Mathematics Test

Result

Mathematics Test - 3

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

Let p(x) be a polynomial of degree
4 having extremum at x = 1, 2 and
$\lim_{x \to 0} (1 + \frac{p (x)}{x^{2}})$ = 2. Then

the value of p(2) is.

A

0

B

1

C

2

D

3
Question 2
1 / -0

The line passing through the extremity A of the major axis and extremity B of the minor axis of the ellipse x^2 + 9y^2 = 9 meets its auxiliary circle at the point M. Then the area of the triangle with vertices at A, M and the origin O is

A

27/10

B

29/10

C

21/10

D

31/10
Question 3
1 / -0

A

Option C

B

Option B

C

Option A

D

None of these
Question 4
1 / -0

A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses required. The conditional probability that X ≥ 6 given X > 3 equals

A

25/36

B

25/216

C

125/216

D

5/36
Question 5
1 / -0

Find the the statements/expressions of Ellipse

A

Points of the conic have parametric representation x = √3(1- t^2)/(1+ t^2), y = 2t/ (1 + t^2)

B

The eccentricity of the conic lies in the interval 1 ≤ x < ∞

C

Points z in the complex plane satisfying |z + 2| – |z – 2| = ± 3

D

Points z in the complex plane satisfying Re(z + 1)^2 = |z|^2 + 1
Question 6
1 / -0

Interval contained in the domain of definition of non-zero solutions of the differential equation (x – 3)^2 y′ + y = 0

A

(0, π/8)

B

(-π/2, π/2)

C

(0, π/2)

D

All of these
Question 7
1 / -0

A signal which can be green or red with probability 4/5 and 1/5 respectively, is received by station A and then transmitted to station B. The probability of each station receiving the signal correctly is 3/4. If the signal received at station B is green, then the probability that the original signal was green is

A

20/23

B

3/5

C

6/7

D

9/20
Question 8
1 / -0

If the sum of first n terms of an A.P. is $c n^{2}$ , then the sum of squares of these n terms is

A
$\frac{[n (4 n^{2} - 1) c^{2}]}{3}$

B
$\frac{[n (4 n^{2} - 1) c^{2}]}{6}$

C
$\frac{[n (4 n^{2} + 1) c^{2}]}{3}$

D
${\frac{n (4 n^{2} + 1) c}{6}}^{2}$

Solution

Given:

$S_{n} = c n^{2}$

$S_{n - 1} = c {(n - 1)}^{2} = c n^{2} + c - 2 c n$

$T_{n} = 2 c n - c$

$T n^{2} = {(2 c n - c)}^{2} = 4 c^{2} n^{2} + c^{2} - 4 c^{2} n$

Required sum

$= \sum T n^{2} = 4 c^{2} \sum n^{2} + n c^{2} - 4 c^{2} \sum n$

$= \frac{4 c^{2} n (n + 1) (2 n + 1) + n c^{2} - 2 c^{2} n (n + 1)}{6}$

$= \frac{2 c^{2} n (n + 1) (2 n + 1) + 3 n c^{2} - 6 c^{2} n (n + 1)}{3}$

$= \frac{n c^{2} [4 n^{2} + 6 n + 2 + 3 - 6 n - 6]}{3}$

$= \frac{n c^{2} (4 n^{2} - 1)}{3}$
Question 9
1 / -0

A

1/4

B

- 1/4

C

- 1/8

D

1/8
Question 10
1 / -0

A

1/3

B

1/e

C

1/2

D

1

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

Mathematics Test - 3

Result

Mathematics Test - 3

Score

-

Rank

-

SHARING IS CARING

Question 1

0

1

2

3

Question 2

27/10

29/10

21/10

31/10

Question 3

Option C

Option B

Option A

None of these

Question 4

25/36

25/216

125/216

5/36

Question 5

Points of the conic have parametric representation x = √3(1- t^2)/(1+ t^2), y = 2t/ (1 + t^2)

The eccentricity of the conic lies in the interval 1 ≤ x < ∞

Points z in the complex plane satisfying |z + 2| – |z – 2| = ± 3

Points z in the complex plane satisfying Re(z + 1)^2 = |z|^2 + 1

Question 6

(0, π/8)

(-π/2, π/2)

(0, π/2)

All of these

Question 7

20/23

3/5

6/7

9/20

Question 8

[n(4n2-1)c2]3

[n(4n2-1)c2]6

[n(4n2+1)c2]3

n(4n2+1)c62

Solution

Question 9

1/4

- 1/4

- 1/8

1/8

Question 10

1/3

1/e

1/2

1

User

Question Analysis

My Perfomance

Score

-

Rank

-

Results Announcement on: coming Monday

Stay Tuned: We’ll update you on your result via email or SMS.

$\frac{[n (4 n^{2} - 1) c^{2}]}{3}$

$\frac{[n (4 n^{2} - 1) c^{2}]}{6}$

$\frac{[n (4 n^{2} + 1) c^{2}]}{3}$

${\frac{n (4 n^{2} + 1) c}{6}}^{2}$