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Calculate: sin (2 arc tan 3).

The given expression is sin (2 arc tan 3).... View Article

The length and breadth of a rectangular area are 10 m and 20 m respectively. Find its area. (in sq. m).

The length and breadth of a rectangular area are 10 m and 20 m.The area will be 10 × 20 = 200 sq. m.... View Article

If two different dice are rolled together, the probability of getting an even number on both dice, is

Possible outcomes on rolling the two dice are:{(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3,... View Article

In a certain code ‘256’ means ‘you are good’; ‘637’ means ‘we are bad’ and ‘358’ means ‘good and bad’. What represents ‘and’ in that code?

'You are good' = 256 ...(i)'We are bad' = 637 ...(ii)'Good and bad' = 358 ....(iii)From (i) and (iii), 'good' is coded as '5'.From (ii) and... View Article

Show that the points (- 2, 3), (8, 3) and (6, 7) are the vertices of a right triangle.

The given points are A (- 2, 3), B (8, 3) and C (6, 7).... View Article

Write whether the following statements are true or false. Justify your answers. (i) Every quadratic equation has exactly one root. (ii) Every quadratic equation has at least one real root. (iii) Every quadratic equation has at least two roots. (iv) Every quadratic equation has at most two roots. (v) If the coefficient of x² and the constant term of a quadratic equation have opposite signs, then the quadratic equation has real roots. (vi) If the coefficient of x² and the constant term have the same sign and if the coefficient of x term is zero, then the quadratic equation has no real roots.

(i) False. A quadratic equation has two and only two roots.(ii) False.(iii) False. A quadratic equation has two and only two roots.(vi) True.... View Article

In a game of 100 points, A can give B 20 points and C 28 points. Then, B can give C is

In a game of 100 points, A can give 20 points to B then B can score (100 - 20) = 80 points.If A can give 28 points to C then C can score (100 -... View Article

The cost of 5 kilograms of sugar is 72 rupees. Find out the cost of 15 kilograms of sugar.

The cost of 5 kilograms of sugar is 72 rupees.The cost of 1 kilogram of sugar = 72 / 5 = 14.4 rupees.The cost of 15 kilograms of sugar = 14.4 *... View Article

Present age of Rohit and Mayank are in the ratio 11:8.8 years hence the ratio of their ages will be 5:4. Find their present ages.

The ratio in the present ages of Rohit and Mayank = 11 : 8Assume the age of Rohit be 11x and Mayank be 8xAfter 8 years, their ages will beAge of... View Article

Find the mean of the natural numbers from 3 to 12.

The natural numbers from 3 to 12 are given below.... View Article

If GO = 32, SHE = 49, then how SOME is evaluated?

Z = 1, Y = 2, X = 3 B = 25, A = 26 Go = 20 + 12 = 32SHE = 8 + 19 + 22 = 49SOME = 8 + 12 + 14 + 22 = 56... View Article

State true or false: A polygon having 6 sides is called an octagon.

The given statement is false.A polygon having 6 sides is called a hexagon.An octagon will have 8 sides.... View Article

Solve x² – (3 √2 – 2i) x – √2i = 0.

x2 - (3 √2 - 2i) x - √2i = 0... View Article

sin 65 cos 38 =

sin 65 cos 38... View Article

If tan A = √2 – 1, then show that sin A cos A = √2 / 4.

tan A = √2 - 1tan A = perpendicular / base = √2 - 1... View Article

State whether the statement is True or False: When an improper fraction is converted into percentage then the answer can also be less than 100.

The given statement is false.When an improper function changed into a percentage then the value is always greater than 100.... View Article

State the following statement is True or False. The commutative property of multiplication of integers states that, when multiplication is performed on two integers, then by changing the order of the integers, the result does not change.

The given statement is true.The commutative property of integers on multiplication states that, when multiplication is performed on two integers,... View Article

Let y = |tan (π / 4) – x|. Then dy / dx at x = π / 4 is

y = |tan (π / 4) - x|... View Article

Prove that the tetrahedron with vertices at the points O (0, 0, 0), A (0, 1, 1), B (1, 0, 1) and C (1, 1, 0) is a regular one.

The distance between any two points (a, b, c) and (m, n, o) is given by,... View Article

Write the data given below in ascending order and prepare the frequency table. 7, 8, 7, 10, 6, 8, 9, 7, 10, 5, 7, 6, 8, 5, 6, 7, 8, 9, 7, 6, 7, 8.

Arranging the data in ascending order, we get 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8. Observation Frequency 5 2 6 4 7... View Article