Mathematics Test 12

Result

Mathematics Test 12

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Weekly Quiz Competition

Question 1
4 / -1

If the cube roots of unity are 1, ω, ω² then the roots of the equation (x – 1)³ + 8 = 0, are

A
-1 , - 1 + 2ω, - 1 - 2ω²

B
-1 , -1, - 1

C
-1 , 1 - 2ω, 1 - 2ω²

D
-1 , 1 + 2ω, 1 + 2ω²

Solution

(x – 1)³ + 8 = 0
⇒ (x – 1) = (-2) (1)^1/3
⇒ x – 1 = -2 or -2ω or -2ω²
or n = -1 or 1 – 2ω or 1 – 2ω²
Hence, option C is correct.
Question 2
4 / -1

The left and right-hand derivatives of |lnx| at x = 1 are

A
equal

B
1 and –1 respectively

C
–1 and 1 respectively

D
None of these

Solution

For x<1, lnx <0. Hence |lnx| = -lnx
Derivative of -lnx = -1/x
Hence, LHD at x=1^- = -1
Similarly,
for x>1, lnx >0. Hence |lnx| = lnx
Derviative of lnx = 1/x
and RHD at x=1⁺ = 1

Hence C is the correct option.
Question 3
4 / -1

On shifting the origin to the point (2, –5) and keeping the axis parallel the new coordinates of the point (5, –3) will be-

A
(–3, –2)

B
(3, 2)

C
(–7, 8)

D
None of these

Solution

Required point will be
(5 – 2, – 3 – (– 5)) = (3, – 3 + 5) = (3, 2)