1
JEE Main 2017 (Offline)
+4
-1
Let $$a$$, b, c $$\in R$$. If $$f$$(x) = ax2 + bx + c is such that
$$a$$ + b + c = 3 and $$f$$(x + y) = $$f$$(x) + $$f$$(y) + xy, $$\forall x,y \in R,$$

then $$\sum\limits_{n = 1}^{10} {f(n)}$$ is equal to
A
165
B
190
C
255
D
330
2
JEE Main 2017 (Offline)
+4
-1
For any three positive real numbers a, b and c,

9(25$${a^2}$$ + b2) + 25(c2 - 3$$a$$c) = 15b(3$$a$$ + c).
Then
A
b, c and $$a$$ are in G.P.
B
b, c and $$a$$ are in A.P.
C
$$a$$, b and c are in A.P.
D
$$a$$, b and c are in G.P.
3
JEE Main 2016 (Online) 10th April Morning Slot
+4
-1
Let z = 1 + ai be a complex number, a > 0, such that z3 is a real number.

Then the sum 1 + z + z2 + . . . . .+ z11 is equal to :
A
$$- 1250\,\sqrt 3 \,i$$
B
$$1250\,\sqrt 3 \,i$$
C
$$1365\,\sqrt 3 i$$
D
$$-$$ $$1365\,\sqrt 3 i$$
4
JEE Main 2016 (Online) 10th April Morning Slot
+4
-1
Let a1, a2, a3, . . . . . . . , an, . . . . . be in A.P.

If a3 + a7 + a11 + a15 = 72,

then the sum of its first 17 terms is equal to :
A
306
B
153
C
612
D
204
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