Mathematics Test 101

Result

Mathematics Test 101

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Weekly Quiz Competition

Question 1
4 / -1

If A³ = 0 then I+A+A² equals :-

A
I–A

B
(I–A)^–1

C
(I+A)^–1

D
I

Solution

(I–A)^–1= I + A + A² + A³ + ---- ∞ = I + A + A²
Question 2
4 / -1

If x²+ y² + z² = 1, where x, y, z ε R² then greatest value of x²y³z⁴ is :-

A
2⁵/ 3^15/2

B
2¹⁰/ 3¹⁵

C
2¹⁰/ 3^9/2

D
2¹⁵/ 3⁹
Question 3
4 / -1

If p,q,r,s εR then equation :-

(x²+px+3q)(–x²+rx+q )(–x² + sx –2q)=0 has

A
6 real roots

B
at least two real roots

C
2 real and 4 imaginary roots

D
4 real & 2 imaginary roots

Solution

D₁ = p²–12q; D₂ = r² + 4q; D₃ = s²– 8q

Case I - If q<0 then D₁>0,D₃>0 and D₂ may or may not be +ve

Case II- If q > 0 then D₂>0 and D₁,D₃ may or may not be +ve

Case III- If q= 0 then D₁,D₂,D₃

so, given equation has at least two real roots
Question 4
4 / -1

The length of largest continuous interval in which function f (x) = 4x – tan2x is monotonic, is :

A
π/2

B
π/4

C
π/8

D
π/16