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If the number x is chosen from the numbers 1, 2, 3 and a number y is selected from the numbers 1, 4, 9 find the probability that xy < 9.

x can be chosen in 3 ways and in accordance with that there are 3 ways of choosing number y, the 2 numbers can be selected in 9 ways as... View Article

How many even numbers are there in the following sequence of numbers, each of which, is followed by an odd number as well as preceded by an even number? 8 6 7 6 8 9 3 2 7 5 3 4 2 2 3 5 5 2 2 8 1 1 9

There are four such even numbers.... View Article

Can two numbers have 12 as their HCF and 512 as their LCM? Justify your answer.

They cannot have 512 as their LCM.The highest common factor is one of the factors of the least common multiple. In this case, 3, which is a... View Article

Find the next term of the given series: 17, 27, 37, 56, 66, (………).

17 + 10 = 2727 + 10 = 3737 + 19 = 5656 + 10 = 6666 + 10 = 7676 is the next term.... View Article

What is the square root of 72?

72 = 2 × 2 × 2 × 3 × 3√72 = √(2 × 2 × 2 × 3 × 3) = 6 √2= 8.4852... View Article

Prove that the points (0, 0), (5, 5) and (- 5, 5) are the vertices of a right isosceles triangle.

Let A (0, 0), B (5, 5) and C (- 5, 5) be the given points.... View Article

Find the area of a regular hexagon having side a.

To find the area of a regular hexagon having side a.... View Article

How many 5 digit even numbers can be formed using the digits 0, 1, 2, 3, 4, 5.

(i) Without repetition Number of ways = 4 × 4 × 3 × 2 × 2 = 192 ways. Total number of ways = 120 + 192 = 312 ways.(ii)... View Article

Compare the surds: 7√2 and 5√3.

Take 7 √2 and 5 √3.On squaring,49 * 2 and 25 * 398 and 7598 is bigger than 75.7√2 is greater than 5√3.... View Article

What is the derivative of cot² x?

The given function is... View Article

What is 12 per cent of 250?

12% of 250= (12 / 100) * 250= 0.12 * 250= 30... View Article

The differential equation of all circles with a centre at the origin is

The equation of family of circle with the centre at the origin is x2 + y2 = a2.On differentiating, 2x + 2y (dy / dx) = 0 The required equation is... View Article

The perimeter of a triangle ABC is 37 cm and the ratio between the lengths of its altitudes be 6: 5: 4. Find the lengths of its sides. Let the sides be x cm, y cm, and (37 – x – y) cm.

To find the lengths of the sides.... View Article

M	T	W	T	F	S	S
						1
2	3	4	5	6	7	8
9	10	11	12	13	14	15
16	17	18	19	20	21	22
23	24	25	26	27	28	29
30	31

Archives

If the number x is chosen from the numbers 1, 2, 3 and a number y is selected from the numbers 1, 4, 9 find the probability that xy < 9.

How many even numbers are there in the following sequence of numbers, each of which, is followed by an odd number as well as preceded by an even number? 8 6 7 6 8 9 3 2 7 5 3 4 2 2 3 5 5 2 2 8 1 1 9

Can two numbers have 12 as their HCF and 512 as their LCM? Justify your answer.

Find the next term of the given series: 17, 27, 37, 56, 66, (………).

What is the square root of 72?

Prove that the points (0, 0), (5, 5) and (- 5, 5) are the vertices of a right isosceles triangle.

Find the area of a regular hexagon having side a.

How many 5 digit even numbers can be formed using the digits 0, 1, 2, 3, 4, 5.

Compare the surds: 7√2 and 5√3.

What is the derivative of cot² x?

What is 12 per cent of 250?

The differential equation of all circles with a centre at the origin is

The perimeter of a triangle ABC is 37 cm and the ratio between the lengths of its altitudes be 6: 5: 4. Find the lengths of its sides. Let the sides be x cm, y cm, and (37 – x – y) cm.

In Δ ABC, if cos A = sin B – cos C then show that it is a right-angled triangle.

Three angles that add up to 180° are in the ratio 2 : 3 : 7. Find them.

Find the derivative of [ln (tan x)]².

Find the vector equation of the line joining the points (2, 1, 3) and (- 4, 3, – 1).

Integrate ∫1 / [(sin x – 2 cos x) (2 sin x + cos x)] dx.

Find the shortest distance of the point (0, c) from the parabola y = x², where 0 ≤ c ≤ 5.

Using prime factorization, find the HCF and LCM of 36, 84.

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