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Aspirant Academy

Sample questions

1Let H be a subgroup of a finite group G with |G|=84 and |H|=12. What is the number of left cosets of H in G?

A 84
B 7
C 6
D 12

2The area bounded by the curve xy = 1, y = x, x = e and y = 0 is divided by the line x = 1 in the ratio

A 3 : 1
B 1 : 2
C 3 : 2
D 1 : 4

3If √(7√(7√(7√(7√7)))) = 7ˣ, then value of x is –

A 1/32
B 31/32
C 15/16
D 32/31

4The sequence ∑ 1/(nᵖ+nqx²), ∀x ∈ R is uniformly convergent, if -

A p<1
B p>1
C p=0
D p = 1/2

5The polar curves r = a sin theta and r = a cos theta intersect away from the pole. What is the angle of intersection at that point?

A pi/2
B pi/4
C pi/6
D pi/3

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