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Find the arithmetic mean of given numbers

4, 8, 12, 16, 20, 24.

A metal sheet of breadth 10 cm is used to make a cone of radius 14 cm and slant height 20 cm. Then length of sheet if 25% of sheet is wasted is .

Question 3(b)

Given Sara’s present age today is y years. Think of her age in the future or in the past. What will the following expression indicate?

$y+7,y-3,y+4\frac{1}{2},y-2\frac{1}{2}$

1. 2

Find the number of permutations of the letters of the words

(a) MILK (b) WORLD

A circle is inscribed inside a square of area 100 ${cm}^2$. Radius of the circle is

Prove :

(tanθ + sinθ) / (tanθ - sinθ) = (secθ + 1) / (secθ - 1)

Question 1

Which one of the following is a polynomial?



A) $\frac{x^2}{2}-\frac{2}{x^2}$

B) $\sqrt{2x}-1$

C) $x^2+\frac{3x^{\frac{3}{2}}}{\sqrt{x}}$

D) $\frac{x-1}{x+1}$

It is known that two roots of the non-linear equation $x^3-6x^2+11x-6=0$ are $1$ and $3$. The third root will be

Find the remainder when $x^3$−2$x^2$+6x is divided by x−2.

Which of the following inequations is represented by the the number line below?

$\text{If in}△CAB\text{and}△FED,$



$\frac{AB}{EF}=\frac{BC}{FD}=\frac{AC}{ED}$,



$\text{then which of the following is true?}$

Solve the inequalities in exercieses 17 to 20 and show the graph of the solution in each case on number line.

3(1-x) < 2 (x+4)

A right angled triangle of sides $3cm$, $4cm$ and $5cm$ is rotated about the side $3cm$ then, the volume of the cone formed is .

Swapnil invests ₹14950 in ₹100 shares of a company, paying $14\%$ dividend. If her annual income from shares be ₹1610, what will be the market value of each share?

If 2 is a root of the quadratic equation $3x^2+ax-2=0$ and the quadratic equation $a(x^2+6x)-b=0$ has equal roots find the value of b.

The given figure shows a semi-circle with centre O and diameter PQ. If PA = AB and $\angle$ BCQ = ${140}^o$; find measures of angles PAB and AQB. Also, show that AO is parallel to BQ.

Solve the following pair of linear equations.

(i) px + qy = p − q

qx − py = p + q

(ii) ax + by = c

bx + ay = 1 + c

(iii)

ax + by = a² + b²

(iv) (a − b) x + (a + b) y = a²− 2ab − b²

(a + b) (x + y) = a² + b²

(v) 152x − 378y = − 74

− 378x + 152y = − 604

Find the distance between the points (-3, -3), (4, 5). [2 MARKS]

Determine the nature of the roots of the following equations.

(1)

(2)

(3)

(4)

(5)

(6)

The length and breadth of a rectangle are $12cm$ and $5cm$, respectively, then its diagonal is __________ cm.

Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:

From the following extracts of Balance Sheet of Exe Ltd., calculate Cash Flow from Financing Activities:

Additional Information:

1. Equity Shares were issued on 31st March, 2019.

2. Interim dividend on Equity Shares was paid 15%.

3. Preference Shares were redeemed on 31st March, 2019 at a premium of 5%. Premium paid was debited to Statement of Profit and Loss.

4. 12% Debentures of face value ₹ 1,00,000 were issued on 31st March, 2019.

Complete the following sentence : "Mode is the _________".