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Find the smallest number having three different prime factorsl

In an exhibition, the number of rounds of the Giant wheel rotated for a person are charged as follows. Check whether the rotation charges are in direct proportion with the number of rounds of the Giant wheel. [2 MARKS]

4 Rounds Rs.50

8 Rounds Rs.80

12 Rounds Rs.120

24 Rounds Rs.180

Question 51

If x and y are in inverse proportion, then (x + 1) and (y + 1) are also in inverse proportion.

If $x=2+\sqrt{3}$, find the value of $x^3+\frac{1}{x^3}$.

Factorise:

25a^2-35a+12

The figure below shows a square, each of whose sides is 3 centimetres long. Each side is divided into three equal parts and these points are joined to form an octagon:

What is the perimeter of the octagon?

In the following data, the number of class intervals, (by inclusive method), and taking 4 as the magnitude of class intervals will be

31, 23, 19, 29, 22, 20, 16, 10, 13, 34

38, 33, 28, 21, 15, 18, 36, 24, 18, 15

12, 30, 27, 23, 20, 17, 14, 32, 26, 25

18, 29, 24, 19, 16, 11, 22, 15, 17, 10

If I draw 30 face cards in 100 draws of a card (with replacement), then the probability of drawing a number card is?

The dome of a building is hemispherical in shape,having radius of 7 m. It has to be painted at Rs.5 per sq. m. Find the total cost of painting the dome.

Statement 1: A polynomial P(x) of degree greater than or equal to one, when divided by $(x–a)$, leaves a remainder zero.

Statement 2: $(x–a)$ is a factor of the polynomial P(x).

Let $f\left(x\right)=x^2$ and $g\left(x\right)=\sin x$ for all $x\in R$. Then the set of all $x$ satifying $(f\circ g\circ g\circ f)\left(x\right)=(g\circ g\circ f)\left(x\right)$, where $(f\circ g)\left(x\right)=f\left(g\right(x\left)\right)$, is

If 20 students in a class failed an exam, the probability of a student selected at random getting passed in an exam is 0.6. The number of students in the class is = ___ .

In fig., in ∆ABC, AB = AC. The value of x is:

Sand is poured at a rate of $1000\text{c.c/sec}$ on the ground(from a certain height), which is always in the form of cone whose height $\left(h\right)$ is equal to the base radius $r$. If $l$ is its slant height and $S$ is the curved surface area and $h=40\text{cm}$(at an instant), then which of the following(s) is/are true

Recall, π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is, . This seems to contradict the fact that π is irrational. How will you resolve this contradiction?

A right angled $\Delta PQR$, where $\angle PQR={90}^{\circ }$. A circle with centre O is inscribed in this triangle. Find the radius of circle. Length of side PQ = 8 cm and PR is 15 cm.

Find the value of x.

Construct a $△$ABC in which AB + AC = 5.6 cm, BC = 4.5 cm and $\angle B={45}^{\circ }$.

Which of the following should be the SECOND sentence after rearrangement?

​What can you say about the prime factorisations of the denominators of the following rationals:
$\left(i\right)43.123456789$
$\left(ii\right)43.\overline{123456789}$
$\left(iii\right)27.\overline{142857}$
$\left(iv\right)\mathrm{0.120120012000120000....}$

In the given figure, M is the centre of the circle. Chords AB and CD are perpendiculat to each other.

If $\angle$ MAD = x and $\angle$ BAC = y :

(i) express $\angle$ AMD in terms of x.

(ii) express $\angle$ ABD in terms of y.

(iii) prove that : x = y.

The dimensions of a rectangular block are in the ratio of 4:3:2. The volume is 31944 $d{m}^3$. If its entire surface is polished at 3 paise per $d{m}^2$, then the total cost will be:

If $(x^{\frac{1}{3}}+y^{\frac{1}{3}}+z^{\frac{1}{3}}=0)$, then -

∆ABC and ∆DEF are two triangle in which A-B=DF angle ACB=70°, ANGLE ABC=60° Angle DEF=70° and angle EDF=60°

If one of the four angles formed by two intersecting lines us a right angle, then show that each of the four angles is a right angle.

Ungrouped data, not measured in numbers, is represented by

In the figure given below, ABCD is a parallelogram. From the given options, select what could be the values of either $x$ or $y$.

Factorise:
$9x^2-3x-20$

The area of trapezium ABCD, where AB = 45 cm, BC = 20 cm, CD = 20 cm and DA = 15 cm and AB || CD, is