Mathematics Test

Result

Mathematics Test - 7

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Weekly Quiz Competition

Question 1
1 / -0

A
x²(e^x²)

B
1/2x²(e^x² -1)

C
1/2e^x²(x²-1)

D
None of these

Solution
Question 2
1 / -0

A
e^sinx + C

B
e^sinx-cosx + C

C
e^sinx+cosx+ C

D
None of these

Solution
Question 3
1 / -0

A
log (x⁴ + 1) + C

B
1/4 log (x⁴ + 1) + C

C
- log (x⁴ + 1)

D
none of these

Solution
Question 4
1 / -0

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
Question 5
1 / -0

A
(2/3) sin^-1 (cos^3/2 x) + C

B
(3/2) sin^-1(cos^3/2 x) + C

C
(2/3) cos^-1 (cos^3/2 x) + C

D
None of these

Solution
Question 6
1 / -0

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
Question 7
1 / -0

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
1 / -0

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 9
1 / -0

Area of an equilateral triangle is √3 cm². The length of each side of the triangle is

A
1cm

B
2cm

C
3cm

D
None of these

Solution
Question 10
1 / -0

In a triangle, the lengths of the two larger sides are 10 cm and 9 cm respectively. If the angles of the triangle are in A.P, then the length of the third side (in cm) can be

A
(5 - √6) only

B
(5 + √6) only

C
(5 - √6) or (5 + √6)

D
Neither (5 - √6) nor (6 + √6)

Solution
Question 11
1 / -0

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 12
1 / -0

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 13
1 / -0

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 14
1 / -0

The order of a differential equation whose solution is y = a cos x + b sin x, where a and b are arbitrary constants, is

A
1

B
2

C
3

D
Cannot be determined

Solution

The order of differential equation = number of arbitrary constants = 2
Question 15
1 / -0

A
7

B
5

C
13

D
√57

Solution