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Between any two rational numbers there

(a) is no rational number

(b) is exactly one rational number

(c) are infinitely many rational numbers

(d) is no irrational number

Arrange the following steps in the proper order to get a circumcircle from given regular polygon.

(a): Mark the point of intersection of the angle bisector.

(b): With the marked point as a centre and radius OA, draw the circle passing through the vertices of the given polygon.

(c): Draw the right bisector of any two sides of the polygon drawn.

(d): Construct the regular polygon.

Every point on a number line represents

Prove that a line has only one midpoint using Euclid's axioms.

1. -1

Two dice are thrown simultaneously . The probability of getting a mutiple of 2 on one die and a multiple of 3 on the other is ______

PQRS is a rectangle inscribed in a quadrant of a circle of radius 13 cm. A is any point on PQ. If PS = 5 cm, then $ar\left(△RAS\right)$ is

In the figure, ABCD is a parallelogram and E is the mid-point of side BC. If DE and AB when produced meet at F, prove that AF = 2AB.

If $x^4+\frac{1}{x^4}=119,\text{find the value of}{x}^3-\frac{1}{x^3}$.

If each edge of a cube is increased by $50\%$ then percentage increase in its surface area is

(a) $50\%$ (b) $75\%$ (c) $100\%$ (d) $125\%$

$12$ packets of salt, each marked $2$ kg, actually contained the following weights (in kg) of salt:

$\begin{array}{cccccc}1.950& 2.020& 2.060& 1.980& 2.030& 1.970\\ 2.040& 1.990& 1.985& 2.025& 2.000& 1.980\end{array}$

Out of these packets, one packet is chosen at random.

What is the probability that the chosen packet contains more than $2$ kg of salt?

This question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:

(a) Both Assertion (A) and Reason (R) are true and Reason (R) correct explanation of Assertion (A).

(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

(c) Assertion (A) is true and Reason (R) is false.

(d) Assertion (A) is false and Reason (R) is true.

In real life, the type of interest which is most commonly applied is ___

A triangle has base length 7 cm. Its base angle is ${60}^{\circ }$ and the sum of its other 2 sides is 14 cm. What type of triangle is this?

The weights (in grams) of 40 oranges picked at random from a basket are as follows:
40, 50, 60, 65, 45, 55, 30, 90, 75, 85, 70, 85, 75, 80,100 110, 70, 55, 30, 35, 45, 70, 80, 85, 95, 70, 60, 70, 75, 40, 100, 65, 60, 40, 100, 75, 110, 30, 45, 84.
Construct a frequency table as well as a cumulative frequency table.

If the curved surface area of a hemisphere is $8\pi m^2$, then the radius is.

Question 127(i)

An insect is on the 0 point of a number line, hopping towards 1. It covers half the distance from its current location to 1 with each hop.
So, it will be at $\frac{1}{2}$ after one hop, $\frac{3}{4}$ after two hops and so on.



Make a table showing the insects location for the first 10 hops.

Give the equation of two lines passing through $(2,10)$.

Measure of interior angles of a triangle are $(x+{10}^{\circ }),(x+{40}^{\circ })$ and $(2x-{30}^{\circ })$. What is the value of x?

Construct rhombus ABCD with sides of length 5 cm and diagonal AC of length 6 cm. Find the point R on CD such that RA = RB. Then the length of CR is

Question 177(vi)

Find x.

$5^x+5^{x-1}=750$

The locus of centers of all circles passing through two given points A and B is ______.

$\frac{1}{2+\sqrt{3}}$ on simplifying is ___

On what basis, do banks compound interest these days?

Factorise $4x^2-12ax-y^2-z^2-2yz+9a^2$

The x coordinate of point C is ​​​.

Find the measure of the y° in the given figure.

The sides of a rectangle are in the ratio of $6:5$ and its area is $750m^2.$ Find the perimeter of rectangle (in $m$).

Which of the following rational numbers lie between $\frac{25}{4}$ and $\frac{22}{3}$?

In a school, all students play either football or cricket or both. If 250 play football, 300 play cricket and 120 play both the games, then the number of students who play football only are ___.

Factorize

9(x-2y)^2 -4(x-2y)-13

Which among the following uses the positive form of the underlined adjective correctly?

The blue packet of chips seems fuller than the red one.

A polygon is drawn inside a circle of radius 7 cm.

What is the area of the shaded region (in $c{m}^2)$ if the area of the polygon is 24$pi{cm}^2$?

Represent √7 on number line.

If these triangles are congruent, then choose the property by which they are congruent.

Prove that each angle of a rectangle is ${90}^{\circ }$.

Find the compound ratio of:

2 : 3, 9 : 14, and 14 : 27

Respected Sir,

Please help me in solving my below mentioned doubt:

Find the values of a and b, if x² - 4 is a factor of ax⁴ + 2x³ - 3x² + bx - 4.

Let f(x) be a function defined on [0, 1] such that $f\left(x\right)=\{\begin{array}{ccc}x,& ifxϵQ& \\ 1-x,& ifx\text{/}ϵQ& \end{array}$
Then, for all $xϵ[0,1],f\left(f\right(x\left)\right)=$

Question 2
A chord AB of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the major arc and also at a point on the minor arc.

The line $y=-2x$ cuts x – axis at

The coefficient of x² in (7x - 5)(5x² - 3x + 1) is .

We have two equations
$3x–4y=1$ ---------- (1)
$5x–6y=7$ ---------- (2)
In the above equations, to eliminate the coefficients of x, what has to be done?

Find the frequency of getting a number greater than 2 but less than 5.

$\begin{array}{ccccccc}Dice& 1& 2& 3& 4& 5& 6\\ Frequency& 10& 12& 6& 4& 8& 10\end{array}$

Which of the following shows the visualization of the addition of 5x and 2?

1. \N