Mathematics Test

Result

Mathematics Test - 36

Score
-
out of -
Rank
-
out of -

TIME Taken - -

Weekly Quiz Competition

Question 1
3 / -1

Find the value of \(\int \frac{\sec ^{4}(x)}{\sqrt{\tan (x)}} d x\).

A
\(\frac{2}{5} \sqrt{\tan (x)}\left[5+\sec ^{2}(x)\right]\)

B
\(\frac{2}{5} \sqrt{\sec (x)}\left[5+\tan ^{2}(x)\right]\)

C
\(\frac{2}{5} \sqrt{\tan (x)}\left[6+\tan ^{2}(x)\right]\)

D
\(\frac{2}{5} \sqrt{\tan (x)}\left[5+\tan ^{2}(x)\right]\)

Solution

Add constant automatically

Given, \(\int \frac{\sec ^{4}(x)}{\sqrt{\tan (x)}} d x\)

\(=\int \frac{\sec ^{2}(x) \sec ^{2}(x)}{\sqrt{\tan (x)}} d x\)

\(=\int \frac{1+t^{2}}{\sqrt{t}} d t\)

\(=\int\left[\frac{i}{\sqrt{t}}+t^{\frac{3}{2}}\right] d t\)

\(=2 \sqrt{t}+\frac{2}{5} t^{\frac{5}{2}}\)

\(=\frac{2}{5} \sqrt{\tan (x)}\left[5+\tan ^{2}(x)\right]\)
Question 2
3 / -1

A
10!

B
¹⁰C₁₀

C
¹⁰C₁

D
10¹⁰

Solution
Question 3
3 / -1

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 4
3 / -1

A
log (x⁴ + 1) + C

B
1/4 log (x⁴ + 1) + C

C
- log (x⁴ + 1)

D
none of these

Solution
Question 5
3 / -1

If P(1, 0), Q(– 1, 0) and R(2, 0) are three given points, then the locus of point S, which satisfies the relation (SQ)² + (SR)² = 2(SP)², is (where SQ, SR and SP are line segments)

A
a straight line || to x-axis

B
a circle through the origin

C
a circle with centre at the origin

D
a straight line || to y-axis

Solution

Let the point be (h, k)

So, SQ² = (h + 1)² + k²

SR² = (h - 2)² + k²

SP² = (h - 1)² + k²

Substituting in the given equation and replacing the values of h and k by x and y, we get

x = - 3/2 (A straight line parallel to y-axis).
Question 6
3 / -1

A
e

B
e-1

C
3e/2

D
none of these

Solution
Question 7
3 / -1

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 8
3 / -1

A
1

B
2

C
5

D
7

Solution
Question 9
3 / -1

A
e

B
1/2e

C
2e

D
none of these

Solution
Question 10
3 / -1

The orthocenter of the triangle formed by the lines xy = 0 and x + y = 1 is

A
(1/2,1/2)

B
(1/3,1/3)

C
(0,0)

D
(1/4,1/4)

Solution

The triangle formed by the given lines is a right angle triangle right angled at (0, 0). Hence, it is the orthocenter.