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A circus tent is cylindrical to a height of 4 m and conical above it. If its diameter is 105 m and its slant height is 80 m, calculate the total area of canvas required. Also, find the total cost of canvas used at Rs.15 per metre if the width is 1.5 m.

The age of a father is twice the square of the age of his son. Eight years hence, the age of the father will be 4 years more than three times the age of the son. Find their present ages.

Question 62

Observe all the four triangles FAB, EAB, DAB and CAB as shown in the figure.

State whether the statement is True or False.

All triangles have the same base and the same altitude.

Find the equation of a line which passes through (5, 4) and makes an angle of ${60}^{\circ }$ with the positive direction of the x-axis.

Water in a canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/h. How much area will it irrigate (in $m^2$) in 30 minutes, if 8 cm of standing water is needed?

Consider two pair of equations:
2x+y-5=0
ax+by-12=0
Find the probability such that given pair of equations represent parallel lines, where value of a and b is decided by rolling a pair of dice simultaneously.

An aeroplane takes 1 hour less for a journey of 1200 km if its speed is increased by 100 km/hr than its usual speed. Find its usual speed.

Which of the following is the possible value of $\left(x\right|$ if ${\left(x\right|}^2-6\left(x\right|+8=0$

Which one is in the simplest form for √112?

The quadratic polynomial in x whose zeros are -a, 2a is

If a and b are relatively prime then what is their HCF ?

A cone of radius 3 cm and slant height 5 cm has curved surface area of:

Show that the square of any positive integer cannot be of the form 3m + 2, where m is a natural number.

The scales chosen for both the axes are the same, while drawing a histogram.

In the given figure, AB is the diameter of the circle. Find the value of $\angle$ ACD

1. 90

If x ∝ y , y ∝ z and z ∝ x , then the product of the 3 non - zero variation constant is :

The sum of HCF and LCM of two numbers is 7380.If the LCM of these numbers is 7340 more than their HCF. Find the Product of the two numbers.

How to find the range and domain of any trigonometric ratio

Krishnan bought chocolates for his brothers. When he grouped the chocolates in groups of 4, 1 chocolate was left, if grouped in 5, 4 chocolates were left, if grouped in 6, 1 chocolate was left and if grouped in 7, no chocolate was left ungrouped. If the total number of chocolates bought was less than 50, find the number of chocolates Krishnan bought.

In the given figure, chords $AB=CD,\angle COD={60}^{\circ }$ and $\angle AOD={170}^{\circ }$.

Find the value of $\angle BOC$.

Question 90

In the following question, state whether the given statements are true (T) or false (F).

$a^m\times b^m=(ab{)}^m$

A bag consists of 7 red balls, 9 white balls and 8 green balls. 3 balls are taken out of the bag at random one-by-one. What is the probability that the third ball is neither green nor white if the first two balls are red?

The sum up to $n$ terms of an AP in which the first term is $a$, the last term is $l$, and the common difference is $d$, is ___

$\frac{x+y-8}{2}$ = $\frac{x+2y-14}{8}$ = $\frac{3x+y-12}{11}$​

Solution of the given system of equation is

If the centre of a circle is (2a, a-7), then the values of 'a', if the circle passes through the point (11,-9) and has diameter $10\sqrt{2}$ units will be:

The king, queen and jack of clubs are removed from a deck of 52 playing cards and then shuffled. Find the probability of getting an '8’ of red color if a card is drawn from the remaining cards.

Find the quadratic polynomial, sum and product of whose zeroes are 0 and -1 respectively.

The common difference for the arithmetic progression
$3+2\sqrt{2},3+4\sqrt{2},3+6\sqrt{2},3+8\sqrt{2}$ is

$\text{In the given figure, DE || BC. If AD = 6 cm,}\text{AB = 24 cm and DE = 5 cm, then}\text{BC = \_\_\_\_ cm.}$

Verify that 1/2 , 1 and -2 are the zeroes of the cubic polynomial 2x³ + x² -5x + 2

What is the value obtained when we expand $({1+\sqrt{3})}^2$?

RD in RD account stands for _______.

From an external point P, two tangents are drawn that touches the circle at points Q and R. The triangle PQR is a/an___ triangle.

Difference of zeroes of quadratic equation whose roots are consecutive integer is _________.

Which of the following trigonometric ratios will have the same value as sec(${47}^{\circ }$)?

If $x=asec\theta$ and $y=btan\theta$ then $b^2{x}^2-a^2{y}^2=$

Which of the following are the graphs of odd functions?

1. Mr. prakash invested Rs.52000 on Rs.100 shares at a discount of Rs.20 paying 8% dividend. At the end of one year, he sells the shares at Premium of Rs.20, find:

1. The annual dividend.

2. The profit earned including his dividend.

Solve for x $:9x^2-9(a+b)x+(2a^2+5ab+2b^2)=0$by the quadratic polynomial.

In which of the following situations , does the list of numbers involved make an arithmetic progression , and why?

4) The amount of money in the account every year , when Rs.10,000 is deposited at compound interest at 8%/annum.

On Dividing a quadratic polynomial by a linear polynomial.The quotient obtained is always

a) a Constant

b) a linear polynomial

c) a quadratic polynomial

d) a cubic polynomial