Let A and B denote the statements A: cos α + cosβ + cosγ = 0

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

1.

If the mean deviation of the numbers 1, 1 + d, 1+ 2d, ... , 1 + 100d from their mean is 255, then the d is equal to 

  • 10.0

  • 20.0

  • 10.1

  • 10.1

446 Views

2.

If the roots of the equation bx2+ cx + a = 0 be imaginary, then for all real values of x, the expression 3b2x2 + 6bcx + 2c2 is

  • greater than 4ab

  • less than 4ab

  • greater than -4ab

  • greater than -4ab

134 Views

Advertisement

3.

Let A and B denote the statements
A: cos α + cosβ + cosγ = 0
B : sinα + sinβ + sinγ = 0
If cos(β – γ) + cos(γ – α) + cos(α – β) = – 3/2, then

  •  A is true and B is false

  • A is false and B is true

  • both A and B are true

  • both A and B are true


C.

both A and B are true

cos(β–γ) + cos(γ – α) + cos(α – β) = –3/2
⇒ 2cos (β – γ) + 2cos(γ– α) + 2cos(α – β) = –3
⇒ Σ(cosβcosγ + 2Σsin α sinβ + 3 = 0
⇒ (cosα+cosβ + cosγ)2+ (sinα + sinβ +sinγ)2=0
⇒ cosα + cosβ + cosγ = 0
sinα + sinα + sinγ = 0

127 Views

Advertisement
4.

If A, B and C are three sets such that A ∩ B = A∩ C and A ∪ B = A ∪ C, then

  • A = B

  • A = C

  • B = C

  • B = C

105 Views

Advertisement
5.

The projections of a vector on the three coordinate axis are 6, - 3, 2 respectively. The direction cosines of the vector are

  •  6, –3, 2 

  • 6/5, -3/5, 2/5

  • 6/7, -3/7, 2/7

  • 6/7, -3/7, 2/7

199 Views

6.

Three distinct points A, B and C are given in the 2 – dimensional coordinate plane such that the ratio of the distance of any one of them from the point (1, 0) to the distance from the point ( - 1, 0) is equal to 1/3 . Then the circumcentre of the triangle ABC is at the point

  • (0,0)

  • (5/4, 0)

  • (5/2, 0)

  • (5/2, 0)

221 Views

7.

The remainder left out when 82n –(62)2n+1 is divided by 9 is 

  • 0

  • 2

  • 7

  • 7

264 Views

8.

The ellipse x2+ 4y2= 4 is inscribed in a rectangle aligned with the coordinate axes, which in turn is inscribed in another ellipse that passes through the point (4, 0). Then the equation of the ellipse is

  • x2+ 16y2= 16 

  • x2+ 12y2= 16 

  • 4x2+ 48y2= 48 

  • 4x2+ 48y2= 48 

371 Views

Advertisement
9.

The sum to infinity of the series 1 space plus space 2 over 3 space plus space 6 over 3 squared space plus space 10 over 3 cubed space plus space 14 over 3 to the power of 4 space plus.... space is

  • 2

  • 3

  • 4

  • 4

147 Views

10.

The differential equation which represents the family of curves y=c1ec2xe, where c1 and c2 are arbitrary constants, is

  • y' =y2

  •  y″ = y′ y

  • yy″ = y′

  • yy″ = y′

120 Views

Advertisement