RvZxq wek¦we`¨vj‡qi cÖkœcÎ - 2010 1 2 K¨vjKzjvm-I

(Z) mgvKjbxq aª“eK wK? [What is the constant of integration?]

NUH-2010 [Ch-9F: Quiz-3]
(_) Bw›UMÖvj K¨vjKzjv‡mi †gŠwjK Dccv‡`¨i eY©bv `vI| [State the
1| wb‡gœi †h‡Kv‡bv wekwU msw¶ß cÖ‡kœi DËi `vI 1×20=20 fundamental theorem of integral caluclus.] [Ch-10A: Quiz-3]
(K) dvsk‡bi †iÄ- Gi msÁv `vI| [Define range of a function.] (`) r = a (1 + cos θ ) eµ‡iLvwU AsKb Ki| [Sketch the flgure of the
[Ch-1: Quiz-5]
(L) f ( x ) = ln x dvsk‡bi †Wv‡gb KZ? [What is the domain of the curve r = a (1 + cos θ ) .] [Ch-14B: Quiz-6(i)]
(a) mvBK¬‡qW wK? [What is cycloid?] [Ch-14A: Quiz-5]
function f ( x ) = ln x ?] [Ch-1: Quiz-33]
(b) Mvgv dvsk‡bi msÁv `vI [Define Gamma function.]
(M) A‡f` dvskb Kv‡K e‡j? [What is called the identity function?] [Ch-12: Quiz-1]
[Ch-1: Quiz-16] =
(c) r a cos 4θ eµ‡iLvi KqwU duvm Av‡Q? [How many loop’s are in
(N) D`vniYmn †Rvo I we‡Rvo dvskb msÁvwqZ Ki| [Define even and =r a cos 4θ ?] [Ch-14B: Quiz-18]
odd function with Example.] [Ch-1: Quiz-17, 18, 19, 20] (d) cÖ_g †kªYxi AcÖK…Z Bw›UMÖvj Kv‡K e‡j? [What is called the first kind
(O) x = a we›`y‡Z GKwU dvsk‡bi Awew”QbœZvi msÁv `vI| [Define of improper integral?] [Ch-13: Quiz-2]
continuity of a function at x = a .] [Ch-2B: Quiz-1] (e) y = f ( x ) eµ‡iLvi ( x1 , y1 ) we›`y‡Z ¯úk©‡Ki mgxKiYwU wjL| [Write
dy dy
(P) R¨vwgwZKfv‡e wK wb‡`©k Ki? [What is in geometrically?] the equation of tangent of the curve y = f ( x ) at ( x1 , y1 ) .]
dx dx
[Ch-3A: Quiz-3] [Ch7A: Quiz-8]
(f) AveZ©bRwbZ Nbe¯‘ Kv‡K e‡j? [What is called the solid of
(Q) x Gi mv‡c‡¶ y = x n Gi n Zg Aš—iR KZ? [What is the n-th
revolution?] [Ch-16: Quiz-1]
derivative of y = x n with respect to x?] [Ch-3B: Quiz-1] L- wefvM
(R) ‡Kv‡bv eµ‡iLvi mwÜwe›`y ej‡Z wK eySvq? [What are the critical
2| (K) y = x 2 − 7 x + 10 dvsk‡bi †Wv‡gb I †iÄ wbY©q Ki| [Find domain
points of a curve?] [Ch-6B: Quiz-11]
(S) cÖ_g Mogvb Dccv‡`¨i eY©bv `vI| [State the first mean value and range of the function y =
x 2 − 7 x + 10 .] [Ch-1: Ex-2(xi)]
theorem] [Ch-4: Quiz-5] (L) wb‡gœi dvskbwUi ‡jLwPÎ AsKb Ki [Sketch the graph of the
(T) dvsk‡bi Mwiôgvb Kv‡K e‡j? [What is the maximum value of a followeing function]: [Ch-1: Ex -22]
function?] [Ch-6B: Quiz-14] 2 − x hLb ( when ) x > 1
0 
(U) Awb‡Y©q AvKvi ej‡Z wK eyS? [What do you mean by = f ( x) x hLb ( when ) 0 < x ≤ 1
0

0 − x hLb ( when ) x ≤ 0
indeterminate form?] [Ch-8: Quiz-1]
0 3| (K) wjwg‡Ui ( δ,∈) msÁv e¨envi K‡i †`LvI †h, [Using the ( δ,∈)
(V) `yÕwU eµ‡iLvi Aš—M©Z †KvY msÁvwqZ Ki| [Define angle of
x2 − 9
intersection between two curves.] [Ch-7A: Quiz-10] definition of limit to show that] lim = 6 [Ch-2A: Ex -2(vi)]
x →3 x − 3
(W) cÖwZ‡Wwi‡fwUf wK? [What is antiderivatives?] [Ch-9F: Quiz-1]
1 x
(X) AcÖK…Z Bw›UMÖv‡ji msÁv wjL| [Define inproper integral.] (L) sec −1 2 Gi mv‡c‡¶ tan −1 Gi Aš—ixKiY Ki|
[Ch-13: Quiz-1] 2x −1 1 − x2
f ′( x) f ′( x) [Differentiable tan −1
x
with respect to sec −1 2
1
.]
(Y) ∫ dx Gi gvb KZ? [What is the value of ∫ dx .] 2x −1
f ( x) f ( x) 1− x 2

[Ch-9F: Quiz-24] [Ch-3A: Ex-7(viii)]

www.scienceview.info www.scienceview.info www.scienceview.info www.scienceview.info www.scienceview.info

 RvZxq wek¦we`¨vj‡qi cÖkœcÎ - 2010 3 4 K¨vjKzjvm-I
dy dy π
4| (K) y = x x n‡j wbY©q Ki| [Find when y = x x .] (L) y = ln ( sec x ) †iLvi x = 0 nB‡Z x = ch©š— Pvc ˆ`N©¨ wbY©q Ki|
dx dx 4
[Ch-3A: Ex -3(ii)] π
[Find the length of the arc of the line y = ln ( sec x ) x = 0 to x = .]
(L)= sin y x sin ( a + y ) n‡j cÖgvY Ki †h,
dy
=
sin 2
( a + y ) [Show 4
[Ch-15A: Ex -4(1)]
dx sin a
dy sin ( a + y ) M-wefvM
2

that = , when= sin y x sin ( a + y ) .] π

dx sin a 10| wb‡gœi dvsk‡bi x = 0 Ges x = we›`y‡Z Awew”QbœZv I Aš—ixKiY‡hvM¨Zv
[Ch-3A: Ex-8(ii)] 2
5| (K) Mogvb Dccv‡`¨i R¨vwgwZK e¨vL¨v `vI| [Give the geometrical cix¶v Ki [Test continuity and differentiability of the following
interpretation of the mean value theorem.] [Ch-4: Art-4.6] π
function at x = 0 and x = ]
e −e
x sin x
e x − esin x 2
(L) lim dx Gi gvb wbY©q Ki| [Evaluate lim dx ]
x → 0 x − sin x x → 0 x − sin x  1 ; hLb ( when ) x < 0
[Ch-8: Ex-4(viii)] 
π
1 − sin x dx f ( x ) = 1 + sin x ; hLb ( when ) 0 ≤ x ≤ [Ch-2C-Ex -4(i)]
6| (K) mgvKjb Ki: [integrate] ∫ dx A_ev ∫  2
x + cos x (1 + x ) 1 − x2
2

2 +  x − π  ; hLb ( when ) x ≥ π
2

[Ch-9C: Ex-8(ii)]   2  2
π
11| ‡iv‡ji Dccv`¨wU eY©bv I cÖgvY Ki| Dnvi R¨vwgwZK e¨vL¨v `vI| [State
(L) gvb wbY©q Ki [Evaluate] t ∫ 2
ln ( sin x ) dx [Ch-10B: Ex -4(i)] and prove Rolle’s theorem. Also give its geometrical
0
π interpretation.] [Ch-4: Art-4.2, 4.3]
A_ev, ∫
0
x ln sin xdx [Ch-10B: Ex -4(v)]
12| hw` y = ( sinh −1 x ) nq Z‡e †`LvI [If y = ( sinh −1 x ) then show that]
2 2

7| (K) ∫ sin n xdx Gi jNyKiY m~Î cÖwZôv Ki| [Find the reduction formula
(1 + x ) y
2
n+2 + ( 2n + 1) xyn +1 + n 2 yn =
[Ch-3C-Ex -10(iii)]
0
for ∫ sin xdx .]n
[Ch-10C: Art-10C Gi (vii)] 13| j¨vMÖvÄ AvKv‡ii Ae‡klmn †Uj‡ii Dccv‡`¨i eY©bv I cÖgvY `vI| [State
and prove Taylor’s theorem with Langrange’s form of remainder.]
(L) cÖgvY Ki [Prove that] : Γ (1 / 2 ) =π [Ch-12: Art-12.6, Cor-1] [Ch-5-Art-5.1]
8| (K) x + y =
2 2
a e„ËwUi cwimxgv wbY©q Ki| [Find the perimeter of the
2
14| wb‡gœi dvskbwUi Mwiôgvb I jwNô gvb wbY©q Ki t [Find the maximum
and minimum value of the following function]
circle x 2 + y 2 =
a 2 .] [Ch-15A: Ex -1]
2 2
f ( x ) = x3 − 6 x 2 + 9 x + 5 [Ch-6B-Ex -1(vi)]
x y
(L) + = 1 Dce„ËwU x A‡¶i Pvwiw`‡K Nyi‡j Drcbœ Nbe¯‘wUi AvqZb π
a 2 b2
wbY©q Ki| [Find the volume of the solid generated by revolving the
15| Walle Gi m~Î eY©bv Ki| Bnvi mvnv‡h¨ ∫
0
2
sin 7 xdx Gi gvb wbY©q Ki
π

x2 y 2
ellipse 2 + 2 = 1 about the x-asis.] [Ch-16: Ex-2(i)]
[State Walle’s formula. Using the formula evaluate ∫
0
2
sin 7 xdx ]
a b [Ch-10C: Art-10C.3, Ex-1]
9| (K) ∫
1 dx
Gi Awfm„wZ cix¶v Ki| [Test the convergent of 16| r = a (1 + cos θ ) KvwW©I‡qW‡K Avw` †iLvi mv‡c‡¶ AveZ©b Ki‡j Drcbœ
( )
0 x 1+ x
Nbe¯‘i Z‡ji †¶Îdj I AvqZb wbY©q Ki| [Find the area of rhe surface
1 dx and the volume of the solid obtainde by revolving the cardioide
∫0 x (1 + x )
] [Ch-13: Ex -3(i)] r = a (1 + cos θ ) about the initial line.] [Ch-16: Ex-9(i)]

www.scienceview.info www.scienceview.info www.scienceview.info www.scienceview.info www.scienceview.info