1

IIT-JEE 2007

MCQ (Single Correct Answer)
Let $$\,{V_r}$$ denote the sum of first r terms of an arithmetic progression (A.P.) whose first term is r and the common difference is (2r-1). Let $${T_r} = \,{V_{r + 1}} - \,{V_r} - 2\,\,\,and\,\,\,{Q_r} = \,{T_{r + 1}} - \,{T_r}\,for\,r = 1,2,...$$

The sum $${V_1}$$+$${V_2}$$ +...+$${V_n}$$ is

A
$${1 \over {12}}n(n + 1)\,(3{n^2} - n + 1)$$
B
$${1 \over {12}}n(n + 1)\,(3{n^2} + n + 2)$$
C
$${1 \over 2}n(2{n^2} - n + 1)$$
D
$${1 \over 3}(2{n^3} - 2n + 3)$$
2

IIT-JEE 2005 Screening

MCQ (Single Correct Answer)
In the quadratic equation $$\,\,a{x^2} + bx + c = 0,$$ $$\Delta $$ $$ = {b^2} - 4ac$$ and $$\alpha + \beta ,\,{\alpha ^2} + {\beta ^2},\,{\alpha ^3} + {\beta ^3},$$ are in G.P. where $$\alpha ,\beta $$ are the root of $$\,\,a{x^2} + bx + c = 0,$$ then
A
$$\Delta \ne 0$$
B
$$b\Delta = 0$$
C
$$c\Delta = 0$$
D
$$\Delta = 0$$
3

IIT-JEE 2004 Screening

MCQ (Single Correct Answer)
An infinite G.P. has first term '$$x$$' and sum '$$5$$', then $$x$$ belongs to
A
$$x < - 10$$
B
$$ - 10 < x < 0$$
C
$$0 < x < 10$$
D
$$x > 10$$
4

IIT-JEE 2002 Screening

MCQ (Single Correct Answer)
Suppose $$a, b, c$$ are in A.P. and $${a^2},{b^2},{c^2}$$ are in G.P. If $$a < b < c$$ and $$a + b + c = {3 \over 2},$$ then the value of $$a$$ is
A
$${1 \over {2\sqrt 2 }}$$
B
$${1 \over {2\sqrt 3 }}$$
C
$${1 \over 2} - {1 \over {\sqrt 3 }}$$
D
$${1 \over 2} - {1 \over {\sqrt 2 }}$$

Joint Entrance Examination

JEE Main JEE Advanced WB JEE

Graduate Aptitude Test in Engineering

GATE CSE GATE ECE GATE EE GATE ME GATE CE GATE PI GATE IN

Medical

NEET

CBSE

Class 12