Insert the appropriate symbol ∈ (belongs to) or ∉ (does not belong to) in the blanks.

In a class there are 40 students. 26 have opted for Mathematics and 24 have opted for Science. How many student have opted for Mathematics and Science.

Verify \(A-(B\cap C)=(A-B)\cup (A-C)\)using Venn diagrams.

In a residential area with 600 families \(\frac{3}{5}\) owned scooter, \(\frac{1}{3}\) owned car, \(\frac{1}{4}\) owned bicycle, 120 families owned scooter and car, 86 owned car and bicylce while 90 families owned scooter and bicylce. If \(\frac{1}{15}\) of families owned all the three types of vehicles, then find
(i) the number of families owned atleast two types of vehicle.
(ii) the number of families owned no vehicle.

Express the following decimal expression into rational numbers -\(21.21\overline {37}\)

Rationalise the denominator and simplify \(\frac { 5\sqrt { 3 } +\sqrt { 2 } }{ \sqrt { 3 } +\sqrt { 2 } } \)

(i) Add 3\(\sqrt{7}\) and 5\(\sqrt{7}\) . Check whether the sum is rational or irrational.
(ii) Subtract 4\(\sqrt{5}\) from 7\(\sqrt{5}\) . Is the answer rational or irrational?

Find the degree of the following polynomials  \(2\sqrt { 5 } { p }^{ 4 }-\frac { { 8p }^{ 3 } }{ \sqrt { 3 } } +\frac { { 2p }^{ 2 } }{ 7 } \)

What must be subtracted from 2x⁴+4x²-3x+7 to get 3x³-x²+2x+1?

What is the remainder when x²⁰¹⁸ + 2018 is divided by x–1

The area of a rectangle is x⁴ + 9x² + 20 sq. units and its length is x² + 4 units. Find its breadth in term of x.

Using algebraic identity, find the coefficients of x², x and constant term without actual expansion.
(i) (x + 5)(x + 6)(x + 7)
(ii) (2x + 3)(2x − 5)(2x - 6)

Let m || n and l is a transversal Such that ∠1 : ∠2 = 11 : 7. Determine all the eight angles.

ABCD is a parallelogram and AP and CQ are perpendic from vertex A and C on diagonal BD. Show that
(i) ΔAPB ≅ ΔCQD
(ii) AP = CQ

Show that the following points A(3, 1), B(6,4) and C(8, 6) lies on a straight line.

A researcher studying the behaviour of mice has recorded the time (in seconds) taken by each mouse to locate its food by considering 13 different mice as 31, 33, 63, 33, 28, 29, 33, 27, 27, 34, 35, 28, 32.Find the median time that mice spent in searching its food.

Find the six trigonometric ratios of the angle \(\theta\) using the given diagram.

Find the value of cos19⁰59'

Find the volume of cube whose side is 10 cm.