MTH TEST FOR IITJEE

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MTH TEST FOR IITJEE

Author: sachina

Q. 13

SECTION - I
Straight Objective Type
This section contains 4 multiple choice questions numbered 13 to 16. Each question has 4 choices (1), (2), (3) and (4), out of which ONLY ONE is correct.

Let

Then which of the following is false?

y = 1 + 2 cos x

3 marks

Q. 14

Let the normal at P (2, 4) on the parabola y² = 8x meet the parabola again at Q. Let C be the centre of the circle described on PQ as a diameter. Then the image of C in the line y = x is

(-4, 1)

(-4, 10)

(10, -4)

(6, 10)

3 marks

Q. 15

Let f : X

Y be a function. Which of the following is true?

3 marks

Q. 16

Let

Suppose (a - b)² + (p - q)² = 25
(b - c)² + (q - r)² = 36
(c - a)² + (r - p)² = 49
then det B equals

162

216

864

288

3 marks

Q. 17

SECTION - II
Assertion - Reason Type
This section contains 1 question numbered 17. Each question contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason). Each question has 4 choices (1), (2), (3) and (4), out of which ONLY ONE is correct.

STATEMENT-1 : The equation x³ - 31x² + 311x - 1001 = 0 has 7 as a root.
because
STATEMENT-2 : 7 divides the constant term of the equation.

Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1

Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1

Statement-1 is True, Statement-2 is False

Statement-1 is False, Statement-2 is True

3 marks

Q. 18

SECTION-III
Linked Comprehension Type
This section contains 2 paragraphs M18 and M19. Based upon each paragraph, 2 multiple choice questions have to be answered. Each question has 4 choices (1), (2), (3) and (4), out of which ONLY ONE is correct.

M18 :Paragraph for Question No. 18
A function f from set A to set B, A and B being non-empty, is a rule that associates each element of A to a unique element of B.
Let A = {1, 2, 3}, B = {1, 2, 3, 4, 5, 6}

Question: Of all the possible functions from A to B, a function is chosen randomly. The probability that the function is increasing is

4 marks

Q. 19

M19 : Paragraph for Question No. 19

Let f(x) = 0 be a polynomial equation with real coefficients. Then between any two distinct real roots of f(x) = 0, there exists at least one real root of equation
f '(x) = 0.

This result is a special version of the Rolle's theorem for polynomials. Much information can be extracted from the roots of f '(x) = 0 about the roots of f(x) = 0.

Question: The range of values of k for which the equation x⁴ - 14x² + 24x - k = 0 has four unequal real roots is

8 < k < 11

4 < k < 8

8 < k < 15

4 < k < 13

4 marks

Q. 20

SECTION-IV
Matrix-Match Type

This section contains 1 question. Each question contains statements given in two columns which have to be matched. Statements (A, B, C, D) in Column I have to be matched with statements (p, q, r, s) in Column II

Match the statements/expressions in column I with the statements/expressions in column II.

Column I		Column II
(A)	The remainder when 5⁹⁹ is divided by 13 is	(p)	3
(B)	The remainder when 3⁵¹ is divided by 8 is	(q)	8
(C)	The remainder when 27¹⁰ + 7⁵¹ is divided by 10 is	(r)	0
(D)	The remainder when 106⁸⁵ - 85¹⁰⁶ is divided by 7 is	(s)	0