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What is rational number

The value of the expression $16x^2+24x+9$ for $x=0$ is _____.

Two real numbers $a$ and $b$ are chosen independently and uniformly at random from the interval $(0,75).$ Let $O$ and $P$ be two points on the plane with $OP=200.$ Let $Q$ and $R$ be on the same side of line $OP$ such that the degree measure of $\angle POQ$ and $\angle POR$ are $a$ and $b$ respectively and $\angle OQP$ and $\angle ORP$ are both right angles. The probability that $QR\le 100$ is equal to

A metallic ball of radius 18 cm is melted to form a certain number of smaller metallic balls of radius 6 cm each. Find the number of such balls.

Question 1
Show that the cube of a positive integer of the form 6q + r, where q is an integer and r = 0, 1, 2, 3, 4, 5 is also of the form 6m + r.

Match the APs to their $n^{\text{th}}$ terms.

Question 7
Draw a right triangle in which the sides (other than hypotenuse) are of lengths 4 cm and 3 cm. Then construct another triangle whose sides are $\frac{5}{3}$ times the corresponding sides of the given triangle.

Solve each of the following equations by using the method of completing the square:
$x^2-6x+3=0$

The diameter of a sphere is 6cm. It is melted and drawn into a wire of diameter 2 mm. Find the length of the wire.

Which of the following trigonometric expressions is equal to ${\text{sec}}^6\theta$ ?

How many minimum number of points are required to draw a single line ?

If $A=\left[\begin{array}{cc}1& 2\\ 3& 4\\ 5& 6\end{array}\right]$ and $B=\left[\begin{array}{cc}-3& -2\\ 1& -5\\ 4& 3\end{array}\right]$,

then the value of $D=\left[\begin{array}{cc}p& q\\ r& s\\ t& u\end{array}\right]$such that $A+B-D=O$

The coodinates of the point which divides the line joining the points $(2,3,4)$ and $(3,-4,7)$ in the ratio $2:4$ externally is:

Half the perimeter of a rectangular room is 46 m, and its length is 6 m more than its breadth. What is the length and breadth of the room?

What property would you use to find angle PTQ?

The largest possible sphere is carved out from a cube of 7 cm side. The volume of the sphere will be

Let $f\left(x\right)$ be a function defined on $[-1,1]$.If the distance between $(0,0)$ and $(x,f(x\left)\right)$ is 1 unit , then the function $f\left(x\right)$ may be.

Question 72

State whether the statement is True or False.

Out of two figures, if one has a larger area, then its perimeter need not to be larger than the other figure.

If the roots of the equation $(b-c)x^2+(c-a)x+(a-b)=0$ are equal, then prove that 2b = a +c.

The median AD of the $\Delta ABC$ is bisected at E, BE meets AC in F, then AF: AC is equal to

Question 5
A 5 m long ladder is placed leaning towards a vertical wall such that it reaches the wall at a point 4m high. If the foot of the ladder is moved 1.6m towards the wall then find the distance by which the top of the ladder would slide upwards on the wall.

The minute hand of a clock is 15 cm long. Calculate the area swept by it in 20 minutes. [ Take $\pi$ = 3.14.]

When 6 is added to the numerator of a fraction, the numerator becomes twice the denominator. 10 times the denominator exceeds 5 times the numerator by 30. The number of solutions for the fraction is

A chord AB of a circle is equal to the radius of the circle. Find the angles subtended by the chord at points on the major arc and the minor arc, respectively.

Q2. Find:

(i) (ii) (iii)

(iv)

1. 2

Find the four numbers in AP whose sum is 50 and in which the greatest number is 4 times the least .