1
IIT-JEE 2008 Paper 2 Offline
MCQ (Single Correct Answer)
+4
-1

Match the Statements/Expressions in Column I with the Statements/Expressions in Column II.

Column I Column II
(A) The minimum value of $${{{x^2} + 2x + 4} \over {x + 2}}$$ is (P) 0
(B) Let A and B be 3 $$\times$$ 3 matrices of real numbers, where A is symmetric, B is skew-symmetric and (A + B) (A $$-$$ B) = (A $$-$$ B) (A + B). If (AB)$$^t$$ = ($$-1$$)$$^k$$ AB, where (AB)$$^t$$ is the transpose of the matrix AB, then the possible values of k are (Q) 1
(C) Let $$a=\log_3\log_3 2$$. An integer k satisfying $$1 < {2^{( - k + 3 - a)}} < 2$$, must be less than (R) 2
(D) If $$\sin \theta = \cos \varphi $$, then the possible values of $${1 \over \pi }\left( {\theta + \varphi - {\pi \over 2}} \right)$$ are (S) 3

A
A - iii; B - ii, iv; C - iii, iv; D - i, iii
B
A - iii; B - ii; C - iii, iv; D - i, iii
C
A - ii; B - ii, iv; C - iii, iv; D - i
D
A - ii; B - ii, iv; C - iii, iv; D - i, iii
2
IIT-JEE 2008 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1

Let a and b be non-zero real numbers. Then, the equation

$$(a{x^2} + b{y^2} + c)({x^2} - 5xy + 6{y^2}) = 0$$ represents :

A
four straight lines, when c = 0 and a, b are of the same sign
B
two straight lines and a circle, when a = b, and c is of sign opposite to that of a
C
two straight lines and a hyperbola, when a and b are of the same sign and c is of sign opposite to that of a
D
a circle and an ellipse, when a and b are of the same sign and c is of sign opposite to that of a
3
IIT-JEE 2005 Screening
MCQ (Single Correct Answer)
+2
-0.5
If $$y=y(x)$$ and it follows the relation $$x\cos \,y + y\,cos\,x = \pi $$ then $$y''(0)=$$
A
$$1$$
B
$$-1$$
C
$${\pi - 1}$$
D
$$ - \pi $$
4
IIT-JEE 2005 Screening
MCQ (Single Correct Answer)
+2
-0.5
For the primitive integral equation $$ydx + {y^2}dy = x\,dy;$$
$$x \in R,\,\,y > 0,y = y\left( x \right),\,y\left( 1 \right) = 1,$$ then $$y(-3)$$ is
A
$$3$$
B
$$2$$
C
$$1$$
D
$$5$$
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