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1 FINALTERM EXAMINATION 9 (Session - ) Clculus & Anlyticl Geometry-I Question No: ( Mrs: ) - Plese choose one f ( x) x According to Power-Rule of differentition, if d [ x n ] n x n n x n n x + ( n ) x n+ n where n is rel numer, then Question No: ( Mrs: ) - Plese choose one If function g is differentile t point x nd function f is differentile t point g(x), then the is differentile t point x. Composition (f o g) Quotient ( f / g ) Product (f. g) Sum (f + g) Question No: 3 ( Mrs: ) - Plese choose one If ( ( ( ))) y f g h x ( ( )) u g h x
2 ( ) v h x then dy dy du dv.. du dv dy du dv du dv dv du dy.. du dv Question No: ( Mrs: ) - Plese choose one If function f is.. on closed intervl [,], then f hs oth mximum nd minimum vlue on [,]. Continuous Discontinuous None of these Question No: ( Mrs: ) - Plese choose one x t dt The expression, represents function of : t Both x nd x Question No: 6 ( Mrs: ) - Plese choose one cf ( x) if c is constnt c
3 c f ( cx) f ( x) Question No: 7 ( Mrs: ) - Plese choose one In the following figure, the re enclosed is ounded elow y : y x + y x x x 6 Question No: 8 ( Mrs: ) - Plese choose one y x nd y x + 6 At wht points the two curves: intersect? x nd x x nd x 3 x nd x 3 x nd x 3 Question No: 9 ( Mrs: ) - Plese choose one Wht is the sum of following series? n
4 n + ( n + )( n + ) n( n + ) n( n + ) Question No: ( Mrs: ) - Plese choose one d x If > then [ ] x x ln x ln Question No: ( Mrs: ) - Plese choose one Let S e solid ounded y two prllel plnes perpendiculr to the x-xis t x nd x.if, for ech x in [,], the cross-section re of S perpendiculr to the x-xis is A(x),then wht is the volume of the solid? V V A( y) A( x) A( x) V [ ]
5 A( x) V [ + ] Question No: ( Mrs: ) - Plese choose one y x ; x, x Let the solid generted y the region enclosed etween nd the x-xis is revolved out the y-xis. Which of the following eqution gives the volumes of solid y cylindricl shells? V π x x V x x V x x V x x Question No: 3 ( Mrs: ) - Plese choose one If slope m of none verticl line is m then the ngle of inclintion of the line is π π π
6 Question No: ( Mrs: ) - Plese choose one The PYTHAGORAS theorem descries the reltionship etween the sides of. Right ngle tringle Isoceleous tringle Equilterl tringle Question No: ( Mrs: ) - Plese choose one If quntity y depends on nother quntity x in such wy tht ech vlue of x determines exctly one vlue of y, we sy tht y is. of x reltion function not function not reltion Question No: 6 ( Mrs: ) - Plese choose one y x x + The grph of the eqution will represent Prol Stright line Two stright lines Ellipse Question No: 7 ( Mrs: ) - Plese choose one The lim f ( x)... where f ( x) x ( is constnt) + + Question No: 8 ( Mrs: ) - Plese choose one x + Consider the indefinite integrl
7 Let t x + Is the following sustitution correct? dt x + t Yes No Question No: 9 ( Mrs: ) - Plese choose one log t log t log t + log t log t Question No: ( Mrs: ) - Plese choose one How the series cn e expressed in sigm nottion? ( ) ( + ) ( ) ( + ) ( + )
8 ( + ) Question No: ( Mrs: ) - Plese choose one n * ( ) f x x The sum is nown s: Riemnn Sum Generl Sum Integrl Sum Geometric Sum Question No: ( Mrs: ) - Plese choose one Wht does 'n' represent in the Riemnn Sum No. of Circles No. of Suintervls No. of Loops No. of Squres n * ( ) f x x? Question No: 3 ( Mrs: ) - Plese choose one If w nd v re continuous functions of y on n intervl [c, d] nd w( y) v( y) for c y d, then re is ounded y the lines prllel to: : Y-xis X-xis Both X-xis nd Y-xis Question No: ( Mrs: ) - Plese choose one () + () + (3) + () + () How the series cn e expressed in sigm nottion?
9 Question No: ( Mrs: ) - Plese choose one n 3 n( n + ) [ n( n + )] 8 n( n + )(n + ) ( n + )(n + ) 6 Question No: 6 ( Mrs: ) If < < 3 <... < n <... Nondecresing Decresing Incresing Nonincresing - Plese choose one { } n, then sequence is... Question No: 7 If ( Mrs: ) - Plese choose one 3... n... { } n, then sequence is... Incresing Nondecresing
10 Decresing Nonincresing Question No: 8 ( Mrs: ) - Plese choose one If the difference etween successive terms is nown s: Incresing Decresing Nondecresing Nonincresing Question No: 9 { } n For sequence nown s: ( Mrs: ) - Plese choose one if the rtio of successive terms n > + n { } then the sequence n + > n then the sequence is n Incresing Decresing Nondecresing Nonincresing Question No: 3 ( Mrs: ) - Plese choose one { } n For sequence nown s : Incresing Decresing Nondecresing Nonincresing if the rtio of successive terms n + n then the sequence is Question No: 3 ( Mrs: ) - Plese choose one f ( n) f ( n) n If is the nth term of the sequence nd is differentile nd f '( n ) > then the sequence will e: Incresing Decresing
11 Nondecresing Nonincresing Question No: 3 ( Mrs: ) - Plese choose one 3 + r + r + r r +... where ( ) If the geometric series then which of the following is true for the given series? Converges Diverges Gives no informtion, r < Question No: 33 ( Mrs: ) - Plese choose one 3 + r + r + r r +... where ( ) If the geometric series, then which of the following is true for the given series? Converges Diverges Gives no informtion r Question No: 3 ( Mrs: ) - Plese choose one If the series u u will Converge solutely Diverge Converge conditionlly converges ut the series u does not converge, then Question No: 3 ( Mrs: ) - Plese choose one u Let e series with nonzero terms nd suppose tht then which of the following is true? u + ρ lim > u The series u converges
12 u The series diverges No conclusion cn e drwn. Question No: 36 ( Mrs: ) - Plese choose one Suppose f nd g re integrle functions on [, ] nd c is constnt, then c [ f ( x) + g( x)] f ( cx) + g( cx) f ( x) + g( x)] c f ( x) + c g( x) Question No: 37 ( Mrs: ) - Plese choose one Which of the following is surfce re S generted y revolving the curve y f(x) etween x nd x out the x-xis? S π f ( x) + [ f ( x)] S π f ( x) + [ f '( x)] S π f ( x) + [ f '( x)]
13 S + [ f '( x)] Question No: 38 ( Mrs: ) - Plese choose one Which of the following is re of the surfce generted y revolving the curve y x ; x out the x-xis? ( ) ( ) π x + x ( ) ( ) π x + x ( ) π + + x ( ) ( ) π x + x Question No: 39 ( Mrs: ) - Plese choose one Which of the following is the wor done W if n oject moves in the positive direction long coordinte line while suject to force F(x) in the direction of motion over n intervl [,3]? W W W x 3x F( x)
14 W 3 F( x) Question No: ( Mrs: ) - Plese choose one If f ( x) -3-3 nd f ( x) then which of the following is vlue of f ( x)? Question No: ( Mrs: ) x Derivtive of function is. Find the originl function. Question No: ( Mrs: ) ρ lim u + If is series with positive terms nd cses for the series to e convergent, divergent or none. u ; then write the three Question No: 3 ( Mrs: ) Evlute the following integrl: 3 x Question No: ( Mrs: 3 ) Use the first fundmentl theorem of clculus to evlute the definite integrl: x ; x < f ( x) where f ( x) 3 x ; x Question No: ( Mrs: 3 ) Show tht the series ( ) ( )! converges solutely.
15 Question No: 6 ( Mrs: 3 ) Express the following definite integrl s limit of Riemnn Sum. (Do not evlute the integrl) π π Cos x Question No: 7 ( Mrs: ) Express re of the shded region s definite integrl. Question No: 8 ( Mrs: ) How much wor is required to wind the chin onto the pulley if -ft length of steel chin weighting l/ ft. is dngling from pulley? Question No: 9 ( Mrs: ) Evlute the following integrl: x + x x Question No: ( Mrs: ) Use L Hopitl s Rule to evlute lim ( + sin x ) x cot x
FINALTERM EXAMINATION 2011 Calculus &. Analytical Geometry-I
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