# JEE Advanced Mock Test 4

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. Let ABCD be a square of side length 2 units. C₂ is the circle through vertices A, B, C, and D. C₁ is the circle touching all the sides of the square ABCD. L is a line through A. If P is a point on C₁ and Q is another point on C₂, then (PA² + PB² + PC² + PD²)/(QA² + QB² + QC² + QD²) is equal to.

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2. Perpendicular drawn from points on the line (x + 2)/2 = (y + 1)/(-1) = z/3 to the plane x + y + z = 3. The feet of perpendiculars line on the line.

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3. The number(s) of points in (-∞, ∞) for which x² - x Sinx - Cosx = 0 is/are.

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4. Let g(x) = (x - 1)ⁿ/(ln Cosᵐ(x - 1)); 0 < x 0, and let p is the left hand derivative of |x - 1| at x = 1. If Lim(x → 1⁺)(g(x)) = p, then

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5. Let f: R → R is a twice differentiable function such that f"(x) > 0 for all x ∈ R, and f(1/2) = 1/2, f(1) = 1, then

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6. Area of the region {(x, y) ∈ R²: √|x + 3| ≤ y, 5y ≤ x + 9 ≤ 15} is equal to

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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 S₁, S₂,... be squares such that for each n ≥ 1, the length of the side of Sₙ equals the length of the diagonal of Sₙ₊₁. If the length of the side of S₁ is 10 cm, then for which of the following values of n is the area of Sₙ is less than 1 cm²

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8. For a non-zero complex number z, let arg(z) denotes the principal argument with -π < arg(z) ≤ π. Then which of the following statement(s) is/are false. {i = √-1}

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9. Let X and Y be two arbitrary, 3 x 3, non-zero, skew-symmetric matrices and Z be an arbitrary 3 x 3 non-zero, symmetric matrix. Then which of the following matrices is/are skew-symmetric.

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10. Six cards and Six and envelops are numbered 1, 2, 3, 4, 5, 6 and cards are to be placed in envelops so that each envelope contains exactly one card and no card is placed in the envelope bearing the same number and moreover the card number 1 is always placed in the envelope number 2, then the number of ways it can be done is/are.

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## SECTION - (III)

a. This section contains Four questions.
b. The answer to each question is a Whole Number.

11. Let X be a set with exactly 5 elements and Y be a set with is exactly 7 elements. If a is a number of one-one functions from X to Y and b is the number of onto functions from Y to X, then the value of (b - a)/(5!) is.

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12. If a, b, and c are unit vectors satisfying |a - b|² + |b - c|² + |c - a|² = 9, then |2a + 5b + 5c| is.

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13. Let f: [0, 4π] → [0, π] be defined by f(x) = Cos⁻¹(Cosx). The number of points x ∈ [0, 4π] satisfying the equation f(x) = (10 - x)/x is

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14. Consider a triangle ABC and let a, b, and c denotes the length of the sides opposite to vertices A, B, and C respectively. Suppose a = 6, b = 10 and the area of the triangle is 15√3. If angle ACB is obtuse and if r denotes the radius of the incircle of the triangle ABC, then the value of r² is square is equal to.