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Question 55

State whether the following statement is true or false:

The surface area of a cuboid formed by joining face-to-face 3 cubes of side x is 3 times the surface area of a cube of side x.

Which of the following are the factors of
$27a^2-12b^2?$

Factorise the following:

Factorise

(x - y)² + 4xy - z^{​​​​​​2} .

A boy of $45kg$ weight is standing on the piston of cross sectional area $900c{m}^2$. Find the difference in the levels of water in the two tubes.

A dance floor has to be built as a triangular glass platform with the dimensions 7 m, 8 m and 9 m. The total surface area of the glass required to build such a platform is equal to ________ $m^2$.

What would be the exponent of '$a^k$' in $a^k\times a^k\times a^k....$ (upto k times)?

Question 12

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

If $\frac{-4}{3}y=-\frac{3}{4},$ then y is equal to:

(a) ${\left(\frac{-3}{4}\right)}^2$

(b) ${\left(\frac{-4}{3}\right)}^2$

(c) ${\left(\frac{3}{4}\right)}^2$

(d) ${\left(\frac{4}{3}\right)}^2$

The full form of HCF is:

Question 105(iii)

The following histogram shows the frequency distribution of teaching experiences of 30 teachers in various schools :



How many teachers have teaching experience of 10 to 20 years ?

Question 6

The line represented by x = 7 is parallel to the X-axis. Justify whether the statement is true or not.

If the relation R on set A = {1, 2, 3 . . . . . . 13, 14} is defined as R = {(x, y):3x - y = 0}, find the range of R.

If each interior angle of a regular polygon is ${170}^{\circ }$, then the polygon has ___ sides.

Find and correct the errors in the statement: 3x + 2x
= 5x²

The number of edges in a match-box is ___.

The quotient obtained when we divide $a^6-b^6$ by the product of $a^2+ab+b^2$ and $a-b$.

A man deposits 50,000 rupees in a financial company, which gives 9% interest compounded every three months. How much would he get back after one year?

Simplify :$\left\{\frac{1}{6^{(-2)}}-\frac{1}{3^{(-3)}}\right\}÷\left\{\frac{1}{5^{(-2)}}\right\}$

5 is added to a number and its square root is taken, the result is 25. What is the number?

Plot the points (5,0), (5,1), (5,8). Do they lie on a line? What is your observation?

How much water should be filled in a container 21 cm in height, so that it

appears half filled when viewed from the top of the container (given that )

$\frac{2}{3}$ of a number is 20 less than the original number. Find the number.

What is x if (2x+2) = (5x-1)?

1. 3

In a certain code, $PROSE$ is coded as $PPOQE.$ How is $LIGHT$ coded in that code?

Arun draws a regular non-convex polygon, with spokes that extend from each vertex to the center of the board. If each spoke is 8 inches long, and spokes are used nowhere else on the board, what is the sum of the interior angles of the polygon?
(1) The sum of the exterior angles of the polygon is ${360}^{\circ }$.
(2) The sum of the exterior angles is equal to five times the total length of all of the spokes used.

$ab+2ab$ is equal to

Find the value of
$\left[\right(3+4–6÷2+2)+(9÷3+6\times 5)÷11]$

Four persons have weights $50$ lb, $50$ lb, $45$ lb and $45$ lb. The average weight of four persons is .

A $5m60cm$ high vertical pole casts a shadow $3m20cm$ long. Find at the same time the length of the shadow cast by another pole $10m50cm$ high.

$△$ABC is a right angled triangle, right angled at B. BD is a perpendicular as shown. Prove that:



${AB}^2$ = ${AD}^2$ + ${BC}^2$ - ${CD}^2$