1
JEE Main 2014 (Offline)
MCQ (Single Correct Answer)
+4
-1
If $$a \in R$$ and the equation $$ - 3{\left( {x - \left[ x \right]} \right)^2} + 2\left( {x - \left[ x \right]} \right) + {a^2} = 0$$ (where [$$x$$] denotes the greater integer $$ \le x$$) has no integral solution, then all possible values of a lie in the interval :
A
$$\left( { - 2, - 1} \right)$$
B
$$\left( { - \infty , - 2} \right) \cup \left( {2,\infty } \right)$$
C
$$\left( { - 1,0} \right) \cup \left( {0,1} \right)$$
D
$$\left( {1,2} \right)$$
2
JEE Main 2014 (Offline)
MCQ (Single Correct Answer)
+4
-1
Let $$\alpha $$ and $$\beta $$ be the roots of equation $$p{x^2} + qx + r = 0,$$ $$p \ne 0.$$ If $$p,\,q,\,r$$ in A.P. and $${1 \over \alpha } + {1 \over \beta } = 4,$$ then the value of $$\left| {\alpha - \beta } \right|$$ is :
A
$${{\sqrt {34} } \over 9}$$
B
$${{2\sqrt 13 } \over 9}$$
C
$${{\sqrt {61} } \over 9}$$
D
$${{2\sqrt 17 } \over 9}$$
3
JEE Main 2014 (Offline)
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
If the coefficints of $${x^3}$$ and $${x^4}$$ in the expansion of $$\left( {1 + ax + b{x^2}} \right){\left( {1 - 2x} \right)^{18}}$$ in powers of $$x$$ are both zero, then $$\left( {a,\,b} \right)$$ is equal to:
A
$$\left( {14,{{272} \over 3}} \right)$$
B
$$\left( {16,{{272} \over 3}} \right)$$
C
$$\left( {16,{{251} \over 3}} \right)$$
D
$$\left( {14,{{251} \over 3}} \right)$$
4
JEE Main 2014 (Offline)
MCQ (Single Correct Answer)
+4
-1
Three positive numbers form an increasing G.P. If the middle term in this G.P. is doubled, the new numbers are in A.P. then the common ratio of the G.P. is :
A
$$2 - \sqrt 3 $$
B
$$2 + \sqrt 3 $$
C
$$\sqrt 2 + \sqrt 3 $$
D
$$3 + \sqrt 2 $$
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