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Question 9 (i)

How many numbers lie between squares of the following numbers?



12 and 13

Question 3(ii)

Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube:

128

Question 5
Find the values of the letters in the following and give reasons for the steps involved.
$AB$
$\underset{–}{\times 3}$
$\underset{–}{CAB}$

Following bearings are observed while traversing with a compass.

I construct quadrilateral with 3 sides and 2 included angles being ${75}^{\circ }$ and ${105}^{\circ }$ respectively and no sides are equal. What is the type of quadrilateral I am constructing?

Question 56

The side of the square of area $9y^2$ is ___

The following data gives the information number of runs scored by 20 players in a match.

Arrange the given in grouped frequency distribution.

$\begin{array}{cccccccccc}11& 15& 23& 25& 31& 33& 39& 42& 43& 49\\ 51& 56& 65& 75& 79& 89& 99& 98& 92& 91\end{array}$

Find the area of the rhombus having each side equal to 17 cm and one of its diagonals equal to 16 cm.

The radius of Jupiter is 11 times the radius of earth. Calculate the ratio of the volume of Jupiter and earth. How many times earth can Jupiter accommodate?

Question 1 (iv)

What will be the unit digit of the squares of the following number:

3853

Find the value of $6!?$

Factorise. $365y^4{z}^3–146y^2{z}^4$

The are 16 workers working to construct a wall and it will take 48 hours to build it. But due to some accident, 4 workers injured and left. Now, the contractor wants the wall to be built in 32 hours. How many more workers are required to complete the job?

If a square has a side of length $4cm$, what is the length of the diagonal?

The rational number $\frac{110}{-132}$ when reduced to its standard form is:

Find the cube-roots of:

(i) 2.744 (ii) 9.261 (iii) 0.000027

(iv) -0.512 (v)-15.625 (vi)-125 \times 1000

Question 167

Find three machines that can be replaced with hook-up of $(\times 5)$ , machines.

If 20 oranges can be bought for Rs. 40, then how many oranges can be bought for Rs. 52?

The population of cattle in a farm increases so that the difference between the population in year n+2 and that in year n is proportional to the population in n + 1. If the populations in years 2010, 2011 and 2013 were 39, 60 and 123, respectively, then the population in 2012 was

Which among the following is not a factor of $4y(y+3)$?

Question 92 (xviii)

Factorise the following using the identity $a^2-b^2=(a+b)(a-b).$

$a^4-(a-b{)}^4$

Two farmers A and B together own a stock of grocery. They agree to divide it by its value. Farmer A takes 72 bags while B takes 92 bags and gives Rs 8,000 to A. What is the cost of each bag?

Question 85 (g)

Evaluate
$\frac{6^4\times 9^2\times {25}^3}{3^2\times 4^2\times {15}^6}$

$\text{Meenakshi sells a pen for Rs.54 and loses}\frac{1}{10}\text{of her outlay. Find (i) the cost price of the pen,and (ii) the loss per cent.}$

What is the difference between the compound interests on ₹10,000 for 2 years at 20% per annum compounded yearly and half-yearly?

At what rate percent of simple interest will the interest on Rs. 3750 be one-fifth of itself in 4 years? To what will it amount in 15 years?

Draw a quadrilateral with equal diagonals, which is not a rectangle.

In a regular polygon if the ratio of inner and outer angle is 7:2, then find the number of sides in the polygon.

Question 126 (a) (iii)

Architects design many types of buildings. They draw plans for houses, such as the plant shown in the following figure.

An architect wants to install a decorative moulding around the ceilings in the rooms. The decorative moulding costs Rs. 500/ meter.

Find how much moulding will be needed for dining room

With reference to the figure below, consider the two statements:

Statement I: The points A, B, and C will lie on a straight line if x + y = ${180}^{\circ }$.

Statement II: If the angle between two lines is ${180}^{\circ }$, then all the points on both the lines lie on a straight line.

Given a cylindrical tank, in which situation will you find the surface area and in which situation volume.
(a) To find how much it can hold
(b) Number of cement bags required to plaster it
(c) To find the number of smaller tanks that can be filled with water from it.

Match the following polygons with their respective sum of internal angles.

Construct the histogram for the following grouped frequency distribution.

Question 24

Discount = ___ - ___

Find the measure of the smallest angle if the measure of one angle in a right angled triangle is 55${}^0$?