If a, b, c are unit vectors such that a + b + c = 0, then th

Subject

Mathematics

Class

JEE Class 12

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 Multiple Choice QuestionsMultiple Choice Questions

31.

The degree of the differential equation 1 + dydx22 = d2ydx2 is

  • 3

  • 2

  • 1

  • 4


32.

cos2x - cos2θcosx - cosθdx is equal to

  • 2sinx + xcosθ

  • 2sinx - xcosθ

  • 2sinx + 2xcosθ

  • 2sinx - 2xcosθ


33.

If a = 2i^ + λj^ + k^ and b = i^ + 2j^ + 3k^ are orthogonal, then value of λ is

  • 3/2

  • 1

  • 0

  • - 5/2


Advertisement

34.

If a, b, c are unit vectors such that a + b + c = 0, then the value of a · b + b · c + c · a is equal to

  • 3/2

  • 1

  • 3

  • - 3/2


D.

- 3/2

We have, a, b, c are unit vectors a = b = c = 1Also, we have            a + b + c = 0 a . a + b + c = a . 0 a . a + a . b + a . c = 0  a2 + a . b + a . c = 0              a . b + a . c = - a2 = - 1        ...iSimilarly,b . a + b . c = - 1             ...iiand c . a + c . b = 1          ...iiiOn adding Eqs (i), (ii) and (iii), we get 2a . b + b . c + c . a = - 3 a . b + b . c +c . a = - 32


Advertisement
Advertisement
35.

The plane 2x - 3y + 6z - 11 = 0 makes an angle sin-1(α) with X-axis, the value of α is equal to

  • 23

  • 27

  • 32

  • 37


36.

0.23.5xdx is equal to

  • 3.5

  • 4

  • 4.5

  • 3


37.

The perpendicular distance of the point P(6, 7, 8) from XY-plane is

  • 6

  • 7

  • 5

  • 8


38.

The integrating factor of the differential equation x . dydx + 2y = x2 is x  0

  • x

  • logx

  • x2

  • elogx


Advertisement
39.

0π2tan7xcot7x + tan7xdx is equal to

  • π4

  • π2

  • π6

  • π3


40.

Reflexion of the point α, β, γ in XY-plane is

  • 0, 0, γ

  • - α, - β, γ

  • α, β, - γ

  • α, β, 0


Advertisement