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The mean of the following distribution is:

$$\begin{array}{ccccc}{x}_i& 10& 13& 16& 19\\ f_i& 2& 5& 7& 6\end{array}$$

The Simple interest wasn't added to the amount and so there was a correction made in the balance amount by the bank. The incorrect amount was Rs. 6500 and the correct amount was Rs. 7540. What was the interest?

Find the area of the triangle ABC.

Given that base BC = 5 cm and the corresponding altitude, AP = 4 cm.

In the adjoining figure,. Prove that

∠ABC − ∠DCB + ∠CDE = 180°

In the given figure, AC = AE, AB = AD and ∠BAD = ∠EAC. Show that BC = DE.

$\text{The bisectors of}\angle Band\angle C\text{of an isosceles triangle with AB = AC intersect each other at a point O. BO is produced to meet AC at a point M Prove that}\angle MOC=\angle ABC.$

In the given figure, ABCD is a parallelogram then ar($\Delta AFB$) is

In the given figure, if AB || CD || EF, PQ || RS, $\angle RQD={25}^{\circ }$ and $\angle CQP={60}^{\circ }$, then $\angle ARS$ is equal to

Verify that : $x^3+y^3+z^3-3xyz=\frac{1}{2}(x+y+z)[{(x-y)}^2+{(y-z)}^2+{(z-x)}^2)]$

To construct a square with diagonal AC =6.2 cm which of the following properties of a square do we use?

Degree of a constant polynomial is _____.

The HCF of the polynomials 9(x+a)^p (x-b)^q (x+c)^r and 12(x+a)^p+3 (x-b)^q-3 (x+c)^r+2 is ________

3(x+a)⁶ (x-b)⁶ (x+c)⁶ then the value of p+q-r is _________

Question 3

In the given figure, $\Delta \text{CDE}$ is an equilateral triangle formed on a side CD of a square ABCD. Show that $\Delta \text{ADE}\cong \Delta \text{BCE}$

What is the value of (a + b) (a – b)?

Find two irrational numbers between √3 and √5

Debbie has an ice-cream parlour where she is making batches of chocolate ice-cream. If each batch makes $50$ ice-creams and she makes $23$ batches everyday, how many ice-cream will she make in the month of march?

Which of the following is a correct statement?

1. 13

Let two non-singular matrices are given as$A=\left[\begin{array}{ccc}a& x& f\\ b& y& g\\ c& z& h\end{array}\right]$ and $B=\left[\begin{array}{ccc}h& 2c& z\\ g& 2b& y\\ f& 2a& x\end{array}\right],$ then which of the following is correct?

Write the number $0.\overline{35}$ in the form $\frac{p}{q}$, where p and q are integers and $q\ne 0$, is

Construct a square of 9 cm and construct a triangle ADE of area equal to the area of this square ABCD. Which of the following illustrates the construction involved.

Find the volume of the right circular cone with

(i) radius 6 cm, height 7 cm

(ii) radius 3.5 cm, height 12 cm

Based on the graph, the pair of linear equations has _______________solution(s).

The goals scored by Arsenal in the 2014 Premier League is 96 across 32 matches in the 1st season. The next 2 seasons the number of goals declined to 87 and 82.

What is the Mean number of goals scored by Arsenal across the 3 seasons?

If $y=4x^2+6$, then match the corresponding value of y for the given values of x.