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

46

qQuestion 29

Fill in the blank to make the statememt true
${\left[{\left(\frac{-1}{4}\right)}^{16}\right]}^2=\text{\_\_}$

From the point A (0, 3) on the circle $x^2+4x+(y-3{)}^2=0$ a chord AB is drawn and extended to a point M such that AM =2AB. The equation of the locus of M is___

Consider two right-angled triangles inscribed in a square such that their hypotenuse intersect at a point O inside the square. What is the angle between the hypotenuse of the triangle and the base of the square?

Find the area of a rhombus having diagonals of length 10 cm and 20 cm.

Dipanshu invested a sum of money from May 2006 to May 2008 at the rate of 12% per annum. If the interest received by him is ₹1620, find the invested money.

Question 55

In the following question, fill in the blanks to make the statements true.

The standard from for 32500000000 is ___ .

If a square park has side 12.5 m, then its area is _____ $m^2$

Identify the region which represents the power $2^2.$

Curved surface area of cylinder of radius r and height h is:

Question 2(iii)
Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube:
72

Prove that x² − 6x + 9 is a perfect square for all natural numbers x. What can you say about its square root?

How many 4-digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 97 and no digit appears more than once?

Write down ten positive rational numbers such that the sum of the numerator and the denominator of each is 11. Write them in decreasing order.

Construct a triangle ABC, whose perimeter is 13.5 cm and whose base angles are 60° and 75°.

The number of people in various age groups in a town are given in the following table:

Draw a bar graph to represent the given data.(Take 1 unit length = 20 thousand)

Question 4

Find the values of the letters in the following and give reasons for the steps involved.

$AB$

$\underset{–}{+37}$

$\underset{–}{6A}$

-6 divided by 0 is ____

In the figure AD = EC, which additional information is needed to show that $△ABD$ and $△EBC$ will be congruent by A - A - S test?

Take away 8x − 7y − 8p + 10q from 10x + 10y − 7p + 9q.

Which of the following is the complete factorization of $14x^3?$

Question 34



Fill in the blanks to make the statement true.



A pentagonal prism has ___ faces.

Find the value of ($3^2$ + $4^{-1}$) $\times$ $2^2$

The ages of Ashu and Raju are in the ratio 5: 7. If Ashu was 9 years older and Raju 9 years younger, the age of Ashu would have been twice the age of Raju. Find their present ages.

The figure shows a regular heptagon and a regular hexagon are put together. Then the measures of $\angle ABC$ is

Suppose $L=\{p,q,r,s,t\}$ is a lattice represented by the following Hasse diagram:



For any $xyϵL$, not necessarily distinct, $x\vee y$ and $x\wedge y$ are join and meet of $x,y$ respectively. Let $L^3=\left\{\right(x,y,z):x,y,zϵL\}$ be the set of all ordered triplets of the elements of $L$. Let $p_r$, be the probability that an element $(x,y,z)ϵL^3$ chosen equiprobably satisfies $x\vee (y\wedge z))=(x\vee y)\wedge (x\vee z)$. Then

The difference between the two adjacent angles of a parallelogram is 20°. Find measures of all the angles of the parallelogram.

6 : 5 when expressed as a percentage, is