Mathematics Test

Result

Mathematics Test - 35

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Weekly Quiz Competition

Question 1
3 / -1

A
Invertible

B
Injective but not surjective.

C
Surjective but not injective

D
Neither injective nor surjective.

Solution
Question 2
3 / -1

In ΔABC, if tan A/2 tan C/2 = 1/2, then a, b, c are in

A
AP

B
GP

C
HP

D
None of these

Solution
Question 3
3 / -1

A
1/3

B
2

C
1/2

D
3/2

Solution
Question 4
3 / -1

A
2,6

B
6,2

C
2,2

D
2,3

Solution

Square the differential equation to remove the fraction,

We get, order = degree = 2
Question 5
3 / -1

If \(\log _{10} 5+\log _{10}(5 x+1)=\log _{10}(x+5)+1\), then \(x\) is equal to-

A
\(1\)

B
\(3\)

C
\(5\)

D
\(10\)

Solution

Given-

\(\Rightarrow \log _{10} 5+\log _{10}(5 x+1)=\log _{10}(x+5)+1\)
\(\Rightarrow \log _{10}[5(5 x+1)]=\log _{10}[10(x+5)]\)
\(\Rightarrow 5(5 x+1)=10(x+5)\)
\(\Rightarrow 5 x+1=2 x+10\)
\(\Rightarrow 3 x=9\)
\(\Rightarrow x=3\)
Question 6
3 / -1

If the sum of odd coefficients of (1+z)⁵ is x, find the number of solutions of a+b+c+d=x where -x

A
³⁴C₃

B
³³C₃

C
³⁵C₃

D
³⁶C₄

Solution
Question 7
3 / -1

In a ΔABC, a = 13 cm, b = 12 cm and c = 5 cm. The distance of A from BC is

A
25/13

B
60/13

C
65/12

D
144/13

Solution
Question 8
3 / -1

The lengths of sides of a triangle are in the ratio 5 : 12 : 13 and its area is 270 cm². The respective lengths of sides of the triangle (in cm) are

A
5, 12, 13

B
10, 24, 26

C
15, 36, 39

D
20, 48, 52

Solution

Let the lengths of sides of the triangle be 5x, 12x, 13x; Obviously, the triangle is right-angled.

Hence, area of the Δ = ½ (12x) (5x) ⇒ 30x² = 270 ⇒ x = 3

Hence, the lengths of sides (in cm) are 15, 36 and 39.
Question 9
3 / -1

If f(x) = x^a + a^x and g(x) = x^a – a^x, find the value of f(x) + g(x).

A
2x^a

B
5x^a

C
(x^a)²

D
x^a

Solution

f(x) + g(x) = 2x^a
Question 10
3 / -1

If the lengths of the sides of a triangle are 3, 4, 5 units, then R (the circum-radius) is equal to

A
2.0

B
2.5

C
3.0

D
3.5

Solution