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Find the number of sides in a regular polygon, if its each exterior angle is :

(i) $\frac{1}{3}$ of a right angle

(ii) two - fifth of a right - angle.

Question 109

External dimensions of a closed wooden box are in the ratio 5 : 4 : 3. If the cost of painting its outer surface at the rate of Rs. 5 per $d{m}^2$ is Rs. 11750, find the dimensions of the box.

Solve the equation $\frac{17(2-x)-5(x+12)}{1-7x}$ = 8

A circular flower-bed has a radius of 14 cm. Find its perimeter.

The external dimensions of a closed wooden box are 48 cm, 36 cm, 30 cm, The box made of 1.5 cm thick wood. How many bricks of size 6 cm $\times$ 3 cm $\times$ 0.75 cm can be put in this box?

The number 125 is the cube of the number ______ .

If $5x–20<5(8-x)$ ,then the highest integral value of x is,

Medals won by the U.S. in Winter Math Olympics are as follows:





Identify the outlier corresponding to the number of medals won in different years.

Find each of the following products:

$(9x+5y)\times (4x+3y)$

The value of $(27\times 125{)}^{\frac{1}{3}}$ is __.

1. 8

Determine the side of a square whose area is $4\sqrt{125}{\text{unit}}^2.$

Factorise : $64x^3-729y^3$

$ab-mn+an-bm=?\left(a\right)(a-b)(m-n)\left(b\right)(a-m)(b+n)\left(c\right)(a-n)(m+b)\left(d\right)(m-a)(n-b)$

Can’t you do these in your head?

(i) (13 × 8) + (7 × 8)

(ii) (15 × 9) + (5 × 9)

(iii)

(iv)

Prove that if I add a number to itself, the resulting number is divisible by 2.
[2 MARKS]

If $A=\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]$ , then $A^2$ equal to …….

On dividing $x^4-2x^2-9x-9$ by a polynomial g(x), the quotient is $(x^2-x-4)\text{and the remainder is (3-2x).}\text{Find g(x)}$

Question 2(iii)
Use the identity $(x+a)(x+b)=x^2+(a+b)x+ab$ to find the following products:
$(4x-5)(4x-1)$

Question 116

Find x, so that



${\left(\frac{2}{9}\right)}^3\times {\left(\frac{2}{9}\right)}^{-6}={\left(\frac{2}{9}\right)}^{2x-1}.$

The sides of a rectangle drawn on paper are in the ratio 5 : 6. When the rectangle is constructed in reality, it is 30 times the one drawn on paper.

If the length of the real rectangle is 720 cm, then find the perimeter of the rectangle which is on paper in cm.

1. 88

Find the greatest common factors (GCF / HCF) of the following polynomials :

$12a{x}^2,6a^2{x}^3\text{and}2a^3{x}^5$

The numerator of a fraction is 2 less than the denominator. If 1 is added to both the numerator and denominator, then it becomes $\frac{3}{5}.$ Find the fraction.

Yash Shah deposits Rs 500 per month in his R.D. Account for 4 years. If at the time of maturity he gets Rs 28410 find rate of interest.

Which among the following is a composite number?

When we start constructing a quadrilateral whose 2 diagonals and 3 sides known, in how many ways can the construction be started.

If a+b+c =9 and a² + b²+ c²=35 find the value of a³ + b³ + c³ - 3ab

Find the square of 42.

Question 122

If $\frac{5^m\times 5^3\times 5^{-2}}{5^{-5}}=5^{12},$ then find m.

Construct a triangle ABC in which AB = 5 cm, BC = 5 cm and AC = 4.3 cm.

(i)

Express $49$ as the sum of $7$ odd numbers.

(ii)

Express $121$ as the sum of $11$ odd numbers.

Which of the following polynomials has the highest degree?

If there are 10 apples, 10 oranges and 10 mangoes in a fruit basket, then find the probability of not picking a mango.