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This mock test of Mathematics Test 9 - Limits And Continuity, Coordinate Geometry, Application Of Derivatives for JEE helps you for every JEE entrance exam.
This contains 25 Multiple Choice Questions for JEE Mathematics Test 9 - Limits And Continuity, Coordinate Geometry, Application Of Derivatives (mcq) to study with solutions a complete question bank.
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QUESTION: 1

Solution:

√3 sin(π/6+h) - cos( π/6+h)

2(√3/2 sin(π/6+h) - 1/2 cos( π/6+h))

2(cos(π/6) sin(π/6+h) - sin(π/6) cos( π/6+h))

2sin(π/6+h -π/6)

2 sin (h)

similarly in the denominator (this next step is not entirely necessary but I think it makes it eaiser)

(√3 cos(h) - sin(h))

2(cos(h+π/6))

lim h-->0 4 sin (h)/2√3 h cos(h+π/6)

(2/√3) (sin h / h)(1/cos h+π/6)

lim h-->0 (sin h / h) = 1

lim h-->0 (1/cos h+π/6) = sec(π/6) = 2/√3

(2/√3)^{2} = 4/3

QUESTION: 2

Solution:

QUESTION: 3

Solution:

QUESTION: 4

Solution:

QUESTION: 5

Solution:

lim(x----∞) [x*x(2-3/x)(3-4/x)]/[x*x(4-5/x)(5-6/x)]

= (2*3)/(4*5)

= 6/20

= 3/10

QUESTION: 6

................................................ equals

Solution:

QUESTION: 7

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

Solution:

QUESTION: 8

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

Solution:

QUESTION: 9

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

Solution:

QUESTION: 10

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 15^{0} with the first line is

Solution:

QUESTION: 11

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

Solution:

QUESTION: 12

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

Solution:

QUESTION: 13

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

Solution:

QUESTION: 14

Equation of the circle whose radius is 5 and which touches externally the circle x^{2} + y^{2} -2x - 4y - 20 = 0 at

the point (5,5) is

Solution:

QUESTION: 15

The number of integral values of for λ which x^{2} + y^{2} +λx + (1 - λ) y + 5 = 0is the equation of a

circle whose radius cannot exceed 5 is

Solution:

QUESTION: 16

The angle at which the circle x^{2} + y^{2} = 16 can be seen from the point (8,0) is

Solution:

QUESTION: 17

The slope of the tangent at the point (h,h) of the circle x^{2} + y^{2} = a^{2}is

Solution:

QUESTION: 18

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

Solution:

QUESTION: 19

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

Solution:

QUESTION: 20

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

Solution:

*Answer can only contain numeric values

QUESTION: 21

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

Solution:

*Answer can only contain numeric values

QUESTION: 22

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

Solution:

*Answer can only contain numeric values

QUESTION: 23

If m is the slope of common tangent of y = x^{2} – x + 1 & y = x^{2} – 3x + 1, then |m| is

Solution:

Let point on curve y = x^{2} – x + 1 be

(x_{1},x^{2}_{1 }– x_{1 }+ 1)

∴ Tangent is (y – x^{2}_{1} + x_{1} – 1) = (2x_{1} – 1)(x – x_{1})

⇒ L_{1} : y = (2x_{1} – 1)x – x_{1}^{2} + 1

Let point on curve y = x^{2 }– 3x +1 be (x_{2}, x_{2}^{2 }– 3x_{2 }+ 1)

∴ Tangent is (y – x_{2}^{2} + 3x_{2} – 4) = (2x_{2} – 3)(x – x_{2})

⇒ L_{2} : y = (2x_{2} – 3)x – x_{2}^{2} + 1

For common tangent, L_{1} & L_{2} are same.

⇒ –x_{1}^{2} + 1 = –x_{2}^{2} + 1

⇒ x_{1} = ±x_{2}

& 2x_{1} – 1 = 2x_{2} – 3

x_{1} = x_{2} gives –1 = –3 (rejected)

x_{1} = –x_{2} gives x_{1} = – 1/2, x_{2} = 1/2

⇒ m = –2.

*Answer can only contain numeric values

QUESTION: 24

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

Solution:

*Answer can only contain numeric values

QUESTION: 25

If expression x + 1/x^{2} (x > 0) attains its minimum value at x = α, then α^{3} is

Solution:

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