JEE Advanced Mock Test 1

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JEE Advanced Test 1

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Section - (I)

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

Q.1 Let ƒ(x) = x³ + x² + 1; g(x) = x² – 1. If the roots of ƒ(x) are a, b and c, then the value of g(a).g(b).g(c) + 17g(abc) is...

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Q.2 Consider the quadratic equation a(x – 1)² + x – 3 = 0. If a is of the form k(k + 1)/2 , k ∈ Q, then roots of equation are necessarily...

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Q.3 If y² – x²y – 2x = 0, x,y > 0 and \int \dfrac{y^{2}-x}{\left( y^{2}+x\right) \left( x^{2}+y\right) }dy=f\left( y\right) +C, where C is an arbitrary constant, then the value of ƒ'(y) at x = 1 is...

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Q.4 If the plane passing through the points (a,1,1), (1,2,1) and (2,3,4) is parallel to the line r = b(i + j + k), {b ∈ R}, then the value of a is equal to...

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Q.5 Let ƒ, g are two continuous and twice derivable functions such that ƒ(0) = ƒ(3) = 0; ƒ(1).ƒ(2) < 0; g(0) = g(3) = 0. Number of roots of equation ƒ"(x).g(x) + ƒ'(x).g'(x) = 0 in the interval (–1,5) cannot be...

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Q.6 If a, b, c ∈ R are distinct numbers in Arithmetic Progression (AP) ; a, u ,b are in Geometric Progression (GP); b, v, c are also in G.P., then u², b², v² will be in...

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SECTION – (II)

1. This section contains Two paragraphs.
2. Based on each paragraph, there are TWO questions.
3. Each question has FOUR options (A), (B), (C) and (D) ONLY ONE of these four options is correct.

Paragraph for Questions 7 and 8

Let L₁ be a line 5x – 7y = 35 which cuts x-axis and y-axis at A & B respectively. Variable line L₂, which is perpendicular to L₁ cuts x-axis and y-axis at C & D respectively. Locus of point of intersection of lines joining AD and BC is the curve S.

Q.7 Area of the region enclosed by curve S is (in sq. units)...

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Q.8 Coordinates of a point P, which is farthest from origin, on the curve S is...

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Paragraph for Questions 9 and 10

Let P(z) is a variable point in argand plane which satisfies \left( z+\overline{z}\right) \left( \left| z-2i\right| -1\right) \leq 0

Q.9 If amp(z) is least, then |z| is equal to...

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Q.10 If P(z) also satisfies arg(z + 1 – 2i) = -(π/4), then the number(s) of such points P, is/are...

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SECTION - (III)

1. This section contains Two questions.
2. Each question has Matching List-I with Matching List-II. The answer codes for the Matching Lists have choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Q.11 Match Matching List-I with Matching List-II and select the correct answer using the code given below the list.

Matching List - I

(P) If a, b, and c are three positive, consecutive terms of a G.P., such that the harmonic mean of a and b is 12 and the arithmetic mean of b and c is 16/3, then the geometric mean of a, b, and c is...

(Q) If the line r = u(ai + 2j - 12k), u ∈ R, a > 0 makes an isosceles triangle with the planes r.(2i + j + 3k) = 1 and r.(i + 2j - 3k) = 1 , then ten's digit of a is...

(R) Value of x in the interval (0, 2π) where ƒ(x) = [sin[x]] is discontinuous, is (where [.] denotes greatest integer function)...

(S) Let ƒ be a derivable function satisfying f\left( x\right) =x^{2}+\int ^{x}_{0}e^{-t}f\left( x-t\right) dt then degree of polynomial function ƒ(x²) is...

Matching List - II

(1) 8
(2) 4
(3) 6
(4) 7

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Q.12 Match Matching List-I with Matching List-II and select the correct answer using the code given below the list.

Matching List - I

(P) If mutually perpendicular tangents can be drawn from A(0,–b) to the hyperbola (x/a)² - (y/b)² = 1 which touches the hyperbola at B and C, then value of (a/b)² is...

(Q) If x – y + 2 = 0 is a tangent to parabola y² = 4ax + b, then ka² – 2ka + b = 0, where k is...

(R) Least distance of point (–4,7) from y² = 4x is a√2, where a is...

(S) If tangents drawn at A(x₁, y₁), B(x₂, y₂) on the ellipse (x/√10)² + (y)² = 1 are mutually perpendicular, then the value of |(x₁x₂)/(y₁y₂)| is...

Matching List - II

(1) 2
(2) 4
(3) 5
(4) 10

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