Mathematics Test 220

Result

Mathematics Test 220

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
4 / -1

If x and y are two positive numbers such that x + y = a, then the minimum value of

A
1 + a⁻¹

B
1 − 2a−1

C
a − a⁻¹

D
1 + 2a⁻¹

Solution
Question 2
4 / -1

The negative of q∨ ~ (p ∧ r) is

A
~q ∧ ~ (p∧r)

B
~q ∧ (p ∧ r)

C
~q ∨ (p ∧ r)

D
None of these

Solution

As we know from De Morgan's law, that ~(p∨q) ≡ ~p∧~q

Therefore, ~(q∨ ~ (p ∧ r)) ≡ ~q ∧ (~(~(p ∧ r)))

Hence, ~(q ∨ ~(p ∧ r)) ≡ ~q ∧ (p ∧ r)
Question 3
4 / -1

For hyperbola which of the following remains constant with change in α?

A
Vertices

B
Foci

C
Eccentricity

D
Directrix

Solution
Question 4
4 / -1

The centre of a circle passing through the points (0,0),(1,0) and touching the circle x²+ y2 = 9 is

A

B

C

D

Solution

We have,

x² + y² = 9

Radius, OP = 3 units.

Hence, radius of required circle = 3/2 units.

Equation of required circle is

(x − h)²+ (y − k)²= 9/4 ...(i)

This is passing through (0,0) and (1,0), so

h²+ k² = 9/4 ...(ii)

(h − 1)²+ k² = 9/4 ...(iii)

Subtracting (ii) & (iii)ii & iii, we get

(h − 1)²= h²

⇒ 2h = 1

⇒ h = 12
Question 5
4 / -1

A
1/3

B
2/3

C

D

Solution
Question 6
4 / -1

Given then for non-zero values of x,f(x) equals

A

B

C
cos⁻¹(x)

D
None of these

Solution
Question 7
4 / -1

A is a set containing n elements, subset P of A is chosen. The set A is reconstructed by replacing the elements of P, subset Q of A is chosen. The number of ways of selecting P and Q so that P and Q are non intersecting, is

A
2ⁿ − 1

B
3ⁿ − 1

C
3ⁿ − 2

D
3ⁿ + 1

Solution

Let A = {a₁, a₂, a₃......a_n}P, Q are subsets of A elements in P, Q can be chosen in following ways

Case I: a_i ∈ P a_i ∈ Q i = 1,2,...n

Case II: a_i ∈ P a_i ∉ Q i = 1,2,....n

Case III: a_i ∉ P a_i ∈ Q i = 1,2,....n

Case IV: a_i ∉ P a_i ∉ Q i = 1,2,...n

∵ P, Q are non intersecting sets every element can be chosen as in case (II), case (III), case (IV) i.e. every elements can be chosen in 3 ways. Total number of ways

= 3 × 3.....n = times = 3ⁿ ways

But one case needs to be excluded when P = ϕ, Q = ϕ

∴ Number of ways = 3ⁿ − 1
Question 8
4 / -1

If 3a + 2b + 6c = 0, the family of straight lines ax + by + c = 0 passes through a fixed point whose coordinates are given by

A
(1/2 , 1/3)

B
(2, 3)

C
(3, 2)

D
(1/3 , 1/2)

Solution
Question 9
4 / -1

The equation of the common tangent to the equal parabolas y²= 4ax and x²= 4ay is

A
x + y + a = 0

B
x + y = a

C
x − y = a

D
None of these

Solution
Question 10
4 / -1

A dice is rolled three times, then the probability of getting a larger number than the previous number each time is

A
5/35

B
3/42

C
5/54

D
7/67

Solution

Exhaustive number of cases is 6³= 216.

Now if a larger number appears than the previous number each time, all the three numbers are distinct.

Now three numbers can be selected from six numbers in ⁶C₃ ways and there is only one way in which three selected numbers can appear.

Hence, probability is 20/216 = 5/54.