JEE Main Maths Test- 9 - JEE MCQ

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If f(a) = 2, f`(a) = 1, g(a) = –1, g`(a) = 2, then value of

The vertices of a triangle ABC are (2,1),(5,2) and (3,4)respectively. The circumcentre is the point

If A and B are the points (–3,4) & (2,1). Then the co-ordinates of point C on AB produced such that AC = 2 BC are

The equation of the line passing through the intersection of x - √3 y + √3 - 1 = 0 and x y–2 = 0 and
making an angle of 15⁰ with the first line is

If 2x² + λxy + 2y² +(λ - 4)x + 6y - 5 = 0is the equation of a circle, then its radius is

Equation of circles which pass through the points (1,–2) and (3,–4) and touch the x-axis is

The circle whose centre is on the x-axis and the line 4x–3y–12 = 0 and whose radius is the distance
between the line 4x–3y–32 = 0 and 4x–3y–12 = 0 has equation

Equation of the circle whose radius is 5 and which touches externally the circle x² + y² -2x - 4y - 20 = 0 at
the point (5,5) is

The number of integral values of  for λ which  x² + y² +λx + (1 - λ) y + 5 = 0is the equation of a
circle whose radius cannot exceed 5 is

The angle at which the circle x² + y² = 16 can be seen from the point (8,0) is

The slope of the tangent at the point (h,h) of the circle  x² + y²  = a²is

If f (x) = [x sin p x] { where [x] denotes greatest integer function}, then f (x) is

The equation of the locus of the mid-points of the chords of the circle 4x² + 4y² - 12x + 4y +1 = 0that subtend an anlge of 2π / 3 at its centre is

The distance of the point (1,2) from the radical axis of the circles x² + y² +6x - 16 = 0 and x² + y² -2x + 6y = 0  is

Let f(x) be a twice-differentiable function and f''(0) = 2. Then evaluate. 

The minimum value of  f(x) = ∣3 - x∣ +  ∣2 + x∣ + ∣5 - x∣  is:

If m is the slope of common tangent of y = x² – x + 1 & y = x² – 3x + 1, then |m| is 

The volume of a tetrahedron DABC is 9 cubic units. If ∠ACB = π/6 and 2AD + AC + BC = 18, then  the length AD is

If expression x + 1/x² (x > 0) attains its minimum value at x = α, then α³ is