Mathematics Test

Result

Mathematics Test - 12

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Weekly Quiz Competition

Question 1
1 / -0

The minimum value of √(e^x² - 1) is

A
1

B
e

C
0

D
none of these

Solution
Question 2
1 / -0

A
1/2

B
0

C
1

D
None of these

Solution

On applying the L' hospital rule, we get Lt_x→0 Sin x = 0.
Question 3
1 / -0

A
e³

B
e^3/2

C
e⁶

D
None of these

Solution
Question 4
1 / -0

If sin (sin-1 1/7 + cps-1 x) = 1, then x is equal to

A
1

B
0

C
6/7

D
1/7

Solution
Question 5
1 / -0

If (√8+i)⁵⁰ = 3⁴⁹ (a + ib), then a² + b² is

A
3

B
9

C
16

D
√8

Solution
Question 6
1 / -0

If the roots of the equation ax² + bx + c = 0 are of the form k+1/k and k+2/k+1 then (a + b + c)² is equal to

A
2b² − ac

B
a²

C
b² − 4ac

D
b² − 2ac

Solution
Question 7
1 / -0

A
x

B
a

C
2a + 3x

D
x²

Solution
Question 8
1 / -0

The coefficient of x⁵ in (1+2x+3x²+……….up to infinite term)^-3/2 is

A
21

B
25

C
26

D
None of these

Solution

(1+2x+3x²+………)^–3/2

=((1–x)^–2)^–3/2

= (1 − x)³ = 1 − 3x + 3x² − x³

∴coefficient of x⁵ = 0.
Question 9
1 / -0

The equation of the normal to the ellipse x²/a² + y²/b² = 1 at the positive end of the latus rectum is

A
x + ey + e³a = 0

B
x − ey − e³a = 0

C
x − ey − e²a = 0

D
None of these

Solution
Question 10
1 / -0

If the latus rectum of a hyperbola through one focus, subtends 60 ° angle at the other focus, then its eccentricity is

A
√2

B
√3

C
√5

D
√6

Solution