HSC Science (General) 11th Standard - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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If the line 4x − 3y + k = 0 touches the ellipse 5x² + 9y² = 45 then the value of k is

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The equation of the ellipse is 16x² + 25y² = 400. The equations of the tangents making an angle of 180° with the major axis are

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The equation of the tangent to the ellipse 4x² + 9y² = 36 which is perpendicular to the 3x + 4y = 17 is,

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Centre of the ellipse 9x² + 5y² − 36x − 50y − 164 = 0 is at

Find the equation of the ellipse in standard form if the length of major axis 10 and the distance between foci is 8

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Find the equation of the tangent to the ellipse x² + 4y² = 100 at (8, 3)

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The variance of 19, 21, 23, 25, and 27 is 8. The variance of 14, 16, 18, 20, and 22 is:

First 6 faced die which is numbered 1 through 6 is thrown then a 5 faced die which is numbered 1 through 5 is thrown. What is the probability that the sum of the numbers on the upper faces of the dice is divisible by 2 or 3?

A card is drawn from a pack of 52 cards. What is the probability that, card is either red or black?

A girl is preparing for National Level Entrance exam and State Level Entrance exam for professional courses. The chances of her cracking National Level exam is 0.42 and that of State Level exam is 0.54. The probability that she clears both the exams is 0.11. Find the probability that

1. She cracks at least one of the two exams
2. She cracks only one of the two
3. She cracks none.

A bag contains 75 tickets numbered from 1 to 75. One ticket is drawn at random. Find the probability that, number on the ticket is a perfect square or divisible by 4

The probability that a student will pass in French is 0.64, will pass in Sociology is 0.45, and will pass in both is 0.40. What is the probability that the student will pass in at least one of the two subjects?

Find the square root of the following complex number: −8 − 6i

Find the square root of the following complex number:

7 + 24i 

Find the square root of the following complex number:

`1 + 4sqrt(3)"i"`

Find the square root of the following complex number: 

`3 + 2sqrt(10)"i"`

Find the square root of the following complex number: 

`2(1 - sqrt(3)"i")`

Answer the following:

Find the square root of −16 + 30i

Answer the following:

Find the square root of 15 – 8i

Answer the following:

Find the square root of `2 + 2sqrt(3)"i"`