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Assertion : Two dice are thrown simultaneously. There are 11 possible outcomes (2,3,4,5,6,7,8,9,10,11,12) and each of them has a probability $\frac{1}{11}$.
Reason : Probability of an event (E) is defined as P(E) $=\frac{\text{Number of outcomes favourable to E}}{\text{Total number of possible outcomes}}$.

A bacterial population doubles every hour. If there are 1000 bacteria now, when were 125 bacteria present?

Question 1 (iii)
Find the squares of the following numbers:

86

Solve for x:
$\frac{x+5}{6}-\frac{x+1}{9}=\frac{x+3}{4}$

If x y = x + y - xy, then 13 7 = __

The mean of 15 observations is 8. If the mean of the first eight observations is 7 and that of the last eight observations is 10, then the value of the 8^th observation is ___ .

The area of a trapezium shaped field is 600 m², the distance between two parallel sides is 10 m and one of the parallel side is 20 m. Find the other parallel side.

Factorising $x^2+16x+63$ we get, $(x+7)$ and .

A bus travels 500 km with 70 litres of petrol. The distance covered by the bus in litres of petrol is ___.

The number 456318 is divisible by:

In the quadrilateral ACBD, AB is a diagonal. If AC = AD and AB bisects $\angle A$, by which congruence property is $\Delta ACB\cong \Delta ADB$?

The sum of two squares of two numbers is 20 and their product is 2 .Find the difference between them

Amount to be paid under compound interest is given by the formula

Find the product:
$\left(\frac{2}{3}xy\right)\times \left(\frac{-9}{10}{x}^2{y}^2\right)$

The altitude of a triangle is two third the length of its corresponding base.If the altitude is increased by 4 cm and base is decreased by 2 cm, the area of triangle remains the same.Find the base and the altitude of the triangle

Which one of the following is not a parallelogram?

In the figure, AB || CD and $\angle 1:\angle 2=3:2$. The measure of $\angle 6$ is

A general wishes to draw up his 36562 soldiers in the form of a perfect square. After arranging them, he found that some of them are left out. How many are left out?

The exterior angle of a regular polygon is one third of its interior angle. How many sides does polygon has?

A) 10

b) 8

c) 9

d) 13

If the line represented by the equation $3x+4y+c=0$ passes through the origin, then $c$ =.

In both the figures, AB || CD

Fig(ii) shows a paralellogram with two adjacent sides equal and one angle ${90}^{\circ }$.

Identify the two figures.

Question 62

In questions which of the following vary directly and which vary inversely with each other and which are neither of the two?
(i) The quantity of rice and its cost.
(ii) The height of a tree and the number of years.
(iii) Increase in cost and number of shirts that can be purchased, if the budget remains the same.
(iv) Area of land and its cost.
(v) Sales tax and the amount of the bill.

Which of the following values of x makes the equation 6x+2 = 4+5x true?

Tick the correct answer in each of the following:

The compound interest on Rs 6250 at $8\%$ per annum for 1 year, compounded half yearly, is

(a) Rs 500 (b) Rs 510 (c) Rs 550 (d) Rs 512.50

Question 14
The multiplicative inverse of $-1\frac{1}{7}$ is
(a) $\frac{8}{7}$
(b) $\frac{-8}{7}$
(c) $\frac{7}{8}$
(d) $\frac{-7}{8}$

If each side of a square is increases by 2 units, then the new area is .

If (x + a) is a factor of $x^2+px+q$ and $x^2+mx+n$,then the value of a is

A number was increased by $20\%$. By what percent this again is to be decreased to obtain the original number?

Represent 0.78888888…. In a rational form.

A cistern can be filled by a tap in 4 hours and emptied by an outlet pipe in 9 hours. If both the tap and the pipe are opened together, how long will it take to fill the cistern?

In a race, three people started from A, B and C respectively and stopped at the endpoint. Find out the radius of track B, given that the radius of track A is 14m and distance between B and the end point is 22 m (as given in the figure).

Question 9
Find the values of the letters in the following and give reasons for the steps involved.
$2AB$
$\underset{–}{+AB1}$
$\underset{–}{B18}$

Number of apples of Golden delicious is:

5² =

Without actual division ,proovd that 2x^4-8x^3+3x^2+12x-9 is actually divisible by x^2-4x+3?

A polygon has $27$ diagonals. How many sides does it have?

What is the quotient obtained when $-28x^6$ is divided by $-7x^2$ ?

How much smaller is 15x-18y+19z than 22x-20y-13z+26?

Find the amount in ₹10800 for 3 years at $12\frac{1}{2}\%$ per annum compounded annually( with process)

Convert the following decimals into p/q form

(1) 0.5555.........

​​​​(2) 0.151515..........

(3) 0.78888.................

(4) 31.2999......................

(5) 63.95.............................

Length of a desk is 20 cm and breadth is 15 cm. Find the ratio of its breadth to length.

Evaluate the value of $\frac{4^{-4}}{4^{-7}}$.