If A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8} then state which of the following statement is true..

Let A = {1, 2, 3, 4} and B = {4, 8, 9, 10}. A function f: A ⟶ B given by f = {(1, 4), (2, 8), (3, 9), (4,10)} is a

The value of (1³ + 2³ + 3³ +...+15³) - (1 + 2 + 3 +...+ 15)is 

How many terms are there in the G.P : 5, 20, 80, 320,..., 20480

Graph of a linear equation is a ____________

If \(\triangle\)ABC is an isosceles triangle with \(\angle\)C = 90^o and AC = 5 cm, then AB 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?

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

(1 + tan \(\theta \) + sec\(\theta \)) (1 + cot\(\theta \) - cosec\(\theta \)) 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

9 sec²A  - 9tan²A = ___________

The height and radius of the cone of which the frustum is a part are h₁ units and r₁ units respectively. Height of the frustum is h₂ units and radius of the smaller base is r₂ units. If h₂ : h₁ = 1:2 then r₂ : r₁ is

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 probability of the non-happening of a event is q, then the probability of happening of that event is 

Show that the function f: N ⟶ N defined by f(x) = 2x - 1 is one-one-one but not onto.

In an A.P. the sum of first n terms is \(\frac { { 5n }^{ 2 } }{ 2 } +\frac { 3n }{ 2 } \). Find the 17^th term

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

Determine the nature of the roots for the following quadratic equations
x² - x - 1 = 0

Using quadratic formula solve the following equations.
p²x² + (P² -q²) X - q² = 0

Is \(\triangle\)ABC ~ \(\triangle\)PQR?

In figure OA· OB = OC·OD
Show that \(\angle A=\angle C\ and\ \angle B=\angle D\)

Show that the points P(-1, 5, 3), Q(6, -2) , R(-3, 4) are collinear.

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

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.

A sphere, a cylinder and a cone  are of the same radius, where as cone and cylinder are of same height. Find the ratio of their curved surface areas.

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 the mean and coefficient of variation of a data are 15 and 48 respectively, then find the value of standard deviation.

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.

If f(x) = 2x + 3, g(x) = 1 - 2x and h(x) = 3x. Prove that f o(g o h) = (f o g) o h.

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

Find the value of f(5),

Find the greatest number that will divide 445 and 572 leaving remainders 4 and 5 respectively.

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

Find the GCD of each pair of the following polynomials
12(x⁴ - x³), 8(x⁴ - 3x³ + 2x²) whose LCM is 24x³ (x - 1) (x - 2)

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

A(1, -2) , B(6, -2), C(5, 1) and D(2, 1) be four points Find the slope of the line segment (a) AB (b) CD

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

To a man standing outside his house, the angles of elevation of the top and bottom of a window are 60° and 45° respectively. If the height of the man is 180 cm and if he is 5 m away from the wall, what is the height of the window?(\( \sqrt { 3 } \) = 1.732)

Express cot 85° + cos 75° in terms of trigonometric ratios of angles between 0° and 45°.

A right circular cylinder just enclose a sphere of radius r units. Calculate
(i) the surface area of the sphere
(ii) the curved surface area of the cylinder
(iii) the ratio of the areas obtained in (i) and (ii).

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.

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

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