Mathematics Test

Result

Mathematics Test - 7

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Score
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Rank

Time Taken: -

Question 1/15
1 / -0

Correct

Wrong

Skipped
A
x²(e^x²)

Correct

Wrong

Skipped
B
1/2x²(e^x² -1)

Correct

Wrong

Skipped
C
1/2e^x²(x²-1)

Correct

Wrong

Skipped
D
None of these

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Solutions
Question 2/15
1 / -0

Correct

Wrong

Skipped
A
e^sinx + C

Correct

Wrong

Skipped
B
e^sinx-cosx + C

Correct

Wrong

Skipped
C
e^sinx+cosx+ C

Correct

Wrong

Skipped
D
None of these

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Solutions
Question 3/15
1 / -0

Correct

Wrong

Skipped
A
log (x⁴ + 1) + C

Correct

Wrong

Skipped
B
1/4 log (x⁴ + 1) + C

Correct

Wrong

Skipped
C
- log (x⁴ + 1)

Correct

Wrong

Skipped
D
none of these

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Solutions
Question 4/15
1 / -0

Correct

Wrong

Skipped
A
f (x) /g' (x)

Correct

Wrong

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

Correct

Wrong

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

Correct

Wrong

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

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Solutions
Question 5/15
1 / -0

Correct

Wrong

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

Correct

Wrong

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

Correct

Wrong

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

Correct

Wrong

Skipped
D
None of these

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Solutions
Question 6/15
1 / -0

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

Correct

Wrong

Skipped
A
2.0

Correct

Wrong

Skipped
B
2.5

Correct

Wrong

Skipped
C
3.0

Correct

Wrong

Skipped
D
3.5

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Solutions
Question 7/15
1 / -0

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

Correct

Wrong

Skipped
A
25/13

Correct

Wrong

Skipped
B
60/13

Correct

Wrong

Skipped
C
65/12

Correct

Wrong

Skipped
D
144/13

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Solutions
Question 8/15
1 / -0

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

Correct

Wrong

Skipped
A
AP

Correct

Wrong

Skipped
B
GP

Correct

Wrong

Skipped
C
HP

Correct

Wrong

Skipped
D
None of these

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Solutions
Question 9/15
1 / -0

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

Correct

Wrong

Skipped
A
1cm

Correct

Wrong

Skipped
B
2cm

Correct

Wrong

Skipped
C
3cm

Correct

Wrong

Skipped
D
None of these

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Solutions
Question 10/15
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

Correct

Wrong

Skipped
A
(5 - √6) only

Correct

Wrong

Skipped
B
(5 + √6) only

Correct

Wrong

Skipped
C
(5 - √6) or (5 + √6)

Correct

Wrong

Skipped
D
Neither (5 - √6) nor (6 + √6)

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Solutions
Question 11/15
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

Correct

Wrong

Skipped
A
5, 12, 13

Correct

Wrong

Skipped
B
10, 24, 26

Correct

Wrong

Skipped
C
15, 36, 39

Correct

Wrong

Skipped
D
20, 48, 52

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Solutions

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 12/15
1 / -0

Correct

Wrong

Skipped
A
2,6

Correct

Wrong

Skipped
B
6,2

Correct

Wrong

Skipped
C
2,2

Correct

Wrong

Skipped
D
2,3

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Solutions

Square the differential equation to remove the fraction,

We get, order = degree = 2
Question 13/15
1 / -0

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

Correct

Wrong

Skipped
A
2

Correct

Wrong

Skipped
B
3

Correct

Wrong

Skipped
C
2³

Correct

Wrong

Skipped
D
1

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Solutions

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 14/15
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

Correct

Wrong

Skipped
A
1

Correct

Wrong

Skipped
B
2

Correct

Wrong

Skipped
C
3

Correct

Wrong

Skipped
D
Cannot be determined

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Solutions

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

Correct

Wrong

Skipped
A
7

Correct

Wrong

Skipped
B
5

Correct

Wrong

Skipped
C
13

Correct

Wrong

Skipped
D
√57

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Solutions

Question 1/15

x2(ex2)

1/2x2(ex2 -1)

1/2ex2(x2-1)

None of these

Question 2/15

esinx + C

esinx-cosx + C

esinx+cosx + C

None of these

Question 3/15

log (x4 + 1) + C

1/4 log (x4 + 1) + C

- log (x4 + 1)

none of these

Question 4/15

f (x) /g' (x)

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

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

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

Question 5/15

(2/3) sin-1 (cos3/2 x) + C

(3/2) sin-1(cos3/2 x) + C

(2/3) cos-1 (cos3/2 x) + C

None of these

Question 6/15

2.0

2.5

3.0

3.5

Question 7/15

25/13

60/13

65/12

144/13

Question 8/15

AP

GP

HP

None of these

Question 9/15

1cm

2cm

3cm

None of these

Question 10/15

(5 - √6) only

(5 + √6) only

(5 - √6) or (5 + √6)

Neither (5 - √6) nor (6 + √6)

Question 11/15

5, 12, 13

10, 24, 26

15, 36, 39

20, 48, 52

Question 12/15

2,6

6,2

2,2

2,3

Question 13/15

2

3

23

1

Question 14/15

1

2

3

Cannot be determined

Question 15/15

7

5

13

√57

x²(e^x²)

1/2x²(e^x² -1)

1/2e^x²(x²-1)

e^sinx + C

e^sinx-cosx + C

e^sinx+cosx+ C

log (x⁴ + 1) + C

1/4 log (x⁴ + 1) + C

- log (x⁴ + 1)

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

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

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

2³