The angle of elevation of the summit of a mountain from a point o

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.

Let L denote the line in the xy-plane with x and y intercepts as 3 respectively. Then the image of the point (– 1, – 4) in the line is :

  • 85, 295

  • 115, 285

  • 295, 85

  • 295, 115


2.

If α and β are the roots of the equation 2x(2x + 1) = 1, then β is equal to :

  • 2αα - 1

  • 2αα + 1

  • 2α2

  •  - 2αα + 1


3.

If the tangent tothe curve, y = f(x) = xlogex, (x > 0) at a point (c, f(c)) is parallel to the line-segment joining the points (1, 0) and (e, e), then c is equal to :

  • e  - 1e

  • 1e - 1

  • e1e - 1

  • e11 - e


4.

If the constant term in the binomial expansion of x - kx210 is 405, then k = ?

  • 3

  • 2

  • 1

  • 9


Advertisement
5.

If the normal at an end of latus rectum of an ellipse passes through an extremity of the minor axis, the eccentricity e of the ellipse satisfies : 

  • e4 + 2e2 - 1 = 0

  • e2 +  e - 1

  • e2 + 2e - 1 = 0

  • e4 + e2 - 1 = 0


6.

The set of all real values for which the function

fx = 1 - cos2x . λ + sinx, x   - π2, π2,

has exactly one maxima and exactly one minima, is

  • - 12, 12 - 0

  • - 32, 32

  • - 12, 12

  • - 32, 32 - 0


7.

Consider the statement: For an integer n, if n3  1 is even, then n is odd. The contrapositive statement of this statement is:

  • For an integer n, if n is even, then n3 – 1 is odd

  • For an integer n, if n is even, then n3 – 1 is even.

  • For an integer n, if n3 – 1 is not even, then n is not odd

  • For an integer n, if n is odd, then n3 – 1 is even.


8.

The centre of the circle passing through the point (0, 1) and touching the parabola y = x2 at the point (2, 4) is:

  • 310, 165

  • - 5310, 165

  •  - 165, 5310

  • 65, 5310


Advertisement
Advertisement

9.

The angle of elevation of the summit of a mountain from a point on the ground is 45º. After climbing up one km towards the summitat an inclination of 30º from the ground, the angle of elevation of the summit is found to be 60º. Then the height (in km) of the summit from the ground is

  • 3 + 13 - 1

  • 13 + 1

  • 13 - 1

  • 3 - 13 + 1


C.

13 - 1

In CDFsin30° = z1CD = 1km givenz = 12                    ...icos30° = y1  32now in ABCtan45° = hx + y h = x + y x = h - 32  ...iinowInBDE,tan60° = h - Zx3x = h - 12 3h - 32= h - 12 3 - 1h = 1h = 13 - 1km


Advertisement
10.

Let θ = θ5 and A = cosθsinθ - sinθcosθ. If B = A + A4, Then detB : 

  • 0

  • 1

  • lies in (2, 3)

  • lies in (1, 2)


Advertisement