Mathematics Test

Result

Mathematics Test - 29

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Weekly Quiz Competition

Question 1
3 / -1

The area lying in the first quadrant and bounded by the circle x² + y² = 4, the line x =√3 y and the x-axis is

A
π

B
π/2

C
π/3

D
None of these

Solution
Question 2
3 / -1

A missile fired from the ground level rises x meters vertically upwards in t seconds, where x = 100t - 25/2 t². The maximum height reached is

A
200 m

B
125 m

C
160 m

D
190 m

Solution
Question 3
3 / -1

The area of the figure bounded by the curves y = | x - 1 | and y = 3 - | x | is

A
2

B
3

C
4

D
None of these

Solution
Question 4
3 / -1

If a parallelepiped is formed by planes drawn through the points (5, 8, 10) and (3, 6, 8) parallel to the coordinate planes, then the length of diagonal of the parallelopiped is:

A
2√3

B
3√2

C
√2

D
√3

Solution

According to question, if we draw the parallelepiped in 3D space.

Points \(\mathrm{P}(5,8,10)\) and \(\mathrm{Q}(3,6,8)\) appear to be opposite vertices of parallelepiped.

\(\therefore\) Length of PQ gives the length of diagonal of parallelepiped.

Using distance formula we can find PQ as:

\(P Q =\sqrt{(5-3)^{2}+(8-6)^{2}+(10-8)^{2}}\)

\( PQ=\sqrt{2^{2}+2^{2}+2^{2}}\)

\(PQ=\sqrt{12}\)

\(PQ=2 \sqrt{3} \)

\(\therefore\) Length of diagonal of the parallelepiped is \(2 \sqrt{3}\) units.
Question 5
3 / -1

Period of cot 3 x - cos (4x + 3) is

A
π/3

B
π/4

C
π

D
π/2

Solution

Period of cot 3x is π/3 and period of cos (4x + 3) is π/2

⇒ L.C.M. is π, hence the answer.
Question 6
3 / -1

Three identical dice are rolled. The probability that the same number will appear on each of them is

A
1/6

B
1/216

C
1/36

D
None of these

Solution

Exhaustive number of cases = 6³ = 216.

The same number can appear on each of the dice in the following ways: (1, 1, 1), (2, 2, 2).... (6, 6, 6).

So, favourable number of cases = 6.

Hence, required probability = 6/216 = 1/36.
Question 7
3 / -1

A
8

B
2

C
4

D
None of these

Solution
Question 8
3 / -1

Let f(x) = [x], then f′(1) = ?

A
1

B
0

C
Does not exist

D
None of these

Solution
Question 9
3 / -1

α and β lie between 0 and π/4, cos(α + β) = 12/13 and sin(α - β) = 3/5.

sin 2α =

A
-16/65

B
0

C
56/65

D
64/65

Solution
Question 10
3 / -1

If n(U) = 20, n(A) = 12, n(B) = 9, n(AB) = 4, where U is the universal set, A and B are subsets of U, then n | (A U B)^o| is equal to

A
17

B
9

C
11

D
3

Solution