If there are 1024 relations from a set A = {1, 2, 3, 4, 5} to a set B, then the number of elements in B is

If the ordered pairs (a + 2, 4) and (5, 2a + b) are equal then (a,b) is

7^4k \(\equiv \) ________ (mod 100)

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

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

In ∆LMN, \(\angle\)L = 60^o, \(\angle\)M = 50^o. If ∆LMN ~ ∆PQR then the value of \(\angle\)R is

In a \(\triangle\)ABC, AD is the bisector \(\angle\)BAC. If AB = 8 cm, BD = 6 cm and DC = 3 cm. The length of the side AC is

The equation of a line passing through the origin and perpendicular to the line 7x - 3y + 4 = 0 is

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

If 5x = sec\(\theta \) and \(\frac { 5 }{ x } \) = tan\(\theta \), then x² - \(\frac { 1 }{ { x }^{ 2 } } \) is equal to 

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

A spherical ball of radius r₁ units is melted to make 8 new identical balls each of radius r₂ units. Then r₁:r₂ 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

A girl calculates the probability of her winning in a match is 0.08 what is the probability of her losing the game ___________

Let A = {3,4,7,8} and B = {1,7,10}. Which of the following sets are relations from A to B?
R₁ = {(3,7), (4,7), (7,10), (8,1)}

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

Show that any positive odd integer is of the form 4q + 1 or 4q + 3, where q is some integer.

If α and β are the roots of x² + 7x + 10 = 0 find the values of
\(\frac { \alpha }{ \beta } +\frac { \beta }{ \alpha } \)

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

In the figure, AD is the bisector of \(\angle\)A. If BD = 4 cm, DC = 3 cm and AB = 6 cm, find AC.

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

Find the slope of a line joining the given points (- 6, 1) and (-3, 2)

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

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

Water is flowing at the rate of 15 km per hour through a pipe of diameter 14 cm into a rectangular tank which is 50 m long and 44 m wide. Find the time in which the level of water in the tanks will rise by 21 cm.

Find the depth of a cylindrical tank of radius 28 m, if its capacity is equal to that of a rectangular tank of size 28 m x 16 m x 11 m.

If n = 5 , \(\bar { x } \) = 6, Σx² = 765 then calculate the coefficient of variation.

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 = The set of all natural numbers less than 8, B = The set of all prime numbers less than 8, C = The set of even prime number. Verify that
(A ∩ B) x C = (A x C) ∩ (B x C)

A functionf: (1,6) \(\rightarrow\)R is defined as follows:

Find the value of f(3),

If 1 + 2 + 3 +...+ k = 325, then find 1³ + 2³ + 3³ +...K³.

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

Simplyfy
\(\frac { 4{ x }^{ 2 }y }{ 2{ x }^{ 2 } } \times \frac { 6x{ z }^{ 3 } }{ 20{ y }^{ 4 } } \)

In \(\angle ACD={ 90 }^{ 0 }\) and \(CD\bot AB\) Prove that \(\cfrac { { BC }^{ 2 } }{ { AC }^{ 2 } } =\cfrac { BD }{ AD } \)

A mobile phone is put to use when the battery power is 100%. The percent of battery power ‘y’ (in decimal) remaining after using the mobile phone for x hours is assumed as y  = − 0.25 x + 1
How much time does it take so that the battery has no power?

If the points A(6, 1), B(8, 2), C(9, 4) and D(P, 3) are the vertices of a parallelogram, taken in order. Find the value of P.

A pole 5 m high is fixed on the top of a tower. The angle of elevation of the top of the pole observed from a point ‘A’ on the ground is 60° and the angle of depression to the point ‘A’ from the top of the tower is 45°. Find the height of the tower.(\(\sqrt3\)=1.732)

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

From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and base is hollowed out. Find the total surface area of the remaining solid.

A wooden article was made by scooping out a hemisphere from each end of a cylinder as shown in figure. If the height of the cylinder is 10 cm and its base is of radius 3.5 cm find the total surface area of the article.

In a game, the entry fee is Rs.150. Th e game consists of tossing a coin 3 times. Dhana bought a ticket for entry . If one or two heads show, she gets her entry fee back. If she throws 3 heads, she receives double the entry fees. Otherwise she will lose. Find the probability that she (i) gets double entry fee (ii) just gets her entry fee (iii) loses the entry fee.

C.V. of a data is 69%, S.D. is 15.6, then find its mean.