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The length of the smallest altitude of an isosceles triangle whose sides are a, a and $a\sqrt{2}$ is

A cylindrical containder with diameter of base 56 cm contains sufficient water to submerge a rectangular solid of iron with dimensions 32 cm $\times$ 22 cm $\times$ 14 cm. Find the rise in the level of the water when the solid is completely submerged.

The area of an equilateral triangle ABC is $17320.5c{m}^2$. With each vertex of the triangle as centre, a circle is drawn with radius equal to half the length of the side of the triangle (see Fig. 12.28). Find the area of the shaded region.

$(Use\pi =3.14and\sqrt{3}=1.73205)$

On her birthday Reema distributed chocolates in an orphanage. The total number of chocolates she distributed is given by $(5+\sqrt{11})(5-\sqrt{11})$

In $\Delta ABC,\text{AB is produced to D so that}BD=BC.if\angle B={60}^{\circ }and\angle A={70}^{\circ },provethat:\left(i\right)AD>CD\left(ii\right)AD>AC$

Find the inverse of the given matrix
$\left[\begin{array}{ccc}1& 2& 3\\ 0& 2& 4\\ 0& 0& 5\end{array}\right]$

Question 68

The length and breadth of a school ground are 150 m and 90 m respectively, while the length and breadth of a mela ground are 210 m and 126 m, respectively. Are these measurements in proportion?

On a particular day, at a crossing in a city, the various types of 240 vehicles going past during a time interval were observed as under:

$\begin{array}{cccc}\text{Type of vehicle}& \text{Two - wheelers}& \text{Three - wheelers}& \text{Four - wheelers}\\ \text{Frequency}& 84& 68& 88\end{array}$

what it is the probability that a selected vehicle is a two-wheeler?

Explain how a square is a parallelogram.

1. 320

• Midpoint of x and y is 20


• Midpoint of 10 and x is the same as the midpoint of -20 and y

If one angle of a cyclic quadrilateral measures 60 degrees, then the angle opposite to it measures

Evaluate-

{[√(√5+2)+√(√5-2)]/√(√5+1)}-√(3-2√2)

O is the centre of the circle as shown in the figure, $\angle ORP={35}^{\circ }$ and the distance between P and Q through 'O' is 4 cm. What is the measure of $\angle ROQ$ ?

Which congruency criterion could be used to check for congruency of two right-angled triangles?

The circumference of the base of the joker's cap of height 15 cm is 44 cm. Its volume is

Solve the quadratic equation 4$x^2$+ 5$x$ = 0 by completion of squares method. In the given options one of the options has one root and also the converted form of equation after completing the square. Select this option

If $a+b=10$ and $ab=16$ find, the value of $a^2-ab+b^2$ and $a^2+ab+b^2$

The quadilateral that is formed after the construction with mean proportional of sides of rectangle have _________ sides.

If $\overrightarrow{a}=4\hat{i}+6\hat{j}$ and $\overrightarrow{b}=3\overrightarrow{j}+4\overrightarrow{k}$ then the vector form of component of $\overrightarrow{a}$ along $\overrightarrow{b}$ is

The decimal expansion that a rational number cannot have is

(a) 0.25

(b) $0.25\overline{28}$

(c)$0.\overline{2528}$

(d) 0.5030030003...

Consider the below figure. Here, $z$ = ___.

Write the value of $co{s}^2{76}^{\circ }+co{s}^2{16}^{\circ }-cos{76}^{\circ }cos{16}^{\circ }$

In the adjoining figure, chords AB = BC = CD /ABC = 132⁰.

Calculate : ∠BAC & ∠AEB.

Calculate $\frac{\text{sin}{70}^{\circ }}{\text{cos}{20}^{\circ }}+\frac{\text{cosec}{36}^{\circ }}{\text{sec}{54}^{\circ }}-2\text{cos}{43}^{\circ }\text{cosec}{47}^{\circ }$.

The inverse of the matrix $A=\left[\begin{array}{ccc}1& 0& 0\\ a& 1& 0\\ b& c& 1\end{array}\right]$ is

1. 165

ABCD is a parallelogram. Then $\Delta ABC\cong$ _____

If a die is thrown 50 times and six appears 8 times, then the probability of getting a six is _______.

If a + b equal to 7 and ab equals to 12 then find the value of a minus b