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The quadrilateral formed by joining the midpoints of the sides of a quadrilateral ABCD, taken in order, is a rhombus, if

(a) ABCD is a parallelogram

(b) ABCD is a rhombus

(c) diagonals of ABCD are equal

(d) diagonals of ABCD are perpendicular to each other

If A and B are two points on a circle such that m$\left(\overline{AB}\right)={260}^o$. A possible value for the angle subtended by are BA at a point on the circle is

The circumference of the base of a 10 m height conical tent is 44 meters.Calculate the length of canvas used in making the tent if width of canvas is 2 m.(Use $\pi =\frac{22}{7})$

Two angles of a triangle are equal and the third angle is greter than each of those angles by ${30}^{\circ }$. Determine all the angles of the triangle.

The points (a, a) (–a, -a) and $(–\sqrt{3}a,\sqrt{3}a)$ form the vertices of an

The distance between A (1, 3) and B (x, 7) is 5. The value of x (> 0) is :

Which of the following is a rational number?

(a) $\sqrt{5}$

(b) 0.101001000100001........

(c) $\pi$

(d) 0.853853853.....

A cone and a hemisphere have equal bases and equal volumes. The ratio of their heights is

The distribution of the heights of 50 children are given. If the mean height for the distribution is 117.8 cm, then complete the following table.
$\begin{array}{ccccccc}Height& 110& 115& x_1& 120& 121& 125\\ Numberofstudents& 6& 8& 14& f_1& 4& 3\end{array}$

Number of sides in a quadrilateral?

Which one of the following statement is true?

Question 8
In the following figure, ABC is a right triangle right angled at A. BCED, ACFG and ABMN are squares on the sides BC, CA and AB respectively. Line segment $AX\perp DE$ meets BC at Y. Show that:

(i) $\Delta MBC\cong \Delta ABD$
(ii) $area\left(BYXD\right)=2area\left(\Delta MBC\right)$
(iii) $ar\left(BYXD\right)=ar\left(ABMN\right)$
(iv) $\Delta FCB\cong \Delta ACE$
(v) $ar\left(CYXE\right)=2ar\left(\Delta FCB\right)$
(vi) $ar\left(ACFG\right)=ar\left(CYXE\right)$
(vii) ar (BCED) = ar(ABMN) + ar(ACFG)

1) X/6+y/15=4

X/3-y/12=19/4

Solved it by elimination of substitution

A cube of edge 4 cm is converted into a cuboid of height 4 cm, so the area of the base of the cuboid must be

There is $80\%$ increase in an amount in 8 years at simple interest. What will be the compound interest of Rs. 14,000 after 3 years at the same rate?

1. 19

Which of the following surds is/are pure surds?

Give a method to find the centre of a given circle ?

The pairs of linear equations whose solution is x = 2, y = –3 are

Point (-3,-5) lies in the ______ quadrant.

Two matrices $A=[a_{ij}{]}_{p\times q},B=[b_{ij}{]}_{m\times n}$ are equal if.

Visualize (x+2)(x+3).

1. \N

Find the area of this paperplane. [4 MARKS]

Renuka has a square plot with the measurement as shown in the figure. She wants to construct a house in the middle of the plot. A garden is developed around the house. The total cost of developing a garden around the house at the rate of ₹ 55 per $m^2$ is

Two concentric circles are of radii 13 cm and 5 cm. Find the length of the chord of the outer circle which touches the inner circle.

The mean of 40 observations was 250. It was detected that the value of 150 was wrongly copied as 110. Find the correct mean ?

$\pi$ is

(a) a rational number

(b) an integer

(c) an irrational number

(d) a whole number

Write two equivalent versions of Euclid's fifth postulate

Which of these can be the probability of an event?

Prove that $a^2+b^2+c^2-ab-bc-ca$ is always non-negative for all values of a, b and c.

Draw a line segment AB of length 5.8 cm. Draw the perpendicular bisector of this line segment.

Evaluate ${525}^2$- ${475}^2$

Express $63km/h$ into $m/s$

Find the length which at a distance of 5280m will subtend an angle of 1' at the eye.

If the perimeter of a regular hexagon is 120 cm, Find its area.

In the figure, it is given that AB = CD and AD = BC. Prove that $\Delta ADC\cong \Delta CBA.$

The angles of a triangle are $(x-40{)}^{\circ },(x-20{)}^{\circ }$ and ${(\frac{1}{2}x-10)}^{\circ }$. Find the value of $x$.

Factorize $a^3+3a^{2}b+3a{b}^2+b^3-8$

In the given figure, ABCDE is a pentagon with AC = 5 cm. A line through B parallel to AC meets DC produced at F.If the altitude of $△$ABC (perpendicular to AC) is 6 cm.The area of $△$AFC is _____.

In the adjoining figure, ABCD is a trapezium in which AB || DC and P, Q are the midpoints of AD and BC respectively. DQ and AB when produced meet at E. Also, AC and PQ A intersect at R. Prove that (i) DQ = QE, (ii) PR II AB and (iii) AR = RC.