JEE Advanced Mock Test 5

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JEE Advanced Mock Test 5

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Section - (I)

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.

1. For every real number p, the quadratic equation (p² + 2)x² – 2(a + p)²x + (p² + 2p + b) = 0 has a root 1, where a, b ∈ R. Then which of the following statement(s) is(are) correct ?

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2. If y = e√ˣ + e⁻√ˣ, then dy/dx will be.

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3. Consider the equation Cos⁻¹(a) + Sin⁻¹(x² - 6x + 17/2) = π/2, in terms of x, then.

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4. If A = \left( \prod ^{45}_{i=1}\sin \left( i^{0}\right) \right) \left( \prod ^{89}_{j=46}\sec \left( j^{0}\right) \right), then.

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SECTION – (II)

a. This section contains One paragraphs.
b. Based on each paragraph, there are TWO questions.
Each question has FOUR options (A), (B), (C) and (D) ONE OR MORE of these four options is/are correct.

Paragraph for Questions 5 and 6

Let U(x) be a polynomial satisfying \lim _{x\rightarrow \infty }\dfrac{xU\left( x\right) }{x^{6}+2021}= 1, such that U(0) = 1, U(2) = 9, U(3) = 28, U(4) = 65, U(6) = 217, then

5. The value of the definite integral \int ^{9}_{-3}\left( \cup \left( x\right) -x^{3}\right) dx is.

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6. If \int \dfrac{\left( x-3\right) }{\left( U\left( x\right) -x^{3}-1\right) }dx = (1/P)ln|(x - 6)/x| + (1/Q)ln|(x - 2)/(x - 4)| + K, {where K is the integration constant}, then.

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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.

7. The sum of all possible distinct real values of a for which the equation |x² - (a² + 7) + 7a²| + ((x - 3)(x + 2 - 3a))¹/² = 0, in x, has atleast one real solution is.

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8. If the sum of all real values of t satisfying the equation eᵗ([x] - 2) = [x] - 1, {where x ∈ (3, 100), and [.] denotes the greatest integer function} is P, then the value of [P] is.

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9. In a triangle PQR, if Sin2P = Sin2Q, such that P ≠ Q and 3TanP = 4, then the value of 4/(1 + Tan²Q) + 2Sin(Q - P) + CotR(CosQ(1 + Sin²P)¹/² - CosP(1 + Sin²Q)¹/²) is.

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10. Let f(x) = [x]{x} + {x}[x] and f'(5/2) = 1 + ln2 √a. Then the value of a is {where [.] denotes the greatest integer function and {.}denotes the fraction part function}.

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