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The probability of winning a game is $\frac{2}{5}$, the probability of losing is__.

( In decimal form)

We know that Probability of an event E, written as P(E) $=\frac{numberoffavourableoutcomesE\left(m\right)}{totalnumberofoutcomes\left(n\right)}$.
Which of the following options correctly explains the relationship between m and n?

If $\theta$ is an acute angle and sin $\theta$ = cos $\theta$ , find the value of $2ta{n}^2\theta +si{n}^2\theta -1$

Find a quadratic polynomial for the given numbers as the sum and product of its zeroes respectively.

$\frac{1}{4},-1$

In the given figure, if $\angle AOC={130}^{\circ },$ find the value of $\angle ABC$ .

A motor boat has a speed of 18 $\frac{km}{hr}$ in still water. It takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream in $km/hr.$

If a, b, c are in AP, then which of the following will not be in AP?

If ABC is an equilateral triangle of side 4a, then the length of its altitude is ________.

In a class test, if the marks scored by 11 students are 13, 17, 20, 5, 3, 19, 7, 6, 11, 15 and 17. Then, match the following:

$\begin{array}{cccc}& ListI& & ListII\\ A.& Median& i& 17\\ B.& Lowerquartile& ii.& 11\\ C.& Upperquartile& iii.& 6\\ D.& Interquartilerange& iv.& 13\end{array}$

If the circumference of a circle is $100\text{cm}$, then the side of a square inscribed in the circle is

The probability of guessing the correct answer to a certain question is $\frac{p}{12}$. If the probability of not guessing the correct answer to the same question is $\frac{3}{4}$, then find the value of p.

Now in each of the pairs of polynomials given below, check whether the first is a factor of the second:

(i) x + 1, x³ − 1

(ii) x − 1, x³ + 1

(iii) x + 1, x³ + 1

(iv) x² − 1, x⁴ − 1

(v) x − 1, x⁴ − 1

(vi) x + 1, x⁴ − 1

(vii) x − 2, x² − 5x + 1

(viii) x + 2, x² + 5x + 6

(ix)

(x) 1.3x − 2.6, x² − 5x + 6

If A and B are acute angle such that sin A = cos B then (A + B) = ?

(a) ${45}^o$ (b) ${60}^o$ (c) ${90}^o$ (a) ${180}^o$

A house is constructed using 112 bricks. If there are 8 bricks for each wall, then the number of walls in the house is .

By what amount price of carpet marked at Rs 800 be reduced so that after including 10% sale tax on the reduced price the final price is Rs 704.

Draw a cumulative frequency curve (ogive) for each of the following distributions :

(i) $\begin{array}{ccccccc}Classinterval& 10-15& 15-20& 20-25& 25-30& 30-35& 35-40\\ Frequency& 10& 15& 17& 12& 10& 8\end{array}$

(ii) $\begin{array}{cccccc}Classinterval& 10-19& 20-29& 30-39& 40-49& 50-59\\ Frequency& 23& 16& 15& 20& 12\end{array}$

The total surface area of a cylinder is 165πcm². if the radius of its base is 5cm, then its height is ____________.

Given that L.C.M (150, 100) = 300, find H.C.F (150, 100).

What is the slant height of a square pyramid of base perimeter 80 centimeters and volume 1600 cubic centimeters?

Find the image of the point $(-8,12)$ with respect to the line mirror $4x+7y+13=0$.

In Fig. there are three semicircles, A, B and C having diameter 3 cm each, and another semicircle E having a circle D with diameter 4.5 cm are shown. Calculate

(i) The area of the shaded region

(ii) The cost of painting the shaded region at the rate of 25 paise per $c{m}^2$, to the nearest rupee.

Find the sum of the first 25 terms of an A.P. whose nth term is given by $a_n=2-3n$.

Write the value of (1 + $co{t}^2\theta )si{n}^2\theta$.

The product of two consecutive positive integers is 306. Form the quadratic equation to find the integers, if x denotes the smaller integer.

Match the polynomials with their respective factors.