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Factorise

X square-y square-2x+6y-8

The length of a room is 1.5 times of its breadth. The cost of carpeting the at Rs. 5 per sq. m is Rs. 270 and the cost of papering the four walls at Rs. 10 per $m^2$ is Rs. 1720. If a door and 2 windows occupy 8 sq. m, find the height of the room.

If $x=0.\overline{18}$, which of the following statements are true?

(i) $100x=18.\overline{18}$ (ii) $100x-x=17.\overline{18}$ (iii) $99x=18$

Which statement is incorrect about the following sentences?

Kamal and Anand each lent the same sum of money for 2 years at 5% at simple interest and compound interest respectively. Anand received Rs. 15 more than Kamal. Find the amount of money lent by each and the interest received.

The sides of $\Delta \text{ABC}$ have sides AB, BC, AC as $2cm,4cm,\text{and}6cm$ respectively. Find the sides of the larger triangle which is similar to $\Delta \text{ABC}$, if the ratio of corresponding sides is $3$.

The value of p for which x + p is a factor of x² + px + 3 - p is:

Divide Rs. 28,730 between A and B so that when their shares are lent out at 10 per cent compound interest compounded per year, the amount that A receives in 3 years is the same as what B receives in 5 years.

What is the length of the line segment joining the mid points of the diagonals of a trapezium that is parallel to each of the parallel sides having lengths 12 cm and 4 cm.

Which of the following expressions is equivalent to the expression 706 × 695?

What are the lines passing through the point (1,1)?

The point which lies on the x-axis at a distance of 4 units in the negative direction of x-axis is __________ .

Question 128
Fill in the blank to make the statement true.

9128 $\times$ ___ = 9128

Classify the following numbers as rational or irrational

a) √27 b) √441 c) 30.232342345..…… d) 7.484848...

d) 11.2132435465 e) 0.3030030003....

Find the measure of each angle of a parallelogram, if one of its angles is ${30}^{\circ }$ less than twice the smallest angle.

A heap of wheat is in the form of a cone of diameter 9 m and height 3.5 m.Find its volume.How much canvas cloth is required to just cover the heap?$(Use\pi =3.14)$

How many metres of cloth, 2.5 m wide, will required to make a conical tent whose base radius is 7 and height 24 m ?

Factorize:

$2x^2+3\sqrt{5}x+5$

In the given figure, AB||CD and BC||ED. Find the value of x.

Question 39

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

Two different equations can never have the same answer.

In the figure below, $△$ABC $\cong$ $△$BED, $\angle$DEB = ${115}^{\circ }$ and $\angle$CAB = ${25}^{\circ }$, find $\angle$BDE.

Ram and Shyam were playing. Ram asks Shyam to form numbers with the digits 4,3, 8 and 1. He gives him three different cases as

i. Form four digit greatest number with no repetition of digits.

ii. Form four digit greatest number where a digit can be repeated twice.

iii. Form smallest four digit number where repetition of digits is allowed.

So the numbers formed in the three cases will be:

In the given figure, O is the centre of the circle, arc ABC subtends an angle of ${130}^{\circ }$ at the centre. If AB is extended to P, find $\angle PBC$

1. undefined
2. undefined
3. undefined
4. undefined

Following are the details of exam results for Math and English for a class of 100 students.

$$\begin{array}{ccc}& PassedMath& PassedEnglish\\ PassedMath& 25& 20\\ PassedMath& 35& 20\end{array}$$

Find the probability that a student selected at random passed in:
1. both exams
2. exactly one exam
3. at least one exam [3 MARKS]

In a triangle ABC, E is the mid-point of median AD.Then,ar (ΔBED) = $\frac{1}{4}$ar(ΔABC)

Write the coordinates of a point which lies on the y-axis and is at a distance of y units below the x-axis.

In the figure, there is a jogging track which consists of two semi-circular track and two rectangle track that have to be renovated. For the circular parts, the inner and outer radii are 6 m and 8 m respectively. Find the area highlighted in green colour (in square meters).

Which of the following is not true for a point P on the circle?

If D is any point on the base BC produced, of an isosceles triangle ABC, prove that AD > AB. [3 MARKS]

An iron tank with an open top is cylindrical in shape. It has a height 10m and radius 7m. It gets corroded at a rate of 3 sq. meter/day. The number of days in which it gets completely corroded is (Take pi=$\frac{22}{7}$)

If LM $\parallel$ AB, AL=x-3, AC=2x, BM=x-2, BC=2x+3. What is value of AC?

__

A right angled triangle $\Delta ABC$ is right angled at C with sides AB = 10 cm and AC = 6 cm. Find cosine of $\angle$B.

The external dimensions of a wooden box are 18 cm, 10 cm and 6 cm respectively and thickness of the wood is 5 mm. If the empty box weighs 3.15 kg, then the weight of $1c{m}^3$ of wood is ________.

Question 97

Solve the following:

The age of A is five years more than that of B. 5 years ago, the ratio of their ages was 3:2. Find their present ages.

If x and y take only natural number values, find the number of (x,y) pairs satisfying the equation 2x+5y=100

Write the degree of each of the following polynomial.for example? (1)6^x3​​​​​​+4^x2+7^x

The area of a trapezium is 475cm² and the height is 19 cm . Find the length of its parallel sides if one side is 4cm greater than the other

Question 7
Ritu ate $\frac{3}{5}$ part of an apple and the remaining apple was eaten by her brother Somu. How much part of the apple did somu eat? Who had the larger share? By how much?

Simplify ${\left(\frac{7^8}{7^9}\right)}^{17}\times {\left(\frac{7^9}{7^{10}}\right)}^{19}\times {\left(\frac{7^{10}}{7^8}\right)}^{18}$

$△ABC$ , right angled at B, BC = 6 cm and ∠ABC = ${30}^{\circ }$. Determine the length of the side AB and AC.

Let $f,g$ and $h$be real valued functions defined on the interval [0,1] by$f\left(x\right)=e^{x^2}+e^{-x^2},g\left(x\right)=x{e}^{x^2}+e^{-x^2}$ and $h\left(x\right)=x^2{e}^{x^2}+e^{-x^2}$. If a, b and c denote, respectively, the absolute maximum of f, g and h on [0,1], then

$3x–5y=4$
$9x=2y+7$

Solve the above equations by elimination method and find the value of x.

The value of cos $\theta$ in the given triangle is

Find the volume of cone whose height and radius are 6 cm and 5 cm respectively.