Mathematics Test

Result

Mathematics Test - 6

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Weekly Quiz Competition

Question 1
1 / -0

A
e^x - e^y

B

C

D

Solution
Question 2
1 / -0

If X and Y are two sets, then X ∩ (Y ∪ X)` equals:

A
X

B
Y

C

D
None of these

Solution
Question 3
1 / -0

(√3 + 1)⁴ + (√3 – 1)⁴ is

A
a rational number

B
an irrational number

C
a negative integer

D
None of these

Solution

(Ö3 + 1)⁴ + (Ö3 – 1)⁴ = (Ö3)⁴ + ⁴C₁ (Ö3)³ (1) + ⁴C₂ (Ö3)² + ⁴C₃ (Ö3) + ⁴C₄ + (Ö3)⁴ – ⁴C₁ (Ö3)³ (1) + ⁴C₂ (Ö3)² – ⁴C₃ Ö3 + ⁴C₄

= 2 [9 + 6(3) + 1] = 56 = a rational number.
Question 4
1 / -0

The locus of the centre of a circle which cuts off intercepts of length 2a and 2b from x-axis and y-axis respectively, is

A
x + y = a + b

B
x² + y² = a² + b²

C
x² – y² = a²– b²

D
x² + y² = a² – b²

Solution

2 g² – c) = 2a …(i) 2(f² – c) = 2b …(ii)

On squaring (i) and (ii) and then subtracting (ii) from (i), we get g² – f² = a² – b²

Hence, the locus is x² – y² = a² – b².
Question 5
1 / -0

The number of tangents which can be drawn from the point (– 1, 2) to the circle x² + y² + 2x – 4y + 4 = 0 is

A
1

B
2

C
3

D
0

Solution

Since the point lies within the circle, no tangent can be drawn.
Question 6
1 / -0

If a, b, c are consecutive integers then

A
log_eb

B
2 log_eb

C
logb^e

D
½ log_eb

Solution
Question 7
1 / -0

If ⁿC₁₂ = ⁿC₈ find, ²²C_n.

A
462

B
240

C
231

D
None of these

Solution

∴n ! / [(n - 12) ! 12 !] = n ! / [(n - 8)! 8 !]

∴n - 12 = 8 n = 20

∴²²C₂₀ = 22! / [(22 - 20)! 20!] = 231
Question 8
1 / -0

One bag contains 5 white and 4 black balls. Another bag contains 7 white and 9 black balls. A ball is transferred from the first bag to the second and then a ball is drawn from second. The probability that the ball is white, is

A
8/17

B
40/153

C
59

D
4/9

Solution

Required probability = 5/9 x 8/17 + 4/9 x 7/17 = 4/9
Question 9
1 / -0

Three numbers form an increasing GP. If the middle number is doubled, then the new numbers are in AP. The common ratio of the GP is

A
2 - √3

B
2 + √3

C
√3 - 2

D
3 + √2

Solution