If the matrix A = 0a-320-1b10 is skew symmert

Subject

Mathematics

Class

CBSE Class 12

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 Multiple Choice QuestionsShort Answer Type

1.

If a*b denotes the larger of 'a' and 'b' and if a o b = (a*b) + 3, then write the value of (5) o (10), where and o are binary operations.


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2.

If the matrix A = 0a-320-1b10 is skew symmertic, find the values of 'a' and 'b'.


Given, A is skew-symmetric,

∴ (AT = - A)02ba01-3-100-a3-201-b-10Hence, a12 = -a21  a  = -2and a31 = - a13 b = 3


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3.

Find the value of tan-1 3 - cot-1 (-3)


4.

The total cost C(x) associated with the production of x units of an item is given by C(x) = 0.005x3 - 0.02 x2 + 30 x +5000. Find the marginal cost when 3 units are produced, whereby marginal cost we mean the instantaneous rate of total cost at any level of output.


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5.

Differentiate tan-1 1 + cos xsin x with respect x.


6.

Given, A = 2-3-47 compute A-1 and show that 2A- = 9I-A


7.

Prove that:3 sin-1 x  = sin-1 (3x - 4x3), X  -12, 12


8.

Using properties of determinants, prove that

111+3x1+ 3y1111+3z1 = 9 (3xyz + xy + yz + zx)


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9.

Find the equations of the tangent and the normal, to curve 16x2 + 9y2 = 145 at the point (x1,y1) where x1 = 2 and y1 > 0


10.

Find the intervals in which the function f(x)  =  is

a) Strictly increasing

b) Strictly decreasing


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