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Find the value of m, if $6^{-5}\times 5^{-2}\times 6^3\times 5^m\times 6^n=1$. [4 MARKS]

Question 115(iv)

Express each of the following in standard form:
The human body has 1 trillion of cells which vary in shapes and sizes.

Sort the steps for construction of a triangle ABC of three sides of lengths 3 cm, 5 cm and 6 cm.

Question 49

Fill in the blanks to make the statement true.

Two lines in a plane which do not meet at a point anywhere, are called ___ lines.

What is the percentage difference in scores of Batsman number '2' and '3'?

Question 42

Fill in the blanks to make the statement true.

If 3 - x = - 4, then x = ...............

Question 5

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

The value fo $3^5÷3^{-6}$ is :
(a) $3^5$
(b) $3^{-6}$
(c) $3^{11}$
(d) $3^{-11}$

Which of the following rational numbers lie between 0 and 1?

Which of the following correctly represents 98 as the product of its prime power.

The following figure is drawn on a piece of paper. If the paper is folded along the axis and punched at the shown postitions, then the number of holes formed after unfolding the paper is ____ .

Find the interest on $Rs.8000$ for $1$ year at $9\%$ per annum compound half yearly.

Remit's mother gave him $Rs.3x{y}^2$ and his father gave him $Rs5(x{y}^2+2)$.Out of this total money, he spent $Rs.(10-3x{y}^2)$ on his birthday party. How much money is left with him? If $x=2andy=3$ find the total amount left with him. [4 MARKS]

Given: Area of parallelogram = Base $\times$ Height

Statement 1: A diagonal of a parallelogram divides it into two congruent triangles.

Statement 2: Areas of two congruent triangles are exactly equal

The simple interest on a certain sum of money for 3 years at $6\%$ per annum is ₹ 432. Find the Principal

31.76 $÷$ 8 is a :

A number is divided by 5 to get a quotient as 19 and remainder as 2. Find the number.

What is the proper definition of π

Divide Rs. 1301 between A and B, so that the amount of A after 7 years is equal to the amount of B after 9 years, the interest being compounded at 4% per annum.

The decimal number 0.20 is equal to the percentage:

Which out of the following would be the greatest after converting to decimals :

$\frac{32}{6}$ , $\frac{64}{12}$, $\frac{128}{24}$, $\frac{256}{48}$

If $a+b=9$, and $a-b=5$, find the value of $2(a^2+b^2)$.

Which of the following is a perfect number?

The angles that form the shape "Z" when two parallel lines are cut by a transversal are

Consider the figure:

If BC = AC, x = 2y, and angle ∠ACB = 60^o, then find the value of ∠B + y (in degrees).

$Findthevalueofx:2(x+3)-3x+5=2+5x$

The length of a snake is 10 cm and that of a crocodile is 2 m. Pick the correct statement.

Assume that you are participating in a race and driving at an average speed of 180 km/hr. What will be the distance covered by you in 35 minutes?

When 7xy + 5yz - 3zx, 4yz + 9zx - 4y and - 3xz + 5x - 2xy are added, we get

A certain freezing process requires that room temperature should be lowered from 40${}^{\circ }$C at the rate of 5${}^{\circ }$C every hour. What is the room temperature after 10 hours?

Which of the numbers 726 and 938 ,when expressed as factors has greater power of 2?
[2 MARKS]

You went to buy rice from a shop. When the shopkeeper was weighing the rice, he balanced the rice bag with 5 kg, 500 gm, 250 gm and 100 gm weights. What is the weight of rice (in kg) you bought?

The cost of one food packet is ₹ 45 with a fixed delivery charge of ₹ 10. The total cost of $y$ food packets is given by ___.

From the adjoining figure the value of x${}^{\circ }$ is :

Ted's dad was planning to fence the garden with plants. How many saplings should he buy so that his dad can fence the garden with 5 saplings every 2.5 meters?

Question 44

State whether the following statement is true (T) or false (F).

If 6x=18, then 18x=54.

Question 85 (d)

Evaluate
$\frac{3^4\times {12}^3\times 36}{2^5\times 6^3}$

Question 100

In the given figure find the value of $\angle BOC$, if points A, O and B collinear.

Question 53

State whether the statement is True or False.

$\frac{3}{2}$ is the solution of the equation 8x - 5 = 7.

If A = {set of whole numbers < 5} and B = {set of natural numbers < 6}, then A and B are________.

Can ${90}^{\circ }$, ${90}^{\circ }$ and ${20}^{\circ }$ form a triangle?

Add
$t-t^2-14$, $15t^3+13+9t-8t^2$, $12t^2-19-24t$ and $4t-9t^2+19t^3$.

If $t=-1$ find the value of the expression. [4 MARKS]

Find $(121{)}^2$.

Question 107

The measure of three angles of a triangle are in the ratio 5 : 3 : 1. Find the measures of these angles.

Question 74 (a)

Express the following in usual form.
$8.01\times {10}^7$

If an isosceles right - angled triangle has area $200c{m}^2$, then the measure of its hypotenuse is _______________ cm.

Which of the following shows symmetrical design?