Mathematics Test

Result

Mathematics Test - 33

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Weekly Quiz Competition

Question 1
3 / -1

The diagonals of a parallelogram PQRS are along the lines x + 3y = 4 and 6x - 2y = 7. Then PQRS must be a

A
rectangle

B
square

C
cyclic quadrilateral

D
rhombus

Solution

The slope of the first line: - 1/3
Slope of second line is: 3
Hence the diagonals are perpendicular, which is the property of a Rhombus.
Question 2
3 / -1

A
2[√x sin √x + cos √x] + C

B
[√ x sin √x - cos √x] + C

C
2[√x sin √x - cos √x] + C

D
None of these

Solution
Question 3
3 / -1

Find the period of the given function:
f(x) = tan(x/3) + sin(2x)

A
π/2

B
π

C
3π

D
3π/2

Solution

Given, f(x) = tan(x/3) + sin(2x).
Here, tan(x/3) is periodic with period 3π and sin2x is periodic with period π.
Hence, f(x) will be periodic with period 3π.
Question 4
3 / -1

A
7

B
5

C
13

D
√57

Solution
Question 5
3 / -1

In a triangle XYZ, tan X = 2 and tan Y = 4. Then, what is the value of tan Z?

A
$\frac{6}{7}$

B
$\frac{6}{5}$

C
$\frac{5}{6}$

D
$\frac{7}{6}$

Solution

Given,
tan X = 2; tan Y = 4, tan Z =?
As we know that,
If XYZ is triangle, then, X + Y + Z = 180°
Then, tan X + tan Y + tan Z = tan X tan Y tan Z
So,
2 + 4 + tan Z = 2 × 4 × tan Z
⇒ 6 + tan Z = 8tanZ
⇒ 7tan Z = 6
⇒ tan Z = $\frac{6}{7}$
Question 6
3 / -1

A
x²(e^x²)

B
1/2x²(e^x² -1)

C
1/2e^x²(x²-1)

D
None of these

Solution
Question 7
3 / -1

The number of arbitrary constants in the solution of a differential equation of degree 2 and order 3 is

A
2

B
3

C
2³

D
1

Solution

Note: The number of arbitrary constants in a solution of a differential equation of order n is equal to its order.
Order of differential equation = Number of arbitrary constants = 3
Question 8
3 / -1

If the vertices P, Q, R of a triangle PQR are rational points, then which of the following points of the triangle PQR is not always a rational point?

A
Centroid

B
Incentre

C
Circumcentre

D
Orthocentre

Solution

Incentre of is notΔPQR always a rational point.
Question 9
3 / -1

The number of values of k for which the system of equations (k + 1) x + 8y = 4k and
kx + (k + 3)y = 3k - 1 has infinitely many solutions is

A
0

B
1

C
2

D
infinite

Solution
Question 10
3 / -1

A
f (x) /g' (x)

B
f' (x) g (x) -f (x) g' (x)

C
f (x) g' (x) - f' (x) g (x)

D
f (x) g (x) + f (x) g (x)

Solution