Mathematics Test

Result

Mathematics Test - 23

Score
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Rank
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Weekly Quiz Competition

Question 1
1 / -0

Let P and Q be 3 × 3 matrices with P ≠ Q. If P^3 = Q^3 and P^2 Q = Q^2 P, then determinant of (P^2 + Q^2 ) is equal to

A

0

B

–1

C

1

D

–2
Question 2
1 / -0

An ellipse is drawn by taking a diameter of the circle (x – 1)^2 + y^2 = 1 as its semiminor axis and a diameter of the circle x^2 + (y – 2)^2 = 4 as its semi-major axis. If the centre of the ellipse is the origin and its axes are the coordinate axes, then the equation of the ellipse is

A

x^2 + 4y^2 = 8

B

4x^2 + y^2 = 8

C

x^2 + 4y^2 = 16

D

4x^2 + y^2 = 4
Question 3
1 / -0

A

Option 1

B

Option 2

C

Option 3

D

Option 4
Question 4
1 / -0

A

Option 1

B

Option 2

C

Option 3

D

Option 4
Question 5
1 / -0

A

Option 3

B

Option 2

C

Option 4

D

Option 1
Question 6
1 / -0

At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P w.r.t. additional number of workers x is given by dP/dx = 100 - 12√x . If the firm employs 25 more workers, then the new level of production of items is

A

3500

B

2500

C

4500

D

3000
Question 7
1 / -0

A

Option 3

B

Option 4

C

Option 2

D

Option 1
Question 8
1 / -0

If 100 times the 100th term of an AP with non zero common difference equals the 50 times its 50th term, then the 150 th term of this AP is

A

zero

B

150 times its 50 th term

C

–150

D

150
Question 9
1 / -0

A line is drawn through the point (1, 2) to meet the coordinate axes at P and Q such that it forms a triangle OPQ, where O is the origin. If the area of the triangle OPQ is least, then the slope of the line PQ is

A

–4

B

−1/2

C

–2

D

−1/4
Question 10
1 / -0

A

Option 2

B

Option 3

C

Option 1

D

All of these