b2c2bcb + cc2a2cac + aa2b2a ba +&

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

In Z, the set of all integers, the inverse of - 7 w.r.t. * defined by ab = a + b + 7 for all a,b  Z is

  • - 14

  • 7

  • 14

  • - 7


2.

In ABC if 1ab1ca1bc = 0, if then sin2(A) + sin2(B) + sin2(C) is equal to

  • 49

  • 94

  • 33

  • 1


3.

Assuming that the sums and products given below are defined which ofthe following is not true for matrices?

  • AB = AC does not imply B = C

  • A + B = B + A

  • (AB)' = B'A'

  • AB = 0 implies A = 0 or B = 0


4.

Inverse of the matrix 1- 234 is

  • 1101- 234

  • 11042- 31

  • 42- 31

  • 1104- 2- 31


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5.

b2c2bcb +cc2a2cac + aa2b2a ba + b is equal to

  • 1abcab +bc + ca

  • ab  + bc + ca

  • 0

  • a + b + c


C.

0

Given, b2c2bcb +cc2a2cac + aa2b2abca + bMultiplying R1, R2, R3 by a, b, c respectively and divide the whole by abc1abcab2c2abcab +cbc2a2bcabc + aca2b2abcca + bTaking common abc from C1 and C2,abcabcabcbc1ab +acca1bc + abab1ca + bcNow, C1  C1 +C3abcab + bc + ca1ab +acca + bc + ab1bc + abab + bc + ca1ca + bcTaking common ab + bc + ca from C1,abcab + bc + ca11ab +ac11bc + ab11ca + ababcab + bc + ca . 0As C1 = C2, so value of  is zero. b2c2bcb +cc2a2cac + aa2b2abca + b = 0


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6.

sin12cos-145

  • - 110

  • 110

  • - 110

  • 110


7.

The derivative of cos-11 - x21 + x2 w. r. t. cot-11 - 3x23x - x3 is

  • 32

  • 1

  • 12

  • 23


8.

If y = 1 - x + x22! - x33! + x44! ..., then d2ydx2 is equal to

  • - x

  • x

  • y

  • - y


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9.

The slope of the tangent to the curve x = 3t2 + 1, y = t3 - 1 at x = 1 is

  • 12

  • 0

  • - 2


10.

The rate ofchange of the surface area ofthe sphere of radius r when the radius is increasing at the rate of 2 cm/sec is proportional to

  • 1r2

  • 1r

  • r2

  • r


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