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Let $A,B\text{and}C$ be three events, which are pair-wise independent and $\overline{E}$ denotes the complement of an event $E$. If $P(A\cap B\cap C)=0$, then $P\left[\right(\overline{A}\cap \overline{B}\left)|C\right]$ is equal to:

Which of the following is the third element from the left end of step VI?

Question 164(i)

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.

1. print(tuple1.index(45))


2. print(tuple1.count(45))


3. print(tuple1 + tuple2)


4. print(len(tuple2))


5. print(max(tuple1))


6. print(min(tuple1))


7. print(sum(tuple2))


8. print(sorted (tuple1))
   
   print(tuple1)

In the below question, one or more dots are placed in the problem figure (X) followed by four alternatives (a), (b), (c) and (d). One out of these four alternatives contain region(s) common to the circle, square, triangle and rectangle similar to that marked by the dot in figure (X).

A merchant mixes three varieties of rice costing Rs.20/kg, Rs.24/kg and Rs.30/kg and sells the mixture at a profit of $20\%$ at Rs.30/kg. How many kgs of the second variety will be in the mixture if 2 kgs of the third variety is there in the mixture?

Mohan walked 30 m towards South, took a left turn and walked 15 m. He then took a right turn and walked 20 m. He again took a right turn and walked 15 m. How far is he from the starting point?

Who is seated to the immediate right of Malini when Malini, Shakti, Bharat, Sachin and Neelima are sitting around a circle facing the centre?

I. Shakti is $3^{rd}$ to the left of Malini.

II. Bharat is between Shakti and Neelima.

Q. Study the given graph showing the number of people in the country using 3 different brands of soap carefully to answer the questions that follow


What is the average number of people using soap M in the given period? (2004 to 2009)

Q. नीचे दिए गए प्रश्नों का उत्तर देने के लिए दिए गए ग्राफ को ध्यान से देखें जो देश में 3 अलग-अलग ब्रांड के साबुन का उपयोग करने वाले लोगों की संख्या को दर्शाता है :


दी गई अवधि (2004 से 2009) में साबुन M का उपयोग करने वाले लोगों की औसत संख्या क्या है?

Data related to numbers of projects handled by two companies (A & B) during 5 years:
Q. Number of projects handled by company B decreased by what percentage from 2004 to 2006?

For a pure water,

1. 0

In your family, what activities are done individually and as a group?

My mother decides ___________________________________________.

My father decides ___________________________________________.

I decide ___________________________________________________.

We decide _________________________________________________.

Statements:

All black are telegrams.

All telegrams are blue.

All blues are grey.

Conclusions:

I. No telegram is grey.

II. Most blue are telegrams.

Total number of students in School B and School C together in the year 2004 was approximately what percentage of the total number of students in school B and school C together in the year 2007?

Q. In the series – 142, 139, 134, 127, 116, 103, X – what is the value of X?

In a row of 40 girls, when Komal was shifted to her left by 4 places her number from the left end of the row became 10. What was the place of Swati from the right end of the row if Swati was three places to the right of Komal's original position?

If A, B and C invest some money for the same time and after one year the ratio of their profit is 4 : 5 : 6. If the total investment is Rs.60000, find the investment of A.

$\frac{3^{4.5}\times {21}^2\times 4^{3.5}}{2^5\times 3^{2.5}}=2^2\times 3^x\times 7^2,x=$

The ratio between Mira’s expenditure and savings are 3$:$2. After her promotion, her income increases by 10$\%$ but her expenditure also increases by 12$\%$. By what percentage does her savings increase?

What is the position of ‘fame’ to the right of ‘67’ in the second-last step?

The tens digit of $6^{17}$ is -

Rajat cuts out two equilateral triangular pieces of cardboard, each of area 300 sq. cm, and then placed them upon a table, one on top of the other such that the triangles completely coincide with each other. Now, if he rotated one of the two triangles by ${180}^{\circ }$ about a vertical axis passing through its centroid, find the area that is common to both the triangles.

Statements: E * F; G $ H; H # E; G K

Conclusions:

I. HK

II. H*F

For the below question, group the given figures into different classes on the basis of their orientation, shape etc.