Mathematics Test 121

Result

Mathematics Test 121

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 x & y are solutions of equation, 3cosx + 4sinx = 2y² – 4y + 7, then which of the following is true :-

A
tan (2xy) = 3/4

B
cot (2xy) = 3/4

C
tan (xy) = 3/4

D
cot (xy) = 3/4

Solution

3cosx + 4sinx = 2(y – 1)² + 5

maximum value of 3cosx + 4sinx = 5

So it will be true when y = 1

tanx = 4/3

Hence tan(xy) = tan x = 4/3 ⇒ cot x =3/4 = cot xy
Question 2
4 / -1

If in a triangle ABC; sinA, sinB & sinC are in A.P. (C > 90°), then cosA is -

A
3c -4b / 2b

B
3c -4b / 2c

C
4c -3b / 2b

D
4c -3b / 2c

Solution
Question 3
4 / -1

A
In 4

B
In 2

C
(In 2)²

D
1

Solution
Question 4
4 / -1

Let ƒ (x) then ƒ(x) is continuous at :-

A
only one point

B
only two points

C
only three points

D
infinite number of points

Solution

ƒ (x) is continuous at those points where

x³ + 3x² + 6x – 4 = 4x² + 11x – 1

x³ – x² – 5x – 3 = 0

(x – 3)(x + 1)² = 0

x = –1 & 3
Question 5
4 / -1

then f '(0) is

A
equal to – 1

B
equal to 0

C
equal to 1

D
non existent

Solution
Question 6
4 / -1

is differentiable for all x ∈ R, then the value of |λ – μ| is -

A
4

B
6

C
2

D
0

Solution
Question 7
4 / -1

Consider the function then choose correct option(s)

A
ƒƒ(1^–) = 1

B
ƒƒ(2^–) = 0

C
ƒƒ(2⁺) = 4

D
All are correct

Solution

ƒƒ(1^–) = ƒ(0⁺) = 1

ƒƒ(1⁺) = ƒ(3⁺) = 1

ƒƒ(2^–) = ƒ(4^–) = 0

ƒƒ(2⁺) = ƒ(2^–) = 4
Question 8
4 / -1

If f is continuous for all x ∈ R then

A
number of integers in the range of k are 5

B
there are atleast 3 rational values of k

C
the difference between the largest and smallest integral value of k is 3

D
option 2 and option 3 are correct

Solution

x² + kx + k ≥ 0 ∀ x ∈ R

D ≤ 0 ⇒ k ∈ [0, 4] ...(1)

Also, x² + k ≠ 0 ∀ x ∈ R ...(2)

(1) ∩ (2)

k ∈ (0, 4]
Question 9
4 / -1

If y = then dy/dx =

A
2 ln x .

B
(2 ln x + 1). + 1

C
+ 1. ln ex²

D
option 2 and option 3 are correct

Solution
Question 10
4 / -1

In a triangle ABC if

A
a² + b² = c²

B
angles are in A.P.

C

D
All are correct

Solution