Mathematics Test

Result

Mathematics Test - 12

Score
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Rank
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TIME Taken - -

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Weekly Quiz Competition

Question 1
1 / -0

If ⁿP_r= 1680 and ⁿC_r = 70, then 69 n + r! is equal to-

A
128

B
256

C
576

D
625

Solution
Question 2
1 / -0

If for a ΔABC, cot A⋅cot B⋅cot C>0 then the triangle is-

A
Right angled

B
Acute angled

C
Obtuse angled

D
All these options are possible

Solution

cot A⋅cot B⋅cot C>0⇒cot A>0, cot B>0, cot C > 0

Because two or more of cot A, cot B, cot C cannot be negative at the same time in a triangle, as no two angle could be more then 90 degree.
Question 3
1 / -0

The vertices of a triangle are A(x₁, x₁tan α), B (x₂, x₂tan β) and C(x₃, x₃ tan γ) . If the circumcentre of ΔABC coincides with the origin and H (a,b) be its orthocentre, then a/b is equal to: (Here α, β and γ are acute angles)-

A

B

C

D

Solution
Question 4
1 / -0

The number of real values of k for which the lines are intersecting, is-

A
0

B
2

C
1

D
Infinite

Solution
Question 5
1 / -0

If a³ + b⁶ = 2, then the maximum value of the term independent of x in the expansion of

A
42

B
68

C
148

D
84

Solution
Question 6
1 / -0

A
4

B
6

C
2

D
1

Solution
Question 7
1 / -0

Let PQ and RS be tangents at the extremities of the diameter PR of a circle of radius r. If PS and RQ intersect at a point X on the circumference of the circle, then 2r is equal to-

A
√PQ.RS

B

C

D

Solution
Question 8
1 / -0

If ln(x + y) = 2xy, theny′ (0) is equal to-

A
1

B
-1

C
2

D
0

Solution
Question 9
1 / -0

If the tangent and the normal to x²- y²= 4 at a point cut off intercepts a1, a2on the x-axis respectively and b₁, b₂on the y-axis respectively then the value of a₁a₂+ b₁b₂ is-

A
1

B
-1

C
0

D
4

Solution
Question 10
1 / -0

Two vertices of a triangle are (3, -2) and (-2, 3) and its orthocentre is (- 6, 1). The coordinates of its third vertex are-

A
(1, 6)

B
(-1, 6)

C
(1, -6)

D
None of these

Solution