Mathematics Test 214

Result

Mathematics Test 214

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Weekly Quiz Competition

Question 1
4 / -1

A
1/4

B
1/7

C
1/5

D
1/6

Solution
Question 2
4 / -1

If a > 0 and discriminant of ax² + 2bx + c is -ve, then

A
+ve

B
(ac - b²)(ax² + 2bx + c)

C
-ve

D
0

Solution
Question 3
4 / -1

There were two women participating in a chess tournament. Every participant played two games with the other participants. The number of games that the men played between themselves proved to exceed by 66 as compared to the number of games that the men played with the women. Find the number of participants.

A
6

B
11

C
13

D
None of these

Solution

Let number of men be n

Number of games between males = 2(ⁿC₂)

Number of games between players of opposite sex = 2(n x 2) = 4n

By the given condition 2.ⁿC₂ - 4n = 66
Question 4
4 / -1

If p, q, r are positive and are in A.P, the roots of the quadratic equation px² + qx + r = 0 are real for

A

B

C
all p and r

D
no p and r

Solution
Question 5
4 / -1

Let f(x) and g(x) be differentiable functions for 0 ≤ x ≤ 1 such that f(0) = 2, g(0) = 0 and f(1) = 6. Let there exist a real number c in [0, 1] such that f'(c) = 2g'(c). Then, the value of g(1) must be

A
1

B
2

C
-2

D
-1

Solution
Question 6
4 / -1

The lines 2x - 3y = 5 and 3x - 4y = 7 are diameters of a circle having area as 154 sq. units. Then, the equation of the circle is

A
x² + y² + 2x - 2y = 47

B
x²+ y² - 2x + 2y = 47

C
x² + y² - 2x + 2y = 62

D
x² + y² + 2x - 2y = 62

Solution

Coordinate of centre is equal to intersection point of diameters, which is (1, -1).

πR² = 154, R2 = 49

∴ R = 7

∴ Required equation of circle,

(x - 1)² + (y + 1)² = 49

x²+ y² - 2x + 2y = 47
Question 7
4 / -1

One ticket is selected at random from 50 tickets numbered 00, 01, 02, ..., 49. Then, the probability that the sum of the digits on the selected ticket is 8, given that the product of these digits is zero, equals

A
1/7

B
5/14

C
1/50

D
1/14

Solution

Any number in the set, S = {00, 01, 02, ...., 49} is of the form ab, where a ∈ {0, 1, 2, 3, 4} and b ∈ {0, 1, 2, ..., 9}

For the product of digits to be zero, the numbers must be of the form either a0, which are 5 in number because a ∈ {0, 1, 2, 3, 4} or of the form 0b, which are 10 in number because b ∈ {0, 1, 2, ..., 9}.

The only number common to both = 00

Thus, the number of numbers in S, the product of which is zero = 10 + 5 - 1 = 14

Of these, the number whose sum of digits is 8 is just one i.e. 08.

The required probability = 1/14
Question 8
4 / -1

The inverse of the statement 'if the teacher is absent, then the students are happy' is

A
if the students are not happy, then the teacher is absent

B
if the students are not happy, then the teacher is not absent

C
if the teacher is not absent, then the students are not happy

D
if the teacher is absent, then the students are not happy

Solution

Apply basic rules of inverse.

If the teacher is not absent, then the students are not happy.
Question 9
4 / -1

In solving the following Linear Programming Problem, ''minimise f = 6x + 10y subject to x ≥ 6; y ≥ 2; 2x + y ≥ 10; x ≥ 0; y ≥ 0'', the redundant constraint(s) is/are:

A
x ≥ 6, y ≥ 2

B
2x + y ≥ 10, x ≥ 0, y ≥ 0

C
x ≥ 6

D
None of these

Solution

For x ≥ 6, y ≥ 2; 2x + y ≥ 2 × 6 + 2; hence, the constraint 2x + y ≥ 10 is automatically satisfied by every point of the graph of the inequalities x ≥ 6 and y ≥ 2. Also, the graph of x ≥ 6 and y ≥ 2 is a subset of the graph of the inequalities x ≥ 0 and y ≥ 0.
Question 10
4 / -1

The sides of a triangle are sinα,cosα and Then, the greatest angle of the triangle is

A
60°

B
90°

C
120°

D
150°

Solution