All India Engineering / Architecture Entrance Examination (AIEEE)

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AIEEE 2008 MATHEMATICS

Q. 13.

Sol.

Q. 14.

Sol:

Corredt answer is (4)

Q. 15.

Sol.

Note: Questions number 16 to 20 are Assertion-Reason type questions. Each of the following questions contains two statements: Statement-I (Assertion) and Statement-2 (Reason). Each question also has four alternative choices, only one of which is the correct answer. Choose the correct answer.

Q. 16. Let A be a 2 × 2 matrix with real entries. Let I be the 2 × 2 identity matrix.
Denote by tr(A), the sum of diagonal entries of A.
Assume that A² = I

1. Statement-1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1.
2. Statement-1 is true, Statement-2 is false
3. Statement-1 is false, Statement-2 is true.
4. Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1

Sol.

Q. 17. Let p be the statement 'x is an irrational number”, q be the statement “y is a transcendental number”, and r be the statement “x is a rational number iff y is a transcendental number”.

Statement-1: r is equivalent to either q or p.

1. Statement-1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1.
2. Statement-1 is true, Statement-2 is false.
3. Statement-1 is false, Statement-2 is true.
4. Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

Sol. P : x is an irrational number
~ p : x is rational number
q : y is a transcendental number
r : x is a rational number iff y is a transcendental number

We see that s, and r are not equivalent
Also s₂  and r are not equivalent

Q. 18. In a shop there are five types of ice-creams available. A child buys six ice-creams.

Statement-1: The number of different ways the child can buy the six ice-creams is .

Statement-2: The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging 6 A's and 4 B's in a row.

1. Statement-1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1.
2. Statement-1 is true, Statement-2 is false.
3. Statement-1 is false, Statement-2 is true.
4. Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

Sol. The number of different ways the child can buy the b ice-creams

t₁ + t₂ + t₃ + t₄ + t₅ = 6

= ^{6 + 5 - 1}C_5-1 = ¹⁰C₄

Q. 19.

1. Statement-1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1.
2. Statement-1 is true, Statement-2 is false.
3. Statement-1 is false, Statement-2 is true.
4. Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

Sol.

Q. 20.

1. Statement-1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1.
2. Statement-1 is true, Statement-2 is false.
3. Statement-1 is false, Statement-2 is true.
4. Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

Sol.

Q. 21.

Sol.

Q. 22.Let R be the real line. Consider the following subsets of the plane

Which one of the following is true?

1. S is an equivalence relation on R but T is not
2. T is an equivalence relation on R but S is not
3. Neither S nor T is an equivalence relation on R
4. Both S and T are equivalence relations on R

Sol: