1
JEE Advanced 2013 Paper 1 Offline
+4
-1
A curve passes through the point $$\left( {1,{\pi \over 6}} \right)$$. Let the slope of
the curve at each point $$(x,y)$$ be $${y \over x} + \sec \left( {{y \over x}} \right),x > 0.$$
Then the equation of the curve is
A
$$sin\left( {{y \over x}} \right) = \log x + {1 \over 2}$$
B
$$cos\,ec\left( {{y \over x}} \right) = \log x + 2$$
C
$$\,s\,ec\left( {{{2y} \over x}} \right) = \log x + 2\,$$
D
$$\,cos\left( {{{2y} \over x}} \right) = \log x + {1 \over 2}$$
2
IIT-JEE 2009 Paper 2 Offline
+3
-0

Match the statements/expressions in Column I with the values given in Column II:

Column I Column II
(A) The number of solutions of the equation $$x{e^{\sin x}} - \cos x = 0$$ in the interval $$\left( {0,{\pi \over 2}} \right)$$ (P) 1
(B) Value(s) of $$k$$ for which the planes $$kx + 4y + z = 0,4x + ky + 2z = 0$$ and $$2x + 2y + z = 0$$ intersect in a straight line (Q) 2
(C) Value(s) of $$k$$ for which $$|x - 1| + |x - 2| + |x + 1| + |x + 2| = 4k$$ has integer solution(s) (R) 3
(D) If $$y' = y + 1$$ and $$y(0) = 1$$ then value(s) of $$y(\ln 2)$$ (S) 4
(T) 5

A
(A)$$\to$$(P); (B)$$\to$$(Q), (S); (C)$$\to$$(Q), (R), (S), (T); (D)$$\to$$(R)
B
(A)$$\to$$(T); (B)$$\to$$(Q), (S); (C)$$\to$$(Q), (S), (T); (D)$$\to$$(Q)
C
(A)$$\to$$(S); (B)$$\to$$(Q), (S); (C)$$\to$$(P), (R), (S), (T); (D)$$\to$$(R)
D
(A)$$\to$$(P); (B)$$\to$$(Q), (S); (C)$$\to$$(Q), (R), (T); (D)$$\to$$(S)
3
IIT-JEE 2009 Paper 1 Offline
+3
-0

Match the statements/expressions in Column I with the open intervals in Column II :

Column I Column II
(A) Interval contained in the domain of definition of non-zero solutions of the differential equation $${(x - 3)^2}y' + y = 0$$ (P) $$\left( { - {\pi \over 2},{\pi \over 2}} \right)$$
(B) Interval containing the value of the integral $$\int\limits_1^5 {(x - 1)(x - 2)(x - 3)(x - 4)(x - 5)dx}$$ (Q) $$\left( {0,{\pi \over 2}} \right)$$
(C) Interval in which at least one of the points of local maximum of $${\cos ^2}x + \sin x$$ lies (R) $$\left( {{\pi \over 8},{{5\pi } \over 4}} \right)$$
(D) Interval in which $${\tan ^{ - 1}}(\sin x + \cos x)$$ is increasing (S) $$\left( {0,{\pi \over 8}} \right)$$
(T) $$( - \pi ,\pi )$$

A
(A)$$\to$$(P), (Q), (S); (B)$$\to$$(P), (T), (S); (C)$$\to$$(P), (Q), (R), (T); (D)$$\to$$(S)
B
(A)$$\to$$(P), (Q), (S); (B)$$\to$$(P), (T), (R); (C)$$\to$$(P), (Q), (R), (T); (D)$$\to$$(R)
C
(A)$$\to$$(P), (Q), (S); (B)$$\to$$(P), (T), (S); (C)$$\to$$(S), (Q), (R), (T); (D)$$\to$$(S)
D
(A)$$\to$$(P), (T), (S); (B)$$\to$$(P), (T), (S); (C)$$\to$$(P), (Q), (R), (T); (D)$$\to$$(S)
4
IIT-JEE 2008 Paper 2 Offline
+3
-1
Let a solution $$y=y(x)$$ of the differential equation,

$$x\sqrt {{x^2} - 1} \,\,dy - y\sqrt {{y^2} - 1} \,dx = 0$$ satify $$y\left( 2 \right) = {2 \over {\sqrt 3 }}.$$

STATEMENT-1 : $$y\left( x \right) = \sec \left( {{{\sec }^{ - 1}}x - {\pi \over 6}} \right)$$ and

STATEMENT-2 : $$y\left( x \right)$$ given by $${1 \over y} = {{2\sqrt 3 } \over x} - \sqrt {1 - {1 \over {{x^2}}}}$$

A
STATEMENT-1 is True, STATEMENT-2 is True;STATEMENT-2 is a correct explanation for STATEMENT-1
B
STATEMENT-1 is True, STATEMENT-2 is True;STATEMENT-2 is NOT a correct explanation for STATEMENT-1
C
STATEMENT-1 is True, STATEMENT-2 is False
D
STATEMENT-1 is False , STATEMENT-2 is True
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