Mathematics Test 33

Result

Mathematics Test 33

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Weekly Quiz Competition

Question 1
4 / -1

The number of right angled triangles having integral sides and hypotenuse 65 unit is

A
Three

B
Two

C
Four

D
Six

Solution

The hypotenuse is given by k(a²+b²)

Case I. If k = 1
a² + b² = 65 a = 8, b = 1
a = 7, b = 4 (2 triangles)

Case II: If k = 5, a² + b² = 13; a = 3, b = 2 (one triangle)

Case III: If k = 13, a² + b² = 5 ; a = 2, b = 1 (one triangle)
four right angled triangles (integral sides) are possible.
Question 2
4 / -1

Consider the following statements:
(a) Mode can be computed from histogram
(b) Median is not independent of change of scale
(c) Variance is independent of change of origin and scale.
Which of these is/are correct?

A
only (a)

B
only (b)

C
only (a) and (b)

D
(a), (b) and (c)

Solution

Mode can be computed from histogram and median is dependent on the scale.
Hence statement (a) and (b) are correct.
Question 3
4 / -1

If the roots of the equation bx² + cx + a = 0 be imaginary, then for all real values of x, the expression 3b²x² + 6bcx + 2c² is

A
greater than 4ab

B
less than 4ab

C
greater than –4ab

D
less than –4ab

Solution

As, bx² + cx + a = 0 has imaginary roots
So, c² < 4ab
Now, 3b² x² + 6bcx + 2c²
= 3(bx + c)² – c² ≥ – c² ≥ – 4ab
Hence, option C is correct.