Mathematics Test 202

Result

Mathematics Test 202

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Weekly Quiz Competition

Question 1
4 / -1

A

B

C

D
Question 2
4 / -1

If 60^a = 3 and 60^b = 5 then the value of equals

A
2

B
3

C
√3

D

Solution
Question 3
4 / -1

The set of values of x satisfying the inequality

A
(- 3, - 2)

B
(- 3, - 2) ∪ (- 1, ∞)

C
(- 1, ∞)

D
none

Solution

Domain is (- 3, – 2) ∪ (- 1, ∞) ; for x > - 1, LHS is negative & RHS is positive and for - 3 < x < - 2 it is the other way
⇒ x > - 1 is the final answer
Question 4
4 / -1

Given that x + sin y = 2008 and x + 2008 cos y = 2007 where 0 ≤ y ≤ π/2. The value of [x + y], is. (Here [x] denotes greatest integer function)

A
2007

B
2008

C
2009

D
2010

Solution
Question 5
4 / -1

Let p be the statement ' Ram races' and q be the statement 'Ram wins'. Then ~ (p v (~ q)) is

A
Ram does not race and Ram does not win.

B
It is true that Ram races or Ram does not win.

C
Ram does not race and Ram wins.

D
It is not true that Ram races and Ram does not win.

Solution

Given

p : Ram races

q : Ram wins

∴ The statement of given proposition ~ (p v (~ q)) = ~ p ∧ q is "Ram does not race and Ram wins."
Question 6
4 / -1

A vertical pole PS has two marks at Q and R such that portions PQ, PR and PS subtend angles α, β, γ respectively at a point on the ground which is at distance x from the bottom of pole P. If PQ = a, PR = b, PS = c and α + β + γ = 180º, then x² is equal to

A

B

C

D

Solution
Question 7
4 / -1

Then the number of subsets of set A×(A ∩ B) which contains exactly 3 elements is

A
26

B
220

C
280

D
144

Solution

A = {1, 2, 3, 4, 5, 6} ⇒ n(A) = 6

B = {1, 2} ⇒ n(B) = 2

∴ A ∩ B = {1, 2} ⇒ n(A ∩ B) = 2

So, number of elements in A× (A ∩ B) = 12

∴ Number of subsets containing 3 elements = ¹²C₃ = 220
Question 8
4 / -1

The relation P defined from R to R as a P b ⇔ 1+ ab > 0, for all a,b ∈ R is

A
reflexive only

B
reflexive and symmetric only

C
transitive only

D
equivalence
Question 9
4 / -1

If x₁, x₂ & x₃ are the three real solutions of the equation

where x₁ > x₂ > x₃ , then

A
x₁ + x₃ = 2 x₂

B
x₁ . x₃ = x₂²

C

D
x₁^-1 + x₂^-1 = x₃^-1

Solution
Question 10
4 / -1

The variance of 20 observations is 5. If each observation is multiplied by 2 then the new variance of the resulting observations, is

A
5

B
10

C
20

D
40

Solution