# JEE Advanced Mock Test 2

Created on

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## Section - (I)

a. This section contains SIX questions.
b. Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of these four options is correct.

1. Area bounded by √(x + y + 1) > √(y - x + 2) & y < 0 is equal to...

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2. $\lim _{x\rightarrow 0}sgn\left( \cot ^{-1}\left( x\right) -\cot ^{-1}\left( x^{2}\right) \right)$ (where sgn(x) is signum function), then...

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3. If $\int ^{\pi }_{0}\left( \dfrac{x}{1+\sin x}\right) ^{2}dx=a$, then $\int ^{\pi }_{0}\dfrac{2x^{2}\cos ^{2}\left( \dfrac{x}{2}\right) }{\left( 1+\sin x\right) ^{2}}dx$

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4. Equation of the line of shortest distance between the lines x/2 = -y/3 = z and (x - 2)/3 = (1 - y)/5 = (z + 2)/2 is...

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5. Let z₁, z₂, z₃ are roots of the equation z³ + z²(i – 1) + z(2 – i) – 2 = 0, then Re(z₁) + Re(z₂) + Re(z₃) is...

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6. Let P(x₁, y₁) & Q(x₂, y₂) are points lying on hyperbola (x/a)² - (y/b)² = 1. If tangents drawn at the points P & Q are perpendicular, then the value of (x₁x₂)/(y₁y₂) is...

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## SECTION–(II)

a. This section contains Four Questions.
b. Each question has FOUR options (A), (B), (C) and (D) ONE OR MORE of these four options is/are correct.

7. Let a,b,c are three non coplanar vectors such that vector u = a + 2b + 3c, vector v = a + 3b + 4c, vector w = a + b + c, and vector s = 21a + 41b + 54c. If s = pu + qv + rw, then...

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8. Consider a variable plane lx + my + nz = k (k > 0) and l, m, n are direction cosines of normal of the plane. Let the given plane intersects co-ordinate axis at A, B, C, then area of the Triangle ABC may be...

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9. For the parabola y² – 4y + 8 = 4x which of the following is(are) false...

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10. Let tangents PA & PB are drawn from variable point P on the parabola y² = 4x to the circle x² + y² + 10x – 4y + 25 = 0, then locus of circumcentre of Triangle PAB...

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## SECTION - (III)

a. This section contains Four questions.
b. The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9.

11. Let (x, y, z) is three dimensional point which satisfies xyz⁴ = 16 where (x, y, z > 0) its minimum distance from origin is a, then the value of a² is...

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12. If ax² + 2hxy + by² + 2gx + 2ƒy + c = 0 and ax² + 2hxy + by² – 2gx – 2ƒy + c = 0 each represent pair of straight lines and area of parallelogram enclosed by them is |(k|c|)/√(h² - ab)|, then the value of |k| is...

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13. If the parabola y = ax² + bx + c has vertex at (4, 2) and a ∈ [1,3] such that difference between extreme values of abc is D, then |D/1728| is equal to...

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14. Let chord of contact is drawn from every point lying on circle x² + y² = 100 to the ellipse (x/2)² + (y/3)² = 1 such that all the lines touches an standard ellipse whose eccentricity is e, then (81e²)/13 is equal to...