Mathematics

CBSE Class 12

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4.

Find the equation of tangents to the curve y= x^{3}+2x-4, which are perpendicular to line x+14y+3 =0.

Taking the given equation,

y = x^{3}+2x-4

Differentiating the above function with respect to x, we have,

Given that the tangents to the given curve are perpendicular to the line x+ 14y + 3 = 0

Slope of this line, m_{2}=-1/14

Since the given line and the tangents to the curve are perpendicular, we have,

m_{1} x m_{2} =-1

thus equation of the tangent is 14 x- y =-12

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6.

For what values of k, the system of linear equations

x + y + z = 2

2x + y - z = 3

3x + 2y + kz = 4

has a unique solution?

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9.

A typist charges Rs. 145 for typing 10 English and 3 Hindi pages, while charges for typing 3 English and 10 Hindi pages are Rs. 180. Using matrices, find the charges of typing one English and one Hindi page separately. However, typist charged only Rs. 2 per page from a poor student Shyam for 5 Hindi pages. How much less was charged from this poor boy? Which values are reflected in this problem?

Let charges for typing one English page be Rs. x.

Let charges for typing one Hindi page be Rs.y.

Thus from the given statements, we have,

10x + 3y = 145

3x + 10y = 180

Thus the above system can be written as,

Humanity is reflected in this problem.

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10.

If A is a 3 x 3 matrix |3A| = k|A|, then write the value of k.

|3A| = k |A|

|3A| = 27|A|

k = 27

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