If a vector lies in the plane of and , then

**A. **

**B. **

**C. **

**D. **

**Answer : ****Option C**

**Explaination / Solution: **

No Explaination.

No Explaination.

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Consider the vectors , , , such that . Let P_{1} and P_{2} be the planes determined
by the pairs of vectors , and , respectively. Then the angle
between P_{1} and P_{2} is

**A. ** 0˚

**B. ** 45˚

**C. ** 60˚

**D. ** 90˚

**Answer : ****Option A**

**Explaination / Solution: **

No Explaination.

No Explaination.

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The vector equation points = (ˆ *i* - 2 ˆ *j* - ˆ *k* ) + t(6 ˆ *i* - ˆ *k* ) represents a straight line passing through the

**A. ** (0, 6, -1) and (1, -2, -1)

**B. ** (0, 6, -1) and (-1, -4, -2)

**C. ** (1, -2, -1) and (1, 4, -2)

**D. ** (1, -2, -1) and (0, -6,1)

**Answer : ****Option C**

**Explaination / Solution: **

No Explaination.

No Explaination.

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The equation of the normal
to the circle *x*^{2 }+ *y*^{2 }− 2*x *− 2 *y *+1
= 0 which is parallel to the line 2*x *+ 4 *y *= 3
is

**A. ** *x* + 2 *y* = 3

**B. ** *x* + 2 *y* + 3 = 0

**C. ** 2* x* + 4 *y* + 3 = 0

**D. ** *x* - 2 *y* + 3 = 0

**Answer : ****Option A**

**Explaination / Solution: **

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Consider an ellipse whose
centre is of the origin and its major axis is along *x*-axis. If its
eccentrcity is 3/5 and the distance between its foci is 6, then the area of the
quadrilateral inscribed in the ellipse with diagonals as major and minor axis
of the ellipse is

**A. ** 8

**B. ** 32

**C. ** 80

**D. ** 40

**Answer : ****Option D**

**Explaination / Solution: **

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If sin^{−1 }*x *+ sin^{−1 }*y (*2π/3) ; then cos^{−1 }*x *+ cos^{−1 }*y *is equal to

**A. ** 2π /3

**B. ** π /3

**C. ** π /6

**D. ** π

**Answer : ****Option B**

**Explaination / Solution: **

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If cot^{−1 }2 and cot^{−1 }3 are two angles of a
triangle, then the third angle is

**A. ** π/4

**B. ** 3π/4

**C. ** π/6

**D. ** π/3

**Answer : ****Option B**

**Explaination / Solution: **

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If *f *and *g *are
polynomials of degrees *m *and *n *respectively, and if *h*(*x*)
= ( *f *o *g *)(*x*) , then the degree of *h *is

**A. ** *mn*

**B. ** *m* + *n*

**C. ** *m*^{n}

**D. ** *n*^{m}

**Answer : ****Option A**

**Explaination / Solution: **

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The value of ∑(*i*^{n }+ *i*^{n}^{−1 }) is

**A. ** 1+
*i*

**B. ** *i*

**C. ** 1

**D. ** 0

**Answer : ****Option A**

**Explaination / Solution: **

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If *z *is a complex
number such that *z *∈ **C** \**R** and *z *+ 1/z^{ }∈ **R** , then | *z *| is

**A. ** 0

**B. ** 1

**C. ** 2

**D. ** 3

**Answer : ****Option B**

**Explaination / Solution: **

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