The two lines of regressions are x + 2y - 5 = 0 and 2x + 3y - 8 =

Subject

Mathematics

Class

ICSE Class 12

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 Multiple Choice QuestionsShort Answer Type

1.

Find the matrix X for which: 5411X = 1- 213


2.

Solve for x, if:

tancos-1x = 25


3.

Prove that the line 2x - 3y = 9 touches the conics y2 = - 8x, also find point of contact.


4.

Using L'Hospital Rule, evaluate: limx01x2 - cotxx


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5.

Evaluate: tan3xdx


6.

Using properties of definite integrals, evaluate:

0π/2sinx - cosx1 +sinxcosxdx


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7.

The two lines of regressions are x + 2y - 5 = 0 and 2x + 3y - 8 = 0 and the variance of x is 12. Find the variance of y and the coefficient of correlation.


x + 2y = 5

2x + 3y - 8 = 0

and σ2x = 12

On solving these two equations, we get

x = 1 and y = 2

bxy- 23 and byx = - 2

Coefficient of correlation, r = byx × bxy

                                       = - 23 × -2

                                       = 43

byx rσyσx

But σx2 = 12

 σy = byx × σxr = - 23 × 1243 = - 2

Thus, the variance is - 2.

 


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8.

Express 2 +i(1 + i)(1 - 2i) in the form of a + ib. Find its modulus and argument.


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9.

A pair of dice is thrown. What is the probability of getting an even number on the first die or a total of 8 ?


10.

Solve the Differential equation:

xdydx + y = 3x2 - 2


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