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Let $A$ and $B$ be two events such that $P\left(A\right)=0.3$ and $P(A\cup B)=0.8$. If $A$ and $B$ are independent events, then $P\left(B\right)$ is :

The diagonal of a trapezium shaped field is 25m and the perpendiculars dropped on it from the remaining opposite vertices are 8m and 12m. Find the area of the field(in m²).

Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes, and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P,Q and R respectively. What is the proportion of the solution R in the liquid in the tank after 3 minutes?

The value of d (common difference) of an A.P. such that the three consecutive terms of an A.P. are the consecutive terms of the G.P. (a is the first term of the A.P)

Find the perimeter of the right angled triangle if the hypotenuse of the triangle measures 26 m and the radius of the circle is 1 m (O is the centre of the circle).

The probability of getting a multiple of 3 when a dice is rolled is



एक पासे को लुढ़काने पर 3 का एक गुणज प्राप्त होने की प्रायिकता है

Q80. How much does a watch lose per day, if its hands coincide every 64 min?

If the compound ratio of $7:5$ and $8:x$ is $84:60$ find $x$.

Question 1 (ii)

In which of the following situations does the list of numbers involved make an arithmetic progression and why?

(ii) The amount of air present in a cylinder when a vacuum pump removes $\frac{1}{4}$ of the air remaining in the cylinder at a time.

If 2a² - 3a + 15 < 20, then the solution set of 'a' for the inequality is

Statements:

Some tunes are not songs.

All songs are drums.

Some songs are sticks.

Conclusions:

I.Some drums being songs is a possibility.

II.All those drums which are tunes can be songs.

6 letters are to be placed in 6 addressed envelopes. Each letter is assigned for an envelope. In how many ways these letters can be put in these envelopes such that exactly one letter goes in the correct envelope.

In a $\Delta$ ABC, if AB = 6 m, BC = 5 m and AC = 4 cm, then which of the following is correct.

Total number of ways in which 20 identical mangoes can be distributed among 4 persons is?

What does the underlined preposition indicate?

The barricade was placed over the road.

Suppose the seed of any positive integer n is defined as follows:

Seed (n) = n, if n $<$ 10

= seed(s(n)), otherwise,

Where s(n) indicated the sum of digits of n. For example, seed(7)=7, seed(248) = 2+4+8 = seed(14) = seed(1+4) = seed(5) = 5, etc.

How many positive integers n, such that n$<$ 500, will have seed(n)=5?

How many diagonals does a decagon have?

What is the total number of students in the school?

I. The respective ratio of girls and boys is 2 : 3.

II. The number of students has grown by 5$\%$ this year as compared to 4$\%$ last
year from the number 2000 which it was year before last.

Q39. How much water must be added to cask which contains 40 lite of mile costing price Rs 3.5 litre so that the cost of milk reduces to Rs 21 litre?

What are the numbers of ways in which 3 similar balls ball be put in 3 distinct baskets.

What is the remainder obtained when $3^{91}$+${40}^{91}$ is divided by 43 is

Q31. If six bells toll at intervals of 3, 4, 5, 6, 7 and 8 second, respective. Given that these bells toll together at 11.20 a.m. when would they toll together again?

Q31. यदि 3, 4, 5, 6, 7 और 8 सेकंड के अंतराल पर छः घंटियाँ एक साथ बजती हैं। यदि ये घंटियाँ 11:20 बजे एक साथ बजतीं हैं तो पुनः वे एक साथ कब बजेंगी?

Find the highest power of 17 in
$1001\times 2001\times 3001\times 1002\times 2002\times 3002\times 1003\times \mathrm{2003.....1099}\times 2099\times 3099$.

Question 164(iii)

If possible, find a hook-up of prime base number machine that will do the same work as the given stretching machine. Do not use

$(\times 1)$ machines.