If a line makes an angle of π/4 with the positive directions of each of x-axis and y-axis, then the angle that the line makes with the positive direction of the z-axis is

• π/6

• π/3

• π/4

• π/4

If (2, 3, 5) is one end of a diameter of the sphere x²+ y²+ z² − 6x − 12y − 2z + 20 = 0, then the coordinates of the other end of the diameter are

• (4, 9, –3)

• (4, –3, 3)

• (4, 3, 5)

• (4, 3, 5)

Let A(h, k), B(1, 1) and C(2, 1) be the vertices of a right-angled triangle with AC as its hypotenuse. If the area of the triangle is 1, then the set of values which ‘k’ can take is given by  

• {1, 3}

• {0, 2}

• {–1, 3}

• {–1, 3}

Let P = (−1, 0), Q = (0, 0) and R = ( 3, 3 √3) be three points. The equation of the bisector of the angle PQR

If one of the lines of my²+ (1 − m²)xy − mx² = 0 is a bisector of the angle between the lines xy = 0, then m is

• −1/2

• -2

• 1

• 1

Angle between the tangents to the curve y = x² − 5x + 6 at the points (2, 0) and (3, 0) is

• π/2

• π/4

• π/6

• π/6

The image of the point (−1, 3, 4) in the plane x − 2y = 0 is

• 
• 

• (15, 11, 4)

• (15, 11, 4)

The normal to the curve x = a(cosθ + θ sinθ), y = a( sinθ - θ cosθ) at any point ‘θ’ is such that

• it passes through the origin

• it makes angle π/2 + θ with the x-axis

• it passes through (aπ/2 ,-a)

• it passes through (aπ/2 ,-a)

369.

The line parallel to the x−axis and passing through the intersection of the lines ax + 2by + 3b = 0 and bx − 2ay − 3a = 0, where (a, b) ≠ (0, 0) is

• below the x−axis at a distance of 3/2 from it

• below the x−axis at a distance of 2 /3 from it

• above the x−axis at a distance of 3/ 2 from it

• above the x−axis at a distance of 3/ 2 from it

If the angle θ between the line and the plane  is such of sin θ = 1/3 the value of λ is

• 5/3

• -3/5

• 3/4

• 3/4