1
JEE Main 2017 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
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)
MCQ (Single Correct Answer)
+4
-1
Change Language
A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in this party, is:
A
468
B
469
C
484
D
485
3
JEE Main 2017 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
If for a positive integer n, the quadratic equation

$$x\left( {x + 1} \right) + \left( {x + 1} \right)\left( {x + 2} \right)$$$$ + .... + \left( {x + \overline {n - 1} } \right)\left( {x + n} \right)$$$$ = 10n$$

has two consecutive integral solutions, then n is equal to :
A
9
B
10
C
11
D
12
4
JEE Main 2017 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
If S is the set of distinct values of 'b' for which the following system of linear equations

x + y + z = 1
x + ay + z = 1
ax + by + z = 0

has no solution, then S is :
A
an empty set
B
an infinite set
C
a finite set containing two or more elements
D
a singleton
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