If , , are three unit vectors such
that is perpendicular to , and is parallel to then x ( x ) is equal to

**A. **

**B. **

**C. **

**D. **

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

**Explaination / Solution: **

No Explaination.

No Explaination.

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If then a vector
perpendicular to and lies in the plane containing and is

**A. ** *-17iˆ + 21 ˆj - 97kˆ*

**B. ** *17iˆ + 21 ˆj -123kˆ*

**C. ** *-17iˆ - 21 ˆj + 97kˆ*

**D. ** *-17iˆ - 21 ˆj - 97kˆ*

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

**Explaination / Solution: **

No Explaination.

No Explaination.

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If the planes .(2 ˆ*i* - λ ˆ*j* + ˆ*k* ) = 3 and .(4 ˆ*i* + ˆ*j* - μ ˆ*k* ) = 5 are parallel, then the value of λ
and μ are

**A. ** 1/2 , -2

**B. ** –1/2 ,2

**C. ** – 1/2 , -2

**D. ** 1/2 ,2

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

**Explaination / Solution: **

No Explaination.

No Explaination.

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The radius of the circle
passing through the point (6, 2) two of whose diameter are *x *+ *y *=
6 and *x *+ 2 *y *= 4 is

**A. ** 10

**B. ** 2√5

**C. ** 6

**D. ** 4

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

**Explaination / Solution: **

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An ellipse has *OB *as
semi minor axes, *F *and *F *′ its foci and the angle *FBF *′ is
a right angle. Then the eccentricity of the ellipse is

**A. ** 1/√2

**B. ** 1/2

**C. ** 1/4

**D. ** 1/√3

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

**Explaination / Solution: **

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If sin^{−1 }*x *= 2 sin^{−1 }*α *has a solution, then

**A. ** |α| ≤ (1/√2)

**B. ** |α| ≥ (1/√2)

**C. ** |α| < (1/√2)

**D. ** |α| > (1/√2)

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

**Explaination / Solution: **

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sin^{−1 }(2 cos^{2 }*x *−1) + cos^{−1 }(1− 2 sin^{2 }*x*) =

**A. ** π/2

**B. ** π/3

**C. ** π/4

**D. ** π/6

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

**Explaination / Solution: **

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If *α *, *β *, and *γ *are the zeros of *x*^{3
}+ *px*^{2 }+ *qx *+ *r *, then is

**A. ** -*q*/*r*

**B. ** -*p*/*r*

**C. ** *q*/*r*

**D. ** -*q*/*p*

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

**Explaination / Solution: **

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The conjugate of a complex
number is 1/*i*-2 Then, the complex number is

**A. ** 1/[*i*+2]

**B. ** -1/[*i*+2]

**C. ** -1/[*i*-2]

**D. ** 1/[*i*-2]

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

**Explaination / Solution: **

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If (z-1) / (z+1), is purely
imaginary, then | *z *| is

**A. ** 1/2

**B. ** 1

**C. ** 2

**D. ** 3

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

**Explaination / Solution: **

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