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A photograph of a bacteria enlarged 50000 times attains a length of 5 cm. The actual length of bacteria is

(a) 1000 cm (b) ${10}^{-3}cm$

(c) ${10}^{-4}cm$ (d) ${10}^{-2}cm$

Question 131

A photograph of BIlliard/ Snooker table has dimensions as $\frac{1}{10}th$ of its actual size as shown in the given figure.

The portion excluding six holes each of diameter 0.5 cm needs to be polished at the rate of ₹ 200 per $m^2$. Find the cost of polishing.

Sum of the expressions $3x+4y$ and $2y+7x$ is _____.

The factors of 12ab + 9a + 12 + 16b are

Question 53 (b)

Write the following statement in the form of algebraic expressions and write whether is monomial, binomial or trinomial.

Three times of p and two times of q are multiplied and then subtracted from r.

Question 62

Fill in the blanks to make the statement true.

$65÷(-13)=$___ .

In the figure below, lines AB and CD intersect at O.
$\text{If}\angle AOC+\angle BOE={70}^{\circ }$ and $\angle BOD={40}^{\circ }$, find (2$\angle$BOE).

Find the measure of an angle which is 70 degree less than 3times it's complementary angle

If $x-3=9$, then $x$ is equal to ___.

Which of the following fractions are equal to $\frac{20}{4}$?

At what rate percent shall a sum of ₹400 amount to ₹520 in 5 years ?

The set - builder form of the set $\{\frac{2}{3},\frac{3}{4},\frac{4}{5},\frac{5}{6},\frac{6}{7}\}$ is

The simple interest on a certain sum for 3 years at 10% per annum is Rs 829.50 .Find the sum.

A theif is running on a train with12km/h.The police car is moving with 80km/h.Speed of train us 60km/h. What is the speed of police car w.r.t

A rod of a certain length is divided into 4 pieces of lengths 2.03 m, 6.89 m, 1.7 m and 3.76 m. What was the total length of the rod ?

$(9\times {10}^{-2})+(9\times {10}^3)$ in usual form is given as

If the rate of interest is reduced from $5\%$ p.a. to $3\frac{1}{2}\%$,find the decrease in a half-year's interest on $Rs.540$

Two buses are moving in opposite directions at 90 kmph and 135 kmph. Their lengths are 1.65 km and 1.35 km respectively. The time taken by the slower bus to cross the faster bus in seconds is:

If the product of two numbers is zero, it is necessary that one of them should be 0.

If Raju covers a distance of 12 km in 3 hours then find distance that Raju covers in 10 hours, assuming he travels at the same speed.

Using Euler's formula, find the unknown. [4 MARKS]

$\begin{array}{cccc}Faces& ?& 5& 20\\ Vertices& 6& ?& 12\\ Edges& 12& 9& ?\end{array}$

Question 2 (i)
Write the coordinates of B.

The exterior angle of a triangle is equal to ___________.

The marks obtained by a student in different subjects in an exam are given below.

$$\begin{array}{cc}Subject& Marks\\ English& 77\\ Hindi& 90\\ Maths& 70\\ Physics& 86\\ Chemistry& 85\\ Biology& 97\\ ComputerSci.& 59\\ History& 62\\ Geography& 100\\ MoralSci.& 75\end{array}$$

Find the probability that in an exam, she will score
(i)100
(ii)80 or more
(iii) less than 60. [4 MARKS]

Fill in the blank.
___ + 23 = 0

Find the result obained by the addition of
$\frac{2}{3}\text{to the reciprocal of}\frac{-2}{3}.$

Since you were talking about so many concepts, one more point came to your mind. You gathered attention of all curious dwarfs and told, 'Did you all observe this interesting thing?? -1 is at the same distance from 0 as is 1. Same is true for -2, -3 and every other integer. What does it mean??'

One of the council members stood and told, 'They add to become equal to 0.' You smiled and told: Indeed they add to become zero. Such numbers which are negatives of each other are also known as __________ ____________ of each other.

The length of the rectangle whose area is 320 sq m and breadth is 16 m is ______ .

Question 3 (ii)
Explain how a square is:

(ii) A parallelogram

The number of diagonals in a heptagon is

Find the value of $(\frac{-2}{5}{)}^7÷(\frac{-2}{5}{)}^2.$

A dealer is selling an article at a discount of 20%. Find the C.P. if the marked price is Rs 400 and the profit made by the dealer is 25%

In the fig. below, if AB || CD, $\angle$APQ = 50${}^{\circ }$ and $\angle$PRD = 127${}^{\circ }$, find x and y.

How many circular faces does a cylinder have?

The mean of the following distribution is ____.

$$\begin{array}{ccccc}{x}_i& 5& 13& 16& 19\\ f_i& 4& 5& 7& 4\end{array}$$

When we see the decimal equivalent of $\frac{5}{18}$ it is a :

A ball is picked from a bag containing blue balls and red balls, and then replaced into the bag. This experiment is performed 50 times. The result was 15 blue and 35 red. Find the probability of drawing (i) a blue ball (ii) a red ball. [2 MARKS]

Estimate the product of 958 × 387 by rounding off each factor to its greatest place.

Construct a triangle, given that the lengths of its two sides are 3 m and 8 m and the third side makes an angle of 60 degrees with the 3 m side. [3 MARKS]

What will be the value of x for $\frac{x+1}{x+4}$ = $\frac{2}{3}$?

A man X has a land whose area is $3^4$ meter square and a man Y has $4^3$ meter square of land. If the land costs Rs 50 per meter square, who has higher property value? [4 MARKS]

A circle has a circumference of 70 meters. Find its area. [2 MARKS]

The side of a square is equal to twice the radius of the circle. Which of them will have greater area?
[3 MARKS]

Use the sign of >, < or = in the blank to make the statement true.

(-4 $\times$ 2) + 10 __ (6 - 7) $\times$ -2

Which of the following images is/are symmetric? (The circles represent holes cut out from the figures.)

In the given isosceles triangle ABC, AB = AC, $\angle ABC$ = 70°. Find $\angle$ BAC.

For an accurate prediction of events and presenting statistics, select the most important information required and the most suitable option.