Mathematics Test 2

Result

Mathematics Test 2

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Weekly Quiz Competition

Question 1
4 / -1

A spherical balloon is filled with 4500^π cu m of helium gas. If a leak in the balloon causes the gas to escape at the rate of 72 cu m/min, then the rate (in m/min) at which the radius of the balloon decreases 49 min after the leakage began is

A
9/7

B
7/9

C
2/9

D
9/2
Question 2
4 / -1

The equation e^{sin x} – e^{-sin x} – 4 = 0 has

A
infinite number of real roots

B
no real root

C
exactly one real root

D
exactly four real roots
Question 3
4 / -1

If the line 2x + y = k passes through the point which divides the line segment joining the points (1, 1) and (2, 4) in the ratio 3 : 2, then k equals

A
29/5

B
5

C
6

D
11/5
Question 4
4 / -1

Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls, is

A
880

B
629

C
630

D
879
Question 5
4 / -1

Let P and Q be 3 × 3 matrices P = Q. If
P³ = Q³ and P²Q = Q²P, then determinant of (P² + Q²) is equal to

A
–2

B
1

C
0

D
–1
Question 6
4 / -1

The negation of the statement "If I become a teacher, then I will open a school'', is

A
I will become a teacher and I will not open a school

B
Either I will not become a teacher or I will not open a school

C
Neither I will become a teacher nor I will open a school

D
I will not become a teacher or I will open a school
Question 7
4 / -1

Three numbers are chosen at random without replacement from {1, 2, 3, ..., 8}. The probability that their minimum is 3, given that their maximum is 6, is

A
0

B
1/5

C
1/4

D
2/5