The shaded region in the adjacent diagram represents ______________

Sets having the same number of elements are called ___________

Which one of the following is an irrational number.

Rationalising the denominator \(\cfrac { 1 }{ \sqrt [ 3 ]{ 3 } } \)  ___________

The Auto fare is found as minimum Rs. 25 for 3 kilometer and thereafter Rs. 12 for per kilometer. Which of the following equations represents the relationship between the total cost ‘c’ in rupees and the number of kilometers n?

Divide x³-4x²+6x by "x" the result is _____________________

Orthocentre of a triangle is the point of concurrency of _______

The distance between the points (a, 0) and (0, b) is____________

If (1,−2), (3, 6), (x, 10) and (3, 2) are the vertices of the parallelogram taken in order, then the value of x is ______.

Find the mean of the prime factors of 165.

Let be the mid point and b be the upper limit of a class in a continuous frequency distribution. The lower limit of the class is

If cos A = \(\frac { 3 }{ 5 } \), them the value of tan A is

The total surface area of a cuboid is ______________

If A is any event in S and its complement is A' then, P(A′) is equal to _______.

If n(A) = 300, n(A∪B) = 500, n(A∩B) = 50 and n(B′) = 350, find n(B) and n(U).

Write the following in the form of 5ⁿ:
\(\frac{1}{5}\)

Multiply \(\sqrt [ 3 ]{ 40 } \) and \(\sqrt [ 3 ]{ 16 } \) .

Can you reduce the following to surds of same order \(\sqrt [ 4 ]{ 5 } \)

If f(x) = x² - 4x + 3, find the values of f(1), f(-1), f(2), f(3). Also find the zeros of the polynomial f(x).

Find the supplement of the following angles.
Right angle

A line segment AB is increased along its length by 25% by producing it to C on the side of B. If A and B have the coordinates (−2,−3) and (2,1) respectively, then find the coordinates of C.

A, B and C are vertices of \(\Delta\)ABC. D, E and F are mid points of sides AB, BC and AC respectively. If the coordinates of A, D and F are (-3, 5), (5, 1) and (-5, -1) respectively. Find the coordinates of B, C and E.

Using section formula, show that the points A (7, -5), B (9, -3) and C (13, 1), are collinear.

A set of numbers consists of five 4’s, four 5’s, nine 6’s,and six 9’s. What is the mode.

If 3 cot\(\theta\) = 1, then find the value of  \(\cfrac { 3cos\theta -4sin\theta }{ 5sin\theta +4cos\theta } \)

Find the value of sin 3x. sin 6x. sin 9x when x = 10°

Find the area of an equilateral triangle whose perimeter is 150 m.

In a football match, a goalkeeper of a team can stop the goal, 32 times out of 40 attempts tried by a team. Find the probability that the opponent team can convert the attempt into a goal.

If A = {b,c,e,g,h}, B = {a,c,d,g,i} and C = {a,d,e,g,h}, then show that \(A-(B\cap C)=(A-B)\cup (A-C)\).

If A = {2,5,6,7} and B = {3,5,7,8}, then verify the commulative property of intersection of sets

Express the following decimal expression into rational numbers \(3.1\overline { 7 } \)

Rationalise the denominator and simplify \(\frac { \sqrt { 5 } }{ \sqrt { 6 } +2 } -\frac { \sqrt { 5 } }{ \sqrt { 6 } -2 } \)

Simplify;\(\sqrt { 44 } +\sqrt { 99 } -\sqrt { 275 } \)

Show that (x-3) is a factor of x³ + 9x² - x - 105

Solve by cross-multiplication method
(i) 8x − 3y = 12 ; 5x = 2y + 7
(ii) 6x + 7y −11 = 0 ; 5x + 2y = 13
(iii) \(\frac { 2 }{ x } +\frac { 3 }{ y } =5;\frac { 3 }{ x } -\frac { 1 }{ y } +9=0\)

Draw and locate the centroid of the triangle ABC where right angle at A, AB = 4cm and AC = 3cm

Show that the point (11, 2) is the centre of the circle passing through the points (1, 2), (3, –4) and (5, -6)

the mid-point formula to show that the mid-point of the hypotenuse of a right angled triangle is equidistant from the vertices (with suitable points).

If the mean of the following data is 20.2, then find the value of p

(i) If cosec A = sec 34⁰, then find A
(ii) If tan B = cot 47⁰, then find B.

A cube has the Total Surface Area of 486 cm². Find its lateral surface area.

In an office, where 42 staff members work, 7 staff members use cars, 20 staff members use two-wheelers and the remaining 15 staff members use cycles. Find the relative frequencies.

If two polynomials 2x³ + ax² + 4x – 12 and x³ + x² –2x+ a leave the same remainder when divided by (x – 3), find the value of a and also find the remainder.

Factorise  2x³- x² - 12x - 9 into linear factors
 

In the given Fig. if AB = 2, BC = 6, AE = 6, BF = 8, CE = 7, and CF = 7, compute the ratio of the area of quadrilateral ABDE to the area of ΔCDF(Use congruent property of triangles).

Draw an equilateral triangle of side 8 cm and locate its incentre. Also draw the incircle.