August 18, 2021

JEE Advanced Mock Test 2

1 / 14

## 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...

2 / 14

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...

3 / 14

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

4 / 14

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...

5 / 14

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...

6 / 14

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...

7 / 14

## 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** + 2**b** + 3**c**, vector **v** = **a** + 3**b** + 4**c**, vector **w** = **a** + **b** + **c**, and vector **s** = 21**a** + 41**b** + 54**c**. If **s** = p**u** + q**v** + r**w**, then...

8 / 14

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...

9 / 14

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

10 / 14

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...

11 / 14

## 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...

12 / 14

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...

13 / 14

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...

14 / 14

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...

Your score is

The average score is 0%