ 2 }A }{ 1+{ cot }^{ 2 }A } \right) ={ \left( \frac { 1-tan\quad A }{ 1-cot\quad A } \right) }^{ 2 }={ tan }^{ 2 }A\)

A right angled triangle PQR where ∠Q = 90^o is rotated about QR and PQ. If QR = 16 cm and PR = 20 cm, compare the curved surface areas of the right circular cones so formed by the triangle.

If the ratio of radii of two spheres is 4 : 7, find the ratio of their volumes.

A vessel is in the form of a hemispherical bowl mounted by a hollow cylinder. The diameter is 14 cm and the height of the vessel is 13 cm. Find the capacity of the vessel.

A bag contains 12 blue balls and x red balls. If one ball is drawn at random (i) what is the probability that it will be a red ball? (ii) If 8 more red balls are put in the bag, and if the probability of drawing a red ball will be twice that of the probability in (i), then find x.

The probability of happening of an event A is 0.5 and that of B is 0.3. If A and B are mutually exclusive events, then find the probability that neither A nor B happen.

If two dice are rolled, then find the probability of getting the product of face value 6 or the difference of face values 5.

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?

Find the sum of first 24 terms of the list of numbers whose nth term is given by a_n = 3 + 2n.

A two digit number is such that the product of its digits is 18, when 63 is subtracted from the number, the digits interchange their places. Find the number.

Draw a triangle ABC of base BC = 5.6 cm, \(\angle\)A = 40^o and the bisector of \(\angle\)A meets BC at D such that CD = 4 cm.

Draw a circle of radius 4 cm. At a point L on it draw a tangent to the circle using the alternate segment.

Find the equation of a straight line Passing through (-8, 4) and making equal intercepts on the coordinate axes

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

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?

Final the probability of choosing a spade or a heart card from a deck of cards.