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The ratio of the number of boys to the number of girls in a school is 14 : 15. There are 27 more girls than boys. How many girls are there in this school? How many boys?

Construct a triangle ABC in which AB = 5 cm and BC = 4.6 cm and AC = 3.7 cm.

Enter the following transactions in double column cash book of M/s Ambica Traders for November 2010.
$\begin{array}{ccc}& & \text{Rs.}\\ 1& \text{Commenced business with cash}& 50,000\\ 3& \text{Opened bank account with ICICI}& 30,000\\ 5& \text{Purchased goods for cash}& 10,000\\ 10& \text{Purchased office machine for cash}& 5,000\\ 15& \text{Sales goods on credit from Rohan and received cheque}& 7,000\\ 18& \text{Cash sales}& 8,000\\ 20& \text{Rohan's cheque deposited into bank}& \\ 22& \text{Paid cartage by cheque}& 500\\ 25& \text{Cash withdrawn for personal use}& 2,000\\ 30& \text{Paid rent by cheque}& 1,000\end{array}$

Question 58

Find the value of the letters in the following question:

$AAXA\_\_\_\_\_\_\_\_CAB$

and A - B =1

Simplify.(i)$\frac{25\times t^{-4}}{5^{-3}\times 10\times t^{-8}},t\ne 0$, (ii)$\frac{3^{-5}\times {10}^{-5}\times 125}{5^{-7}\times 6^{-5}}$

Question 46

Area of a rhombus $=\frac{1}{2}$ product of ___

1. 81

The word ‘communities’ is most commonly used to refer to

Solve: $\frac{1}{18}+\frac{7}{18}$

Question 140

The perimeters of two squares are 40 m and 96 m, respectively. Find the perimeter of another square equal in area to the sum of the first two squares.

Number of critical points of $f\left(x\right)=x^4{e}^{-x^2}$ is

Question 105(iii)

The following histogram shows the frequency distribution of teaching experiences of 30 teachers in various schools :

How many teachers have teaching experience of 10 to 20 years ?

What is the ratio $\frac{AC}{BC}$ for the following construction method:
A line segment AB is drawn.
A single ray is extended from A and 12 arcs of equal lengths are cut, cutting the ray at $A_1$, $A_2$… $A_{12}$.
A line is drawn from $A_{12}$ to B and a line parallel to $A_{12}$B is drawn, passing through the point $A_6$ and cutting AB at C

The area in $c{m}^2$ of a sector of a circle with radius 6 cm if angle of the sector is

${60}^{\circ }$ is _________

The ratio of the least prime number to the least composite number is :

Question 4(iii)

The adjoining pie chart gives the marks scored in an examination by a student in Hindi, English, Mathematics, Social Science and Science. If the total marks obtained by the students were 540, answer the following questions:



Examine whether the sum of the marks obtained in Social Science and Mathematics is more than that in Science and Hindi.

Is it possible to have a regular polygon each of whose exterior angle is ${50}^{\circ }$?

Factorise:

(i) ; (ii) ; (iii) ;

(iv)

Simplify :

$\left(i\right)\frac{a^5{b}^2}{a^2{b}^{-3}}\left(ii\right)15y^8÷3y^3\left(iii\right)x^{10}{y}^6÷x^3{y}^{-2}\left(iv\right)5z^{16}÷15z^{-11}\left(v\right)\left(36x^2{)}^{\frac{1}{2}}\right(vi\left)\right(125x^{-3}{)}^{\frac{1}{3}}\left(vii\right)\left(2x^2{y}^{-3}{)}^{-2}\right(viii\left)\right(27x^{-3}{y}^6{)}^{\frac{2}{3}}\left(ix\right){(-2x^{\frac{2}{3}}{y}^{-\frac{3}{2}})}^6$

Verghese borrowed 16,000 rupees from a bank at 8% compound interest. After 2 years, the interest rate was lowered to 6%. What is the total amount that Verghese has to repay at the end of 3 years?

1. 5

Ramesh bought two boxes for Rs. 1300. He sold one box at a profit of $20\%$ and the other box at a loss of $12\%$. If the selling price of both boxes is the same, find the cost price of each box.

Point A is (2,-1) and point B is (4,5). What is the equation of the line passing through these two points?

Convert $0.41\overline{6}$ into $\frac{p}{q}$ form.

Find the square root of 7.29.

In the Pythagorean triplet 9,40,41 what is the natural number

a) What information is given by the graph?

b) The marks of a maximum number of students fall in which group.

c) How many students have a score between 60-70?

d) How many students have a score more than 70? [4 MARKS]

Find the least number that must be added to 1300 so as to get a perfect square.

Two congruent circles have centres P and P'. Arc $AXB$ subtends an angle of ${60}^{\circ }$ at the centre P and arc A'YB' subtends an angle of ${20}^{\circ }$ at the centre P'. Then the ratio of arcs $AXB$ and $A^{\prime }Y{B}^{\prime }$ is ?

Factorize $10a^{2}b-4ab+6a{b}^2$

Factorise : $2a{b}^{2}c-2a+3b^{3}c-3b-4b^2{c}^2+4c$

In the given figure, BD bisects $\angle ABC$ and BD is perpendicular to AC. Which of the following statements are correct?

1. 4

Question 29

Tally marks are used to find
(a) class intervals
(b) range
(c) frequency
(d) upper limit

A principal of ₹40,000 is deposited in a bank which offers a simple interest at the rate of 10% per annum. Calculate the amount at the end of 2 years.