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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.

269 Views

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.

181 Views

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

177 Views

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

441 Views

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,
=

286 Views

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.

207 Views

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.

183 Views

8.
• -1/4

• 1/2

• 1

• 2

D.

2

188 Views

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
289 Views

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

958 Views

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