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Simplify:

(1)

(2)

(3)

(4)

(5)

(6)

Which of the following combinations are not possible for a triangle?

I.Sides as 4 cm, 9 cm, 13 cm.

II.Two obtuse angles.

III.Two acute angles.

IV. Sides as 9 cm, 8 cm and 7 cm.

The sum the numerator and denominator of a fraction is 12 if the denominator is increased by 3 the fraction becomes 1\2 find the fraction

In a $△$ABC, right angled at B, AC - AB = 1 unit, and BC = 7 units.

What is $\text{cosec}C$?

At what rate percent per annum at simple interest, will a sum triple itself in $16$ years?
(a) $12\%$
(b) $10.5\%$
(c) $11.5\%$
(d) $12.5\%$

In the figure below, if $\Delta ABC$ is an isosceles triangle and OB and OC are angle bisectors, then $\angle BOC=$

Question 178(ii)

If a = -1, b = 2, then find the value of the following.

$a^b-b^a$

What is the sum of 5p, 6q and 7r?

The cardinal number of $A=\left\{\right(x:x=5n,n\in W,n<4\}$ is ___.

To represent 3 x ( ) which of following fraction form is appropriate.

2/√2=2how?

A collection of facts, such as values or measurements is known as

Find the number(s) that can be multiplied with $672$ to make it a perfect square.

Area of a trapezium = $\frac{1}{2}\times height\times$ sum of ___ sides.

Ajit has a certain average for $9$ innings. In the tenth inning, he scores $100$ runs, thereby increasing his average by $8$ runs. What is his new average?

Question 1 (v)

State whether the pair of triangles in the below figure is similar. Write the similarity criterion used by you for answering the question and also write the pair of similar triangles in the symbolic form:

Find the value of $({\left(\frac{3}{2}{)}^{-1}\right)}^{-2}.$

What other
name can you give to the line of symmetry of

(a) an
isosceles triangle?

(b)a
circle?

There are 40 animals in a zoo out of which 10 animals have recently been transferred from another zoo. What is the fraction of the animals which are old?

A bird shooter was asked how many birds he had in his bag. He replied that there were all sparrows but six, all pigeons but six, and all ducks but six. How many birds did he have in all in his bag?

A. 9

B. 18

C. 27

D. 36

Construct an equilateral $△XYZ$. Whose sides are $4.5cm$.

Find the area of the shaded part in the figure given below. (Take $\pi$ = $\frac{22}{7}$)(All the dimensions are in cm)

A job vacancy at a local law firm wants applicants who are atleast 24 yrs old but not more than 30 years. If $x$ is the age of an applicant, then .

Rotate the red shape about the black point 90 degrees clockwise.

Question 5(vi)

Give expression for the following case.

y is multiplied by - 8 and then 5 is added to the result.

On a number line, 2.5 will lie:

Write a rational number equivalent to $\frac{2}{3}$​ whose numerator is 8.

Question 3(ii)
Solve the following equation by trial and error method:
3m- 14 = 4

The number of faces of a sphere is ______.

If a set has 7 proper subsets, then it contains ___ elements.

In the given figure, AB is the diameter of the circle and $\angle CBA={50}^{\circ }$, then the measure of $\angle CDB$ is equal to

Question 74

Choose a letter x, y, z, p etc...., wherever necessary, for the unknown (variable) and write the corresponding expressions for the given statement:

Write an equation whose solution is not a whole number.

If 6, 8 and c form a Pythagorean triplet, then find the value of c?