What is the largest number that divides 245 and 1029, leaving remainder 5 in each case?

If the product of zeros of the polynomial ax² – 6x – 6 is 4, then a =?

The areas of two similar triangles ΔABC and ΔPQR are 25 cm² and 49 cm² respectively and QR = 9.8 cm. Then BC = ?

If sin (θ + 34°) = cos θ and θ + 34° is acute, then θ = ?

lf cos θ = 0.6, then 5sin θ - 3tan θ = ?

The simplest form of 1095/1168

The pair of linear equations 4x - 5y - 20 = 0 and 3x + 5y -15 = 0 has

If mode = x(median) - y(mean), then

Check whether 6" can end with the digit 0? Justify your answer.

Find the zeros of the polynomial 9x² - 5 and verify the relation between zeros and coefficients.

If 2 sin 2θ = √3 find the value of θ.

In ΔABC, D and E are points on AB and AC respectively such that AD = 5 cm, DB = 8 cm and DE || BC. If AC = 6.5 cm, then find AE.

D is a point on the side BC of ΔABC such that ∠ADC and ∠BAC are equal. Prove that: CA² = DC x CB.

Calculate the mode for the following frequency distribution:

Show that any positive odd integer is of the form (6q + 1) or (6q + 3) or (6q + 5), where q is some integer.

Prove that (3 -√15) is irrational.

Prove that is irrational.

What number must be added to each of the numbers 5, 9, 17, 27 to make the new numbers in proportion?

The sum of two numbers is 18 and the sum of their reciprocals is 1/4. Find the numbers.

If α, β are the zeros of the polynomial (x² - x - 12), then form a quadratic equation whose zeros are 2α and 2β.

Prove that (sin θ + cosec θ)² + (cos θ + sec θ)² = 7 + tan² θ + cot²θ.

If sec θ + tan θ = m, show that = sin θ.

In a trapezium ABCD, O is the point of intersection of AC and BD, AB|| CD and AB = 2 x CD. If area of ΔAOB = 84 cm², find the area of ΔCOD.

In the given figure, AB ⊥ BC, GF ⊥ BC and DE ⊥ AC. Prove that ΔADE ~ Δ GCF.

Find the mean of the following frequency distribution, using step deviation method:

The mean of the following frequency distribution is 78. Find the value of p.

Find the median of the following data:

If two zeroes of the polynomial p(x) = 2x⁴ + 7x³ - 19x²- 14x + 30 are √2 and - √2 then find the other two zeroes.

Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of an equilateral triangle described on one of its diagonals.

Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.

Prove that:

Evaluate:

If sec θ + tan θ = m, prove that

Draw the graph of the following equations: 3x + y- 11 = 0 and x-y- 1 = 0.

Shade the region bounded by these lines and the y-axis.

The table given below shows the frequency distribution of the scores obtained by 200 candidates in a BCA entrance examination:

Draw cumulative frequency curve using 'less than series'.

For what value of k will the following pair of linear equations have infinitely many solutions?

2x - 3y = 7

(k + 1)x + (1 - 2k)y = (5k - 4)

Prove that: (sin θ – cosec θ)(cos θ – sec θ) =

ΔABC is an isosceles triangle with AC = BC. If AB² = 2AC², prove that ΔABC is a right triangle.

The table given below shows the daily expenditure on food of 30 households in a locality:

Find the mean and median of daily expenditure on food.