Mathematics Test 112

Result

Mathematics Test 112

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
4 / -1

If the line ℓx + my + n = 0 is tangent to the circle x² + y² – 2ax = 0, then

A
n² + 2aℓn – a²m² = 0

B
n² + 2aℓn + a²m² = 0

C
n² – 2aℓn + a²m² = 0

D
a²m² + 2aℓn – n² = 0

Solution

A line will be tangent to a circle, if length of perpendicular drawn from centre (a, 0) upon the line ℓx + my + n = 90 is equal to radius = a
Question 2
4 / -1

is equal to

A
A + 2π – π²

B
A – 2π + π²

C
2π – A – π²

D
None of these

Solution
Question 3
4 / -1

then the value of (1/k) is equal to -

(Where C is constant of integration)

A
2010

B
2011

C
2012

D
2013

Solution
Question 4
4 / -1

If a,b,c are unequal real numbers in G.P. and 'a' is their harmonic mean then

(where [.] denotes greatest integer function)

A
7

B
11

C
3

D
None of these

Solution
Question 5
4 / -1

Let (k + ce^x2/2) sin y = 1be the solution of x siny tany dx = x tany dx + dy, then k is equal to -

A
0

B
1

C
2

D
3

Solution
Question 6
4 / -1

One of the possible equation of the chord of x² + y² = 100 that passes through (1,7) and subtends an angle 2π/3 at the origin, is -

A
3y + 4x – 25 = 0

B
x + y – 8 = 0

C
3x + 4y – 31 = 0

D
4x – 3y + 17 = 0

Solution
Question 7
4 / -1

A plane 2x + 3y + 5z = 1 has point P which is at minimum distance from the line segment joining A(1, 0, –3) and B(1, –5, 7), then distance AP is equal to -

A
3√5

B
2√5

C
4√5

D
none of these

Solution
Question 8
4 / -1

The angle of intersection between the curves dt and x-axis is (where x ≠ 0) -

A
tan^-1 1/2

B
cot^-1 2

C
cot^-1 1/2

D
sin^-1 (1/√5)

Solution
Question 9
4 / -1

Let y = g(x) be the inverse of a bijective mapping f : R → R, f(x) = 3x³ + 2x. The area bounded by graph of g(x), the x-axis and the ordinate at x = 5 is -

A
5/4

B
7/4

C
9/4

D
13/4

Solution
Question 10
4 / -1

A 12 digit number starts with 2 and all its digits are prime, then the probability that the sum of any two consecutive digits of the number is prime is 1/2^k, where k is equal to -

A
18

B
16

C
14

D
12

Solution

The prime digits are 2, 3, 5, 7.

If we fix 2 at first place, then other eleven places are filled by all four digits.

So, total number of ways = 4¹¹.

Now sum of 2 consecutive digits is prime when consecutive digits are (2,3) or (2, 5), then 2 will be fixed at all alternate places.