1
JEE Advanced 2017 Paper 2 Offline
+3
-1
If y = y(x) satisfies the differential equation

$${8\sqrt x \left( {\sqrt {9 + \sqrt x } } \right)dy = {{\left( {\sqrt {4 + \sqrt {9 + \sqrt x } } } \right)}^{ - 1}}}$$

dx, x > 0 and y(0) = $$\sqrt 7$$, then y(256) =
A
16
B
3
C
9
D
80
2
JEE Advanced 2014 Paper 2 Offline
+4
-1
The function $$y=f(x)$$ is the solution of the differential equation
$${{dy} \over {dx}} + {{xy} \over {{x^2} - 1}} = {{{x^4} + 2x} \over {\sqrt {1 - {x^2}} }}\,$$ in $$(-1,1)$$ satisfying $$f(0)=0$$.
Then $$\int\limits_{ - {{\sqrt 3 } \over 2}}^{{{\sqrt 3 } \over 2}} {f\left( x \right)} \,d\left( x \right)$$ is
A
$${\pi \over 3} - {{\sqrt 3 } \over 2}$$
B
$${\pi \over 3} - {{\sqrt 3 } \over 4}$$
C
$${\pi \over 6} - {{\sqrt 3 } \over 4}$$
D
$${\pi \over 6} - {{\sqrt 3 } \over 2}$$
3
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
$$\,cos\left( {{{2y} \over x}} \right) = \log x + {1 \over 2}$$
4
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)
Physics
Mechanics
Electricity
Optics
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Coordinate Geometry
Calculus
EXAM MAP
Joint Entrance Examination