Mathematics Test 288

Result

Mathematics Test 288

Score
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TIME Taken - -

Weekly Quiz Competition

Question 1
4 / -1

Let L₁: 2x + ky + 3k = 0 and L₂: x + y − k = 0

Which of the following option is incorrect?

A
If k = 2, then L₁ and L₂ are parallel.

B
If k = −2, then L₁ and L₂ are perpendicular.

C
If k = 2, then L₁ and L₂ are intersecting.

D
If k = 0, then L₁ and L₂ are intersect at (0, 0).

Solution
Question 2
4 / -1

If the point P(α,β) lies on the straight line 5x + 12y − 26 = 0,

A
1

B
2

C
4

D
8

Solution
Question 3
4 / -1

If P denotes the power set of A and A is the void set, then what is number of elements in PPPP(A) ?

A
0

B
1

C
4

D
16

Solution
Question 4
4 / -1

Which of the following statements about definite integrals is correct?

A

B

C
The value of a definite integral depends on the choice of the antiderivative.

D

Solution

Step 1: Analyze each option

(A) is incorrect because the definite integral equals F(b) − F(a), not F(a) − F(b).

(B) is correct because if f(x) is negative over [a,b], the integral will be negative even when a < b.

(C) is false as any two antiderivatives differ by a constant, which cancels out in F(b) − F(a).

(D) is incorrect because the integral gives signed area, not necessarily absolute area.
Question 5
4 / -1

A
3

B
12

C
9

D
6

Solution
Question 6
4 / -1

The option(s) with the values of a and L that satisfy the following equation is(are)

A

B

C

D
None

Solution
Question 7
4 / -1

If x lies in the third quadrant, which of the following expressions must be positive?

A
sin⁡x + cos⁡x

B
tan⁡x + cot⁡x

C
sec⁡x + cosecx

D
sin⁡x ⋅ tan⁡x

Solution
Question 8
4 / -1

A

B

C

D

Solution
Question 9
4 / -1

Mean of 100 items is 49. It was discovered that three items which should have been 60, 70, 80 were wrongly read as 40, 20, 50 respectively. The correct mean is

A
48

B

C
50

D
80

Solution

Step 2: Adjust the total sum to find the correct total sum

The incorrect values read were 40,20 , and 50 . The correct values should have been 60 , 70 , and 80 .

We subtract the sum of incorrect values and add the sum of correct values to the incorrect total sum.
Question 10
4 / -1

A
Purely real

B
Purely imaginary

C
Zero

D
Undefined

Solution