Mathematics Test 166

Result

Mathematics Test 166

Score
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Weekly Quiz Competition

Question 1
4 / -1

If x – 2y + 4 = 0 is a common tangent to y² = 4x and = 1, then the equation of other common tangent is :-

A
x + 2y + 4 = 0

B
x + 2y – 4 = 0

C
2x + y + 4 = 0

D
2x – y + 8 = 0

Solution

Equation of tangent to the parabola y² = 4x, at Q(4,–4) is :-

⇒ – 4y = 2 (x + 4)
Question 2
4 / -1

The vertex of a parabola is at (4, 3) and directrix is x – y + 1 = 0. Then the equation of its latus rectum is :-

A
x – y = 2

B
x – y = 3

C
x – y = 1

D
x + y = 2

Solution
Question 3
4 / -1

Water is dropped at the rate of 2 cm³/sec into a cone of semivertical angle 45°. The rate at which periphery of water surface changes when height of the water in the cone is 2 cm, is :-

A
1 cm/sec

B
2 cm/sec

C
3 cm/sec

D
4 cm/sec

Solution
Question 4
4 / -1

The eccentricity of locus of z satisfying | z – 5 | – | z + 5 | = ± 6, is :- (where z is complex number)

A
5/4

B
5/3

C
4/3

D
2

Solution
Question 5
4 / -1

The dual of statement (p ∨ ~ q) ∧ (~ p), is :-

A
(p ∨ ~ q) ∧ (~ p)

B
(p ∧ ~ q) ∧ (~ p)

C
(p ∨ ~ q) ∨ (~ p)

D
(p ∧ ~ q) ∨ (~ p)

Solution

In dual statement ∨ replace by ∧ and ∧ replace by ∨

so answer is (p ∧ ~ q) ∨ (~ p)
Question 6
4 / -1

The number of ways in which A A B B C C can placed in squares of given figure so that no row remains empty are :-

A
2430

B
1620

C
810

D
7290

Solution
Question 7
4 / -1

A
1

B
2

C
3

D
Does not exists

Solution
Question 8
4 / -1

(where c is constant of integration)

A

B

C

D

Solution
Question 9
4 / -1

The average salary of male employees in a firm was Rs. 520 and that of females was Rs. 420. the mean salary of all the employees was Rs. 500. The percentage of male employees is

A
80

B
60

C
40

D
20

Solution
Question 10
4 / -1

Let y = f(3x), where x takes all values only in [–1, 1] and y takes all values only in [–3, 5] then domain and range of g (x) = 2 + 3f (2x + 1) are [a, b] and [c, d] respectively, then the value of (a + b + c + d) is equal to

A
7

B
8

C
9

D
10

Solution