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Question 130

Solve the following question:

Find three numbers in the ratio 2 : 3 : 5, the sum of whose squares is 608.

In the last problem, for what kind of quadrilateral do we get a rectangle by joining the mid-points?

Look at several examples of rational numbers in the form (q ≠ 0), where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions). Can you guess what property q must satisfy?

Which circle is the biggest of all?

In the given figure, what is the area of the triangle ACD?

The distance between the plates of a capacitor is d. What will be the new capacitance if a metal plate of thickness d/2 is introduced between the plates without touching them

Sort the given expressions in decreasing order.
(Highest on top)
Given:
$a=\frac{1}{3},b=-\frac{1}{3}$

A samsung tablet is to be sent as a gift to a person. The shopkeeper has to wrap the tablet which is in a box of dimensions 20 cm $\times$ 10 cm $\times$ 5 cm. How much paper would be required to wrap it? (assuming negligible thickness)

If the perimeter of one of the faces of a cube is $40\text{cm}$, then find its volume.

The graph for the following system of equations :

$2x+3y=5and6x+9y=40$ is shown

S1: $\frac{a_1}{a_2}$= $\frac{b_1}{b_2}$ ≠ $\frac{c_1}{c_2}$

S2 : The two lines intersect each other.

A point whose abscissa and ordinate are 2 and -5 respectively, lies in

If you have to draw the quadrilateral ABCD given below, what all measurements will you need to draw the quadrilateral ABCD? The measurements are given in the following options. Which of the options can help to draw ABCD?

Find the area of the quadrilateral ABCD in which BCD is an equilateral triangle, each of whose sides is 26 cm, AD = 24 cm, and $\angle BAD={90}^{\circ }.$ Also, find the perimeter of the quadrilateral. $(Given,\sqrt{3}=\mathrm{1.73.})$

(i) Find the class mark of the class 90-120.
(ii) In a frequency distribution, the mid-value of the class is 10 and width of the class is 6. Find the lower limit of the class.
(iii) The width of each of five continuous classes in a frequency distribution is 5 and lower class limit of the lowest class is 10. What is the upper class limit of the highest class?
(iv) The class marks of a frequency distribution are 15, 20, 25, .... Find the class corresponding to the class mark 20.
(v) In the class intervals 10-20, 20-30, find the class in which 20 is included.

ABCD is a rectangle in which diagonal AC bisects $\angle A$ as well as $\angle C$. Show that (i) ABCD is a square, (ii) diagonal BD bisects $\angle B$ as well as $\angle D$.

The price of 1kg of potato is Rs. 60. 1 kg onions costs 10% less than 1 kg potato. If I pay Rs. 180 for potatoes, what will be the cost of onions (of the weight same as the weight of the potatoes)?

Evaluate
(i) $(103{)}^3$ (ii) $(99{)}^3$

The parallel sides of a trapezium are ${}^{\prime }{a}^{\prime }$ and ${}^{\prime }{b}^{\prime }$ respectively. The line joining the midpoints of its nonparallel sides will be

(a) $\frac{1}{2}(a-b)$

(b) $\frac{1}{2}(a+b)$

(c) $\frac{2ab}{(a+b)}$

(d) $\sqrt{ab}$

If $x=(7+4\sqrt{3})$ then $(x+\frac{1}{x})$=?

(a) $8\sqrt{3}$

(b) 14

(c) 49

(d) 48

By how much is $\frac{18}{20}$ greater than $\frac{7}{20}$?

Which number model represents (-2) + (-8)?

A solid iron cuboidal block of dimensions $4.4m\times 2.6m\times 1m$ is recasted into a hollow cylindrical pipe of internal radius $30cm$ and thickness $5cm$. The length of the pipe is ________.

State the power law of exponents.

Construct a quadrilateral $BEAR$ in which $BE=6cm,EA=7cm,RB=RE=5cm$ and $BA=9cm$. Measure its fourth side.

Find the volume, the lateral surface area, the total surface area and the diagonal of a cube, each of whose edges measures 9m. $(Take\sqrt{3}=\mathrm{1.73.})$

A solid cylinder of radius r is placed vertically inside a bigger hallow cylinder of radius R, both having height H. The volume of water that can be filled in the hallow cylinder is $\pi$x__xH ( $x^2$ as x2 in the answer )

If one of the angles of a parallelogram is 80°, the other non-adjacent angle is ___degrees.