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Question 30

In the following question, out of the four options, only one is correct. Write the correct answer.

For a non-zero rational number $p^{13}÷p^8$ is equal to :

(a) $p^5$

(b) $p^{21}$

(c) $p^{-5}$

(d) $p^{-19}$

The area of a trapezium is $475c{m}^2$ and its height is 19 cm. Find the lengths of its two parallel sides if one side is 4 cm greater than the other.

The following histogram represents the life time of different lamps.

Find the number of lamps:

(i) that have life time of more than 700 hours.

(ii) that have life time of between 600 and 700 hours.

The magnitude of ratio is always

The interest on a sum of $Rs.2000$ is being compounded annually at the rate of $4\%$ per annum. Find the period for which the compound interest is $Rs.\mathrm{163.20.}$

(-3)(-9) = _____

If the height of a cylinder becomes one-eighth of the original height and the radius is doubled, then which of the following will be true?

The ___ property states that we can add rational numbers in any order.

In how many years will a sum of money double itself at 10%. Interest per annum.
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what is the remainder when 3²⁰¹⁸ divided by 8

There was an old computer which was written-off in the books of accounts in the previous year. The same has been taken over by a partner Nitin for Rs. 3,000. Journalise the transaction, supposing. That the firm has been dissolved.

Using appropriate properties find:

(i) $-\frac{2}{3}\times \frac{3}{5}+\frac{5}{2}-\frac{3}{5}\times \frac{1}{6}$

(ii) $\frac{2}{5}\times [-\frac{3}{7}]-\frac{1}{6}\times \frac{3}{2}+\frac{1}{14}\times \frac{2}{5}$

If $A=\text{diagonal}(3,3,3)$, then $A^4=$

Simplify the expression:
$(3x+2{)}^2-(3x-2{)}^2$

A coin is tossed once with head as the outcome. On the second toss, what is the probability of getting the tail?

36A2 is divisible by 3 , find the value of A

If the distance travelled by a rickshaw in one hour is $10km$, then the distance travelled by the same rickshaw with the same speed in one minute is

$\left(a\right)\frac{250}{9}m\left(b\right)\frac{500}{9}m\left(c\right)1000m\left(d\right)\frac{500}{3}m$

What a relief when we reach home after crossing all the obstacles and jumping over the head of several toads and turtles! Here is a histogram which is made up of bricks. 1 brick = 10,500 CDs. Carefully observe the histogram and answer the questions that follow:

In which years the number of CDs sold are the same?

Write ten rational number which is greater than 0

Which expression matches the statement

"Subtract the sum of $5x$ and $3x$ from $12y$”?

Find the smallest number by which 243 should be multiplied to get a perfect square.

Make a bar graph from the above data.

$\begin{array}{cc}\text{Month}& {\text{Temperature}}^{\circ }c\\ \text{Jun}& 46\\ \text{July}& 50\\ \text{Aug}& 44\\ \text{Sept}& 32\\ \text{Oct}& 20\\ \text{November}& 10\\ \text{Dec}& 2\end{array}$
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The length of a rectangle is 5cm longer than the breadth and it's peimeter is 150 cm. Find the area of the rectangle.

If the circles $x^2+y^2+2ax+cy+a=0and{x}^2+y^2-3ax+dy-1=0$ interesect in two distinct points P andn Q then the line 5x + by - a = 0 passes through P and Q for
(2005)

If $5^{2x+1}÷25=125$, find the value of $x$.

Solve for m.

$\frac{m+2}{6m+7}=\frac{1}{7}$

Tick $\left(✓\right)$ the correct answer in each of the following:
$(2x^2+3x+1)÷(x+1)=?$

(a) $(x+1)$
(b) $(2x+1)$
(c) $(x+3)$
(d) $(2x+3)$

$\text{Simplify:}\frac{a^{-4}\times b^3\times c^5\times d^{-7}}{a^{-7}\times b^{-3}\times c^2\times d^{-9}}$

Question 46

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

Solve each of the following equations and also verify your solution :

$\frac{1}{2}x+7x-6=7x+\frac{1}{4}$

In the following figure if O is the centre of the circle, AC = 5 cm and BC = 12 cm, then the radius of the circle is