Mathematics Test 103

Result

Mathematics Test 103

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Weekly Quiz Competition

Question 1
4 / -1

If the coefficient of x²¹ in the expansion of is 3640, then the value of 'λ' equals

A
4/3

B
2/3

C
1/3

D
5/3

Solution
Question 2
4 / -1

A
π /2

B
π / 8

C
π

D
π / 4

Solution
Question 3
4 / -1

Number of integers in the domain of the function, ƒ(x) =

A
1

B
4

C
2

D
3

Solution

3 – 2^x – 2^{1 – x} ≥ 0 put 2^x = t

3 – t – 2/t ≥ 0 ⇒ t² – 3t + 2 ≤ 0

(t – 1) (t – 2) ≤ 0 ⇒ t ∈ [1, 2]

x ∈ [0, 1]
Question 4
4 / -1

If one of the root of the quadratic equation λx² + λx + (λ + 1) = 0 is less than 1 and other is greater than 1, then complete range of values of λ is given by (where λ ∈ R)

A
λ ∈ (- 1/4, 0)

B
λ ∈ (0, 1/4 )

C
λ ∈ (- 1/3, 0)

D
λ ∈ (0, 1/3 )

Solution
Question 5
4 / -1

The sum of infinite terms of the series,

A
4

B
6

C
2

D
3

Solution
Question 6
4 / -1

Let x² + y² – 4x – 2y – 11 = 0 be a circle. A pair of tangents from point P(4, 5) with a pair of radii form a quadrilateral of area

A
4

B
8

C
16

D
12

Solution
Question 7
4 / -1

is differentiable everywhere and k = a + b, then value of k is

A
-1

B
2

C
0

D
1

Solution
Question 8
4 / -1

The negation of the statement "If a quadrilateral is a square then it is a rhombus".

A
If a quadrilateral is not a square then it is a rhombus.

B
If a quadrilateral is a square then it is not a rhombus.

C
A quadrilateral is a square and it is not a rhombus.

D
A quadrilateral is not a square and it is a rhombus.

Solution

~(p → q) = p ∧ ~q

A quadrilateral is a square and it is not a rhombus.
Question 9
4 / -1

The variance of the data 2001, 2003, 2006, 2007, 2009, 2010 is

A
7

B
10

C
9

D
8

Solution
Question 10
4 / -1

A
2

B
6

C
8

D
4

Solution