﻿ Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of A × B having 3 or more elements is from Mathematics Class 12 JEE Year 2013 Free Solved Previous Year Papers

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# JEE Mathematics 2013 Exam Questions

#### Multiple Choice Questions

1.

The number of values of k, for which the system of equations
(k+1) x + 8y = 4k
kx + (k+3)y = 3k -1
has no solution, is

• infinite

• 1

• 2

• 3

B.

1

Condition for the system of equations has no solution,

Therefore, k = 3
Hence, only one value of k exists.

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2.

The circle passing through (1,-2) and touching the axis of x at (3,0) also passes through the point

• (-5,2)

• (2,-5)

• (5,-2)

• (-2,5)

C.

(5,-2)

(x − 3)2+ y2+ λy = 0
The circle passes through (1, − 2)
⇒ 4 + 4 − 2λ = 0 ⇒ λ = 4
(x − 3)2+ y2+ 4y = 0
⇒ Clearly (5, − 2) satisfies.

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3.

If the equations x2 + 2x + 3 = 0 and ax2 + bx + c = 0, a, b, c ∈ R, have a common root, then a : b : c is

• 1:2:3

• 3:2:1

• 1:3:2

• 3:1:2

A.

1:2:3

Given equations are
x2 +2x+3 =0  ... (i)
ax2 +bx +c =0 .. (ii)
since, Eq(i) has imaginary roots, So eq (ii) will also have both roots same as eq (i)
thus,

Hence, a:b:c  is 1:2:3

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4.

A ray of light along  get reflected upon reaching X -axis, the equation of the reflected ray is

B.

Given equation of line

Slope of incident ray is
So, slope of reflected ray must be  and the point of incident
So equation of reflected ray

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5.

Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of A × B having 3 or more elements is

• 256

• 220

• 219

• 211

C.

219

Given, n(A) =2, n(B) = B
The number of subsets of AXB having 3 or more elements,
=

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6.

If x, y, z are in A.P. and tan−1 x, tan−1 y and tan−1 z are also in A.P., then

• x= y= z

• 2x =3y = 6z

• 6x = 3y= 2z

• 6x = 4y = 3z

A.

x= y= z

If x, y, z are in A.P.
2y = x + z and
tan−1 x, tan−1 y, tan−1 z are in A.P.
2 tan−1 y = tan−1 x + tan−1
z ⇒ x = y = z.

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7.

The real number k for which the equation, 2x3 +3x +k = 0 has two distinct real roots in [0,1]

• lies between 1 and 2

• lies between 2 and 3

• lies between -1 and 0

• does not exist

D.

does not exist

Let f(x) = 2x3+3x+k
On differentiating w.r.t x, we get
f'(x) = 6x2 + 3> 0, ∀ x ε R
⇒ f(x) is strictly increasing function
⇒ f(x) = 0 has only one real root, so two roots are not possible.

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8.
• -1/4

• 1/2

• 1

• 2

D.

2

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9.

Consider :
Statement − I : (p ∧ ~ q) ∧ (~ p ∧ q) is a fallacy.
Statement − II : (p → q) ↔ (~ q → ~ p) is a tautology.

• Statement -I is True; Statement -II is True; Statement-II is a correct explanation for Statement-I

• Statement - I is True; Statement -II is true; Statement-II is not a correct explanation for Statement-I

• Statement -I is True; Statement -II is False.

• Statement -I is False; Statement -II is True

B.

Statement - I is True; Statement -II is true; Statement-II is not a correct explanation for Statement-I

 p q ~p ~q p^~q ~p^q (p^~q)^(~p^q) T T F F T F T F F F T T F T F T F T F F F F T F F F F F
Fallacy

 p q ~p ~q p ⇒ q ~ q ⇒ ~ p (p ⇒ q) ⇔ (~ q ⇒ ~ p) TTFF T F T F F FT T F T F T T F T T T F T T T T T T
Tautology
S2 is not an explanation of S1
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10.

The sum of first 20  terms of the sequence 0.7,0.77,0.777...... is

C.

Let S = 0.7 + 0.77 +0.777 + .... upto 20 terms

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