# (Paper) AIEEE 2008 EXAMINATION PAPER : Code-A6 (Paper -4)

**PAPER
: AIEEE 2008 EXAMINATION
PAPER
(Code-A6)**

*Paper
- 4*

**76.
**Let a, b, c be any real
numbers. Suppose that there are real numbers x, y, z not all zero such that

x = cy + bz, y = az + cx, and z = bx + ay. Then a2 + b2 + c2 + 2abc is equal to

(1) –1 (2) 0

(3) 1 (4) 2

**Ans. [3]**

**77. **How many different words can be formed by jumbling the
letters in the word MISSISSIPPI in which not

two S are adjacent ?

(1) 6. 7. 8C4 (2) 6. 8. 7C4

(3) 7. 6C4 . 8C4 (4) 8. 6C4 . 7C4

**Ans. [3]**

**78. **The first two terms of a geometric progression add up to
12. The sum of the third and the fourth terms is

48. If the terms of the geometric progression are alternately positive and
negative, then the first term is

(1) – 12 (2) 12

(3) 4 (4) – 4

**Ans. [1]**

**79. **Let f(x) =

=

≠

−

−

0 if x 1

if x 1

x 1

(x 1)sin 1

Then which one of the following is true ?

(1) f is differentiable at x = 0 and at x = 1 (2) f is differentiable at x = 0
but not at x = 1

(3) f is differentiable at x = 1 but not at x = 0 (4) f is neither
differentiable at x = 0 nor at x = 1

**Ans. [2]**

**80. **How many real solution does the equation x7 + 14x5 + 16x3 +
30x – 560 = 0 have ?

(1) 1 (2) 3

(3) 5 (4) 7

**Ans. [1]**

**81. **Suppose the cubic x3 – px + q has three distinct real
roots where p > 0 and q > 0. Then which one of the

following holds ?

(1) The cubic has minima at –

3

p and maxima at

3

p

(2) The cubic has manima at both

3

p and –

3

p

(3) The cubic has maxima at both

3

p and –

3

p

(4) The cubic has minima at

3

p and maxima at –

3

p

**Ans. [4]**

**82. **The value of 2 ∫

π

−

4

sin x

sin x dx is -

(1) x – log | sin (x –

4

π

) | + c (2) x + log | sin (x –

4

π

) | + c

(3) x – log | cos (x –

4

π

) | + c (4) x + log | cos (x –

4

π

) | + c

**Ans.[2]**

**83. **The area of the plane region bounded by the curves x + 2y2
= 0 and x + 3y2 = 1 is equal to -

(1)

3

1 (2)

3

2

(3)

3

4 (4)

3

5

**Ans.[3]**

**84. **Let I = ∫

1

0 x

x sin dx and J = ∫

1

0 x

cos x dx. Then which one of the following is true ?

(1) I <

3

2 and J < 2 (2) I <

3

2 and J > 2

(3) I >

3

2 and J < 2 (4) I >

3

2 and J > 2

**Ans.[1]**

**85. **The differential equation of the family of circles with
fixed radius 5 units and centre on the line y = 2 is -

(1) (y – 2) y′2 = 25 – (y – 2)2 (2) (y – 2)2 y′2 = 25 – (y
– 2)2

(3) (x – 2)2 y′2 = 25 – (y – 2)2 (4) (x – 2) y′2 = 25 – (y
– 2)2

**Ans.[3]**

**86. **The solution of the differential equation

dx

dy =

x

x + y

satisfying the condition y (1) = 1 is -

(1) y = x ln x + x2 (2) y = xe(x–1)

(3) y = x ln x + x (4) y = ln x + x

**Ans.[3]**

**87. **The perpendicular bisector of the line segment joining P(1,
4) and Q(k, 3) has y-intercept -4. Then a

possible value of k is -

(1) 2 (2) –2

(3) –4 (4) 1

**Ans.[3]**

**88. **The point diametrically opposite to the point P(1, 0) on
the circle x2 + y2 + 2x + 4y –3 = 0 is -

(1) (–3, 4) (2) (–3, –4)

(3) (3, 4) (4) (3, – 4)

**Ans.[2]**

**89. **A parabola has the origin as its focus and the line x =2 as
the directrix. Then the vertex of the parabola is

at -

(1) (1, 0) (1) (0, 1)

(3) (2, 0) (4) (0, 2)

**Ans.[1]**

**90 **A focus of an ellipse is at the origin. The directrix is the
line x = 4 and the eccentricity is

2

1 . Then the

length of the semi-major axis is -

(1)

3

2 (2)

3

4

(3)

3

5 (4)

3

8

**Ans.[4]**

**91. **If the straight lines

k

x −1

=

2

y − 2

=

3

z − 3

and

3

x − 2

=

k

y − 3

=

2

z −1

intersect at a point, then the integer k is equal to

(1) 5 (2) 2

(3) –2 (4) –5

**Ans. [4]**

**92. **The line passing through the points (5, 1, a) and (3, b, 1)
crosses the yz-plane at the point

−

2

, 13

2

0,17 .

Then

(1) a = 4, b = 6 (2) a = 6, b = 4

(3) a = 8, b = 2 (4) a = 2, b = 8

**Ans. [2]**

**93. **The non-zero vectors →a , →b and →c are
related by →a = 8 →b and →c = –7 →b . Then the angle
between →a

and →c is

(1)

4

π (2)

2

π

(3) π (4) 0

**Ans. [3]**

**94. **The vector →a = αiˆ + 2 j ˆ + βkˆ lies
in the plane of the vectors →b = iˆ + jˆ and →c = jˆ + kˆ and
bisects the

angle between →b and →c . Then which one of the following gives
possible values of α and β ?

(1) α = 1, β = 2 (2) α = 2, β = 1

(3) α = 1, β = 1 (4) α = 2, β = 2

**Ans. [3]**

**95. **The mean of the numbers a, b, 8, 5, 10 is 6 and the
variance is 6.80. Then which one of the following

gives possible values of a and b ?

(1) a = 5, b = 2 (2) a = 1, b = 6

(3) a = 3, b = 4 (4) a = 0, b = 7

**Ans. [3]**

**96. **A die is thrown. Let A be the event that the number
obtained is greater than 3. Let B be the event that the

number obtained is less than 5. Then P(A ∪ B) is

(1) 0 (2) 1

(3)

5

2 (4)

5

3

**Ans. [2]**

**97. **It is given that the events A and B are such that P(A) =

4

1 , P(A|B) =

2

1 and P(B|A) =

3

2 . Then P(B) is

(1)

3

1 (2)

3

2

(3)

2

1 (4)

6

1

**Ans. [1]**

**98. **AB is a vertical pole with B at the ground level and A at
the top. A man finds that the angle of elevation of

the point A from a certain point C on the ground is 60º. He moves away from the
pole along the line BC

to a point D such that CD = 7 m. From D the angle of elevation of the points A
is 45º. Then the height of

the pole is

(1) ( 3 1)m

2

7 3 + (2) ( 3 1)m

2

7 3 −

(3) m

3 1

1

2

7 3

+

(4) m

3 1

1

2

7 3

−

**Ans. [1]**

**99. **The value of cot

+ −

3

tan 2

3

cosec–1 5 1 is

(1)

17

3 (2)

17

4

(3)

17

5 (4)

17

6

**Ans. [4]**

**100. **The statement p → (q → p) is equivalent to

(1) p → (p ∨ q) (2) p → (p ∧ q)

(3) p → (p ↔ q) (4) p → (p → q)

**Ans. [1]**

**Directions : **Question number 101 to 105 are Assertion-Reason
type questions. Each of these questions

contains two statements: Statement-1 (Assertion) and Statement-2 (reason). Each
of these questions also

has four alternative choices, only one of which is the correct answer. You have
to select the correct choice.

**101.
**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.

**Statement- **1:

If A ≠ I and A ≠ –I, then det A = –1

**Statement -2 **:

If A ≠ I and A ≠ –I, then tr (A) ≠ 0

(1) Statement-1 is true, Statement -2 is true; Statement-2 is a correct
explanation for Statement-1

(2) Statement-1 is true, Statement -2 is true; Statement-2 is not a correct
explanation for Statement-1

(3) Statement-1 is true, Statement -2 is false

(4) Statement-1 is false, Statement-2 is true

**Ans. [4]**

**102. Statement-1:**

For every natural number n ≥ 2.

1

1 +

2

1 + ........ +

n

1 > n

**Statement -2:**

For every natural number n ≥ 2.

n(n +1) < n + 1

(1) Statement-1 is true, Statement -2 is true; Statement-2 is a correct
explanation for Statement-1

(2) Statement-1 is true, Statement -2 is true; Statement-2 is not a correct
explanation for Statement-1

(3) Statement-1 is true, Statement -2 is false

(4) Statement-1 is false, Statement-2 is true

**Ans. [2]**

**103. Statement- 1:**

Σ=

+

n

r 0

(r 1) nCr = (n +2) 2n–1

**Statement -2:**

Σ=

+

n

r 0

(r 1) nCr xr = (1 + x)n + nx (1 + x)n–1

(1) Statement-1 is true, Statement -2 is true; Statement-2 is a correct
explanation for Statement-1

(2) Statement-1 is true, Statement -2 is true; Statement-2 is not a correct
explanation for Statement-1

(3) Statement-1 is true, Statement -2 is false

(4) Statement-1 is false, Statement-2 is true

**Ans. [1]**

**104. **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 10C5

**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 a correct
explanation for Statement-1

(2) Statement-1 is true, Statement -2 is true; Statement-2 is not a correct
explanation for Statement-1

(3) Statement-1 is true, Statement -2 is false

(4) Statement-1 is false, Statement-2 is true

**Ans. [4]**

**105. **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.

**Statement -2 :**

r is equivalent ot ~ (p ↔ ~q)

(1) Statement-1 is true, Statement -2 is true; Statement-2 is a correct
explanation for Statement-1

(2) Statement-1 is true, Statement -2 is true; Statement-2 is not a correct
explanation for Statement-1

(3) Statement-1 is true, Statement -2 is false

(4) Statement-1 is false, Statement-2 is true

**Ans. [4]**