EC PROGRESS GETTER Aptitude Grooming– Topic Specific : Tutorial Series (AA Grade) GWS CODE P V DATE C 1 5B Textual Exercise b ≥ c ∀ x > 0, a > 0, show that 27ab2 ≥ 4c3. x  x2   + f(6 – x2), find points of extrenum of g(x). Q.02 If f’’(x) > 0 ∀ x ∈ R, g(x) = 2 f   2    Q.03 Find Range of ... Q.01 If ax2 + (01) f(x) = ln (cosxcosx + 1), 0 < x < π/2 sin2 x − sin x + 1 (02) f(x) = sin2 x + sin x + 1 Q.04 Let A(1, 1), B(4, 2), C(9, 3) be vertices of ∆ABC. A parallelogram AFDE is drawn with vertices D, E, F on sides BC, CA, AB respectively. Find maximum area of parallelogram. 2   x2 Q.05 Find minimum value of ( x1 − x 2 )2 +  1 − (17 − x x )(x 2 − 13)  , x 1 ∈ R+, x 2 ∈ (13, 17)   20   ******* Conceived and Compiled by… Mentors @ ACE AXIS for ACE AXIS – S.C.O. 58, I-II Floor, Sec. 20C, Chandigarh(U.T.)–160020. Phs.(O) 0172 500 5555, 501 5555 (R) 500 0055 (F) 467 0083 (M) 9216528383, 9316528383, 9041528383, 9041428383 www.aciax.com(in), [email protected], [email protected] aps correspondence desk : BEYOND | 83A, Rani Ka Bagh, Amritsar 143001, Punjab-State (INDIA). Ph. 0183 2220083 EC PROGRESS GETTER Aptitude Grooming– Topic Specific : Tutorial Series (AA Grade) TWS CODE P V DATE C 2 3 Textual Exercise Q.01 Solve the differential equation dy = dx 1  − sin 4 θ  +  ∫ 2   cos 4 θ    (f (cos 2θ − φ)) + f (φ)  f (φ)dφ . dv du + v P(x) = g(x) respectively. It is also given that u(x 1 ) > v(x 1 ), ... + u P(x) = f(x), dx dv f(x) > g(x) for every x > x 1 . Prove that at any point (x, y), where x > x 1 doesn’t satisfy y = u(x), y =v(x) ... simultaneously. Q.02 Let u(x), v(x) satisfy − ∫ dy Q.03 If y 1 , y 2 be the solutions of + y P(x) = Q(x), and y 2 = y 1 z, prove that z = 1 + ae dx Q( x ) dx y1 Q.04 Area of region bounded by curve, x-axis and two ordinates one of which is constant and other variable is equal to ratio of cube of variable ordinate to cube of variable abscissa. Find equations of family of curves. Q.05 A, B are two separate reservoirs of water. Capacity of reservoir A is double the capacity of reservoir B. Both the… reservoirs are filled completely with water, their inlets are closed and then the water is released simultaneously from both the reservoirs. The rate of flow of water out of each reservoir at any instant of time is proportional to the quantity of water in the reservoir at that time. One hour after the water is released, the quantity of water in 1 reservoir A is 1 times the quantity of water in reservoir B. After how many hours do both the reservoir have … 2 the same quantity of water ? ******* Conceived and Compiled by… Mentors @ ACE AXIS for ACE AXIS – S.C.O. 58, I-II Floor, Sec. 20C, Chandigarh(U.T.)–160020. Phs.(O) 0172 500 5555, 501 5555 (R) 500 0055 (F) 467 0083 (M) 9216528383, 9316528383, 9041528383, 9041428383 www.aciax.com(in), [email protected], [email protected] aps correspondence desk : BEYOND | 83A, Rani Ka Bagh, Amritsar 143001, Punjab-State (INDIA). Ph. 0183 2220083