If the order pairs (a, -1) and (5, b) belongs to {(x, y) | y = 2x + 3}, then a and b are __________

44 ≡ 8 (mod12), 113 ≡ 85 (mod 12), thus 44 x 113 ≡______(mod 12):

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

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

Two concentric circles if radii a and b where a>b are given. The length of the chord of the circle which touches the smaller circle is ____________

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

If tan θ + cot θ = 3 then tan²θ + cot²θ is equal to ___________

A spherical steel ball is melted to make 8 new identical balls. Then the radius each new ball is how much times the radius of the original ball?

A cone of height 9 cm with diameter of its base 18 cm is carved out from a wooden solid sphere of radius 9 cm. The percentage of wood wasted 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 ___________

State whether the graph represent a function. Use vertical line test.

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

Solve the following system of linear equations in three variables.
x + y + z = 6; 2x + 3y + 4z = 20;
3x + 2y + 5z = 22

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

Find a relation between x and y such that the point (x, y) is equidistant from the points (7, 1) and (3, 5).

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.

Find the standard deviation for the following data. 5, 10, 15, 20, 25. And also find the new S.D. if three is added to each value.

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

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

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

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

Find the area of a triangle vertices are(1, -1), (-4, 6) and (-3, -5).

If sin 3A = cos (A - 26°), where 3A is an acute angle, find the value at A.

Find the number of coins, 1.5 cm is diameter and 0.2 cm thick, to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm.

Find the co-efficient of variation for the following data: 16, 13, 17,21, 18.

If R = {(a, -2), (-5, b), (8, c), (d, -1)} represents the identity function, find the values of a, b, c and 

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.

In figure 0 is any point inside a rectangle ABCD. Prove that OB² + OD² = OA² + OC²

Find the area of the quadrilateral whose vertices, taken in order, are (-4, -2), (-3, -5), (3, -2) and (2, 3).

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

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?

S.D. of a data is 2102, mean is 36.6, then find its C.V.