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Question 52

If p and q are in inverse propotion, i.e. pq = k (constant), then (p + 2) and (q - 2) are also in inverse proportion.

Question 3(iii)

You are told that 1,331 is a perfect cube. Can you guess with factorization what is its cube root? Similarly guess the cube roots of

32768

A cuboid shaped bank locker has length, breadth and height as 50 cm, 50cm and 2 m respectively.It has to be secured by touch sensor system which is done at Rs. 5 per 100 sq. cm. The total cost of security arrangement is

Select the correct representation of an integer $x$, which is at least $-6$.

Out of the numbers from 0 to 10, what fraction of them are prime numbers?

Question 104

In the given figure, PQ || RT. Find the value of a+b.

Find:

(i) ${64}^{\frac{1}{2}}$ .

Bill heard that in “The Hall of Operations”, there was another ancient temple, named “The Reciprocus”.

Legend says that when an occupant, say “a”, of the “House of Rational Numbers, Q” enters the temple, it exits the temple as a different occupant, “b”,belonging to the same house. Bill observed that, these occupants “a” and “b”, when they enter the hall of multiplication, they exit the hall as “1”.

Bill realized that the numerical counterparts of a and b (Earth 1) are ___________ of each other.

Ajit lives on the 18^th floor of a building. He came down 9 floors and collected his Maths textbook from his friend Karan. Later, he went up along with Karan to Goutham's house which is 12 floors above Karan's for group work. If Goutham lives on the topmost floor of the building, how many floors does the building have?

If the HCF of (306, 657) = 9, find LCM of (306, 657).

Find the ratio of 1 m and 2 m 25 cm.

The ratio between the diameters of two circles is $5:7$. The ratio between their areas is _____.

Match the following triangles with their respective areas.

One day Krishnayya and his 10-year-old granddaughter Subbu are having the following conversation:

Subbu: Grandpa, When were you born?
Krishnayya then gave a Mathematical puzzle to his granddaughter to solve.

Grandfather: Kid, I am 8 more than 6 times your age by now (2015).
Subbu started thinking. Being good at Mathematics, Subbu screamed her grandpa's year of birth in less than a minute.
Which year do you think he was born?

Question 85 (ii)

In the given figure, the length of a green side is given by g and that of the red side is given by p.

Write an expression for the following pattern. Also, write an expression if 100 such shapes are joined together.

In the figure given below, find $x$ if AB || CD.

Match these parts of laws of exponents with their equivalent counterparts.

Multiply:

(1) 3x by 4y

(2) 2y by 4y

(3) 8a by 4m

(4) −4x by 8x

(5) −5a by −8b

(6) −6p by 4pq

(7) 2a² by 5a²

(8) 3x²b² by 5x

(9) −7m²n² by 4m

(10) −5a²b by −7ab²

1. 6

The line segment BD = ________ in the given diagram.

Check if the following relations are correct if $n$ represents an odd integer.

Question 83

The quarterly school fee in Kendriya Vidyalaya for Class VI is Rs. 540. What will be the fee for seven months?

Using the identities of algebraic expressions, Find the following

(i) (a + 9)(a + 9)

(ii) (1.9b + 1.1c)(1.9b - 1.1c)

(iii) (n - 4)(n - 4)

(iv)(-x + y)(-x + y) [4 MARKS]

What is the coefficient of $x^2$ in the polynomial $5x^3-4x^2+3x+10$ ?

Question 26

In the given figure, the value of a is

(a) ${20}^{\circ }$
(b) ${15}^{\circ }$
(c) $5^{\circ }$
(d) ${10}^{\circ }$

If two non intersecting lines x and y are perpendicular to same line then what is the relation between x and y?

If $A(1,2,3),B(2,3,1),C(3,1,2)$ are vertices of $△ABC$, then the length of altitude through $C$ is

Express the rational number $\frac{19}{37}$ to the lowest form.

The side lengths of a non-degenerate triangle $ABC$ are $4$,$11$ and $c$. The value of $c$ is

Match the equivalent fractions and write two more for each.

(i) (a) (iv) (d)

(ii) (b) (v) (e)

(iii) (c)

The perimeter of each square in the given figure is 16 cm. Find the perimeter of the whole figure given below.

Angles which are both supplementary and vertically opposite are:

A triangle of sides YZ = 7 cm, XZ = 3.5 cm and XY = 5 cm is constructed. Then the measure of angle Y is

Karan spends Rs. 5000 on food which is $\frac{5}{8}$th of his income. Karan's income is _____ (in rupees).

Written:

Construct a triangle PQR, in which PQ = 6.7 cm, QR = PR = 5.4 cm.