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Find the angle whose complement is one third of its supplement.

Water is poured into a cylindrical vessel of height 10 m and radius 4 m from a cubical vessel of side 10 m. How much water is left in the cubical vessel?

While plotting irrational numbers on number line I found both the hypotenuse and arc cutted by radius to be root 2

So which one represents root 2

If the area of parallelogram PQRS is 32 cm² and line XY || AS ,then the area of triangle ACS is____

Simplify
$\frac{\left(0.3{)}^{\frac{1}{3}}{\left(\frac{1}{27}\right)}^{\frac{1}{4}}\right(9{)}^{\frac{1}{6}}(0.81{)}^{\frac{2}{3}}}{\left(0.9{)}^{\frac{2}{3}}\right(3{)}^{-\frac{1}{2}}{\left(\frac{1}{3}\right)}^{-2}(243{)}^{-\frac{1}{4}}}$

What is the area of an equilateral triangle whose side is $\text{8 cm}$?

If the coordinates of two points A and B are (3, 4) and (5, – 2) respectively. Find the coordinates of any point P, if PA = PB and area of $△$PAB = 10

There are 8 pipes which take 26 hours to fill a big drum. But when the operations were supposed to begin, two pipes were damaged. It so happened that only one could be retreived back to usable state. What will be the time taken to fill the drum with the existing pipes?

A coin is tossed 500 times with the following frequencies of two outcomes:
head = 245 times
tail = 255 times

What is the probability of getting a head in the next throw?

If ∪ = {2, 4, 6, 8, 10, 12, 14}, where U is Universal set and some set A = {2, 4, 10}.
Which of the following is A^C?

Two rectangular boxes have the same height and lenght, but different widths as shown in the figure.

The difference in the volumes of the boxes is $360c{m}^3.$
What is the height of the boxes?

The average weight of a group of 25 men was calculated to be 78.4 kg. It was discovered later that one weight was wrongly entered as 69 kg instead of 96 kg. What is the correct average ?

Q74. Amit is older than Babloo but younger than Chintoo. Dinesh is younger than Esha but older than Amit. If Chintoo is younger than Dinesh, then who is the oldest of all?

In the given figure $\angle$ AOC=${130}^{\circ }$, The value of $\angle$ ABC (in degrees) is _______.

Match the following.

$\begin{array}{cc}\left(a\right)edge& \left(i\right)point\\ \left(b\right)vertex& \left(ii\right)1-dimension\\ \left(c\right)face& \left(iii\right)2-dimension\end{array}$

If $x=0.\overline{18}$, which of the following statements are true?

(i) $100x=18.\overline{18}$
(ii) $100x-x=17.\overline{18}$
(iii) $99x=18$

The graph of the linear equation 2x + 3y = 6 is a line which meets the x -axis at the point

Michael appeared in an examination and obtained the following marks out of 100

$$\begin{array}{cc}\text{Subject}& \text{Marks}\\ \text{Physics}& 87\\ \text{Chemistry}& 82\\ \text{Biology}& 82\\ \text{Mathematics}& 98\end{array}$$

Find the measures of central tendency for the above data.

The angles of depression of the top and the bottom of a 10 m tall building from the top of a multi-storeyed building are ${30}^{\circ }$ and ${45}^{\circ }$, respectively. Find the height of the multi-storeyed building.

Which is the hypotenuse of this triangle ABC?

1 + $ta{n}^{2}A$ = $se{c}^{2}A$ is valid for which of the following ranges

In which quadrant following point will lie $({log}_{3}27,-{log}_{10}100)$

Which of the following graph shows the correct plotting of point P(-2,3)?

In which of the following quadrant does the point (-6,1) lie?

$(A-B)-(B-C)=$___

In the figure, $\angle BAD={78}^o,\angle DCF=x^{o}and\angle DEF=y^o.$ Find the values of x and y.

$△$ ABC a right-angled triangle, find the length of BD assuming $△ABC\sim △BDC$

In the following figure, the sides AB and BC and the median AD of triangle ABC are respectively equal to the sides PQ and QR and median PS of the triangle PQR. Prove that $\Delta$ PQR are congruent.

What does the l in mode $=I+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)\times h$ stand for? [1 MARK]

If \(2^{4} \times 4^{2} = 16^{x} \), then find the value of x.

If $△ABC\sim △$ DEF such that AB = 12 cm and DE = 14 cm. Find the ratio of areas of $△$ ABC and $△$ DEF.

Question 12

Cost of a dozen pens is Rs 180 and cost of 8 ball pens is Rs 56. Find the ratio of the cost of a pen to the cost of a ball pen.

Find the value of a for which (x + 2a) is a factor of $(x^5-4a^2{x}^3+2x+2a+3)$.

A tank’s capacity is 1600 $c{m}^3$. If the time taken by tap to empty the tank is 20 min, then the rate of emptying the tank is __ $c{m}^3/min$

Prove that $\frac{0.85\times 0.85\times 0.85+0.15\times 0.15\times 0.15}{0.85\times 0.85-0.85\times 0.15+0.15\times 0.15}=1.$

There are 7 observations in a set of data and their mean is 11. If each observation is multiplied by 2, find the new mean. [3 MARKS]

Question 6(a)

Write the predecessor of:
94

If the mean of 25 observations is 27 and each observation is decreased by 7, what will be the new mean?

The red line indicates the girls height distribution. The blue line indicates the boys height distribution.

Find:

i) Maximum no. of girls belong to which height group ?

ii) The difference in the no. of boys to the no. of girls in the class.

The length of the longest bar that can be fixed in a room of dimensions 12 m $\times$ 9 m $\times$ 8 m is ___ m.