Mathematics Test 104

Result

Mathematics Test 104

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Weekly Quiz Competition

Question 1
4 / -1

The area bounded by the curves y² = x and x² = –y is equal to

A
1/3

B
2/3

C
3/4

D
5/3

Solution
Question 2
4 / -1

Solution of the differential equation,

A
log_e|xy| = sin^–1x + C

B
log_e|xy| = 2sin^–1x + C

C
log_e|(x + y)| = sin^–1x + C

D
log_e|(x + y)| = 2sin^–1x + C

Solution

Integrate both sides we get

log_exy = sin^–1x + C
Question 3
4 / -1

Conic represented by x = 4(cost – sint) and y = 5(cost + sint) is (where t is the parameter)

A
Circle

B
Ellipse

C
Parabola

D
Hyperbola

Solution
Question 4
4 / -1

Consider pair of straight lines

ax² + 3xy – 2y² – 5x + 5y + c = 0 representing perpendicular lines. Value of |a + c| equals

A
1

B
2

C
3

D
4

Solution

If the two lines are perpendicular then a = 2

D = 0 ⇒ c = –3

(D = abc + 2fgh – af² – bg² – ch²)
Question 5
4 / -1

All the words formed by writing all the letters of word ZENITH are arranged as in English dictionary. Now the position of word ZENITH is (from beginning)

A
598

B
602

C
532

D
616

Solution

EHINTZ

words starting with E is 5!

words starting with H is 5!

words starting with I is 5!

words starting with N is 5!

words starting with T is 5
Question 6
4 / -1

The relation R = {(1,1), (2,2), (3,3), (1,2), (2,1),(2,3),(3,2)} is defined on set A = {n : 3ⁿ > 4^n–1, n ∈ N}. Relation R is

A
reflexive relation

B
symmetric relation

C
transitive relation

D
equivalence relation

Solution

A = {1,2,3,4}. As (4,4) ∉ R so not reflexive

Also not transitive
Question 7
4 / -1

then n(S) equals (where n(A) denotes number of elements in set A)

A
2

B
3

C
4

D
5

Solution
Question 8
4 / -1

from point P measured along a line inclined at an angle 45° with the line L and is minimum, then value of PQ equals

A
3

B
4

C
5

D
6

Solution
Question 9
4 / -1

and f(0) = 1 then value of f(π/2) equals

A
√3e

B
√3e / 2

C
3e / 2

D
3e

Solution
Question 10
4 / -1

Let A(z₁), B(z₂) and C(z₃) lie on the circle |z – i| = 1 and satisfy the equation 3z₁ + i = 2z₂ + 2z₃. If D is the centre of the circle |z – i| = 1, then area of quadrilateral ABCD equals :-

A
√3 / 4

B
√5 / 4

C
√11 / 4

D
√7 / 4

Solution