If A = 5ab0and A is symmetric matrix, show that a = b.

Subject

Mathematics

Class

ICSE Class 12

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 Multiple Choice QuestionsShort Answer Type

1.

The binary operation *: R × R  R is defined as a * b = 2a + b Find (2*3)*4.


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2.

If A = 5ab0and A is symmetric matrix, show that a = b.


Given, A = 5ab0

A is symmetric matrix.

 A = AT

 5ab0 = 5ab0T

              = 5ba0

Hence, a = b

 


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3.

Solve: 3tan-1x + cot-1x = π


4.

Without expanding at any stage, find the value of:

abca + 2xb +2yc + 2zxyz


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5.

Find the value of constant ‘k’ so that the function f(x) defined as:

fx = x2 - 2x - 3x +1,   x  - 1    k,                     x = - 1

is continuous at x = - 1.


6.

Find the approximate change in the volume ‘V’ of a cube of side x metres caused by decreasing the side by 1%.


7.

Evaluate: x3 +5x2 + 4x +1x2dx.


8.

Find the differential equation of the family of concentric circle x2 + y2 = a2.


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9.

If A and B are events such that P(A) = 12, P(B) = 13 and P(AB) = 14 then find:

(a) P(A/B)

(b) P(B/A)


10.

In a race, the probabilities of A and B winning the race are 13 and 16 respectively. Find the probability of neither of them winning the race.


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