Sig. of Supdt... MRD-XII-(A) MATHEMATICS Roll No... Time Allowed : Hrs. MATHEMATICS Totl Mrks: 00 NOTE : There re THREE sections in this pper i.e. Section A, B nd C. Time : 0 Mins. Section A Mrks: 0 NOTE : Use this sheet for this section. No mrk will be wrded for cutting, ersing or over writing. Q. Insert the correct option (, b, c, d) in the empty bo opposite to ech prt. Ech prt crries one mrk. i) d =... (i) 9 (b) 6 ii) The distnce of point P(0,0) from line + y = 0 is (ii) (b) 0 iii) Degree of constnt polynomil is ; (iii) (b) 0 None of these y iv) The trnsverse is of hyperbol = is long (iv) b - is (b) y = y is z is v) If f() = sin then lim f( ) = (v) 0 0 (b) Undefined dy y vi) Degree of homogenious eqution = d + y is (vi) (b) Zero None of these d vii) ( ) =... (vii) d log e (b) log e log e None The stndrd form of n ellipse with centre t origin length of semi mjor nd minor is re viii) (viii) nd b is given by; + = (b) = = 0 + = i) If l y = then y =.. (i) X (b) e y ) Rdius of circle + y + = 0 is ; () (b) i) If f() = e m then f () =... (i) e m (b) m e m me m m n e m ii) If A(,), B(, 6) then AB = (ii) (b) 0
iii) d (sin ) d =. cos (b) 9 9 iv) The eccentricity e e = c of conic is hyperbol if ; (iv) e < A (b) e = e > e = v) ( + )d =... (v) (b) 6 0 vi) In prbol = Py if P = thn it will be open ; (vi) To left (b) To right Upwrd Downwrd vii) Slope of line psses through two point A(, y ) B(, y ) is given by ; (vii) yy (b) viii) cot d =... (viii) sec (b) l n cos l n sin cosec i) If g + f c = 0 then the circle becomes (i) Point circle (b) Hyperbol Ellipse Prbol ) The line y = m + c is tngent to circle + y = if C = () 9 ± m (b) ± m ± + m ± + m (iii)
MRD-XII-(A) MATHEMATICS Section B & C Totl Mrks : 80 Time Allowed : :0 Hrs. Section B Mrks : 0 Q. Answer ny TEN prts. Ech prt crries equl mrks. (i) Find b when log b 0 =. tn (ii) Evlute lim. 0 (iii) Find dy d when y = t + t + nd = +t. (iv) Use first principle rule to find the derivtive of cos. (v) If F(t) = I + tj + t k nd G(t) = ti + e t j + k, find dy (F G)(t). d (vi) Evlute 7 d. ( 7) (vii) Evlute sec θdθ π 0 (viii) Find eqution of line whose slop is 8 nd y intercept is ½. (i) Find the re of tringle whose vertices re P (0,0), P (,) nd P (,). () Find eqution of circle contins the points (, ), (,) nd hs centre t + y 7 = 0 (i) Find eqution of tngent nd norml t (ii) Solve dy = cos, y(0) =. d (iii) Find the th derivtive of f() = sin ( + b). P, to ellilpse + =. 9 Section C Mrks : 0 NOTE : Attempt ny THREE questions. Ech question crries equl mrks. Q. ) Find the Mclurin s epnsion of f() = sin t 0 = 0. b) Evlute + d Q. ) I = d Find I. + 0 b) Find the ngle between two lines representing the following homogenous eqution + y y = 0 Q. ) Find the length of two tngents drwn from the point P(, ) on the circle + y y = 0. b) Determine the vertices nd foci of hyperbol =. 9 6 Q. 6 ) Determine the vlue of t which the function f() = 0 is incresing or decresing. v b) If v = i j + k uuv, w = i + j k. Find d v uuv (v.tw). dt
Sig. of Supdt... MRD-XII-(A) MATHEMATICS -A Roll No... Time Allowed : Hrs. MATHEMATICS-A Totl Mrks: 00 NOTE : There re THREE sections in this pper i.e. Section A, B nd C. Time : 0 Mins. Section A Mrks: 0 NOTE : Use this sheet for this section. No mrk will be wrded for cutting, ersing or over writing. Q. Insert the correct option (, b, c, d) in the empty bo opposite to ech prt. Ech prt crries one mrk. y i) The trnsverse is of hyperbol = is long (i) b - is (b) y = y is z is ii) If f() = sin then lim f( ) = (ii) 0 0 (b) Undefined dy y iii) Degree of homogenious eqution = d + y is (iii) (b) Zero None of these d iv) ( ) =... (iv) d log e (b) log log e None e The stndrd form of n ellipse with centre t origin length of semi mjor nd minor is re v) (v) nd b is given by; + = (b) = = 0 + = vi) If l y = then y =.. (vi) X (b) e y vii) Rdius of circle + y + = 0 is ; (vii) (b) viii) If f() = e m then f () =... (viii) e m (b) m e m me m m n e m i) If A(,), B(, 6) then AB = (i) (b) 0 ) d (sin ) d =. cos (b) 9 9 i) The eccentricity e e = c of conic is hyperbol if ; (i) e < A (b) e = e > e = ii) ( + )d =... (ii) (b) 6 0 9 ()
iii) In prbol = Py if P = thn it will be open ; (iii) To left (b) To right Upwrd Downwrd iv) Slope of line psses through two point A(, y ) B(, y ) is given by ; (iv) yy (b) v) cot d =... (v) sec (b) l n cos l n sin cosec vi) If g + f c = 0 then the circle becomes (vi) Point circle (b) Hyperbol Ellipse Prbol vii) The line y = m + c is tngent to circle + y = if C = (vii) ± m (b) ± m ± + m ± + m viii) d =... (viii) 9 (b) 6 i) The distnce of point P(0,0) from line + y = 0 is (i) (b) 0 ) Degree of constnt polynomil is ; () (b) 0 None of these
Sig. of Supdt... MRD-XII-(A) MATHEMATICS-B Roll No... Time Allowed : Hrs. MATHEMATICS-B Totl Mrks: 00 NOTE : There re THREE sections in this pper i.e. Section A, B nd C. Time : 0 Mins. Section A Mrks: 0 NOTE : Use this sheet for this section. No mrk will be wrded for cutting, ersing or over writing. Q. Insert the correct option (, b, c, d) in the empty bo opposite to ech prt. Ech prt crries one mrk. i) cot d =... (i) sec (b) l n cos l n sin cosec ii) If g + f c = 0 then the circle becomes (ii) Point circle (b) Hyperbol Ellipse Prbol iii) The line y = m + c is tngent to circle + y = if C = (iii) ± m (b) ± m ± + m ± + m iv) d =... (iv) 9 (b) 6 v) The distnce of point P(0,0) from line + y = 0 is (v) (b) 0 vi) Degree of constnt polynomil is ; (vi) (b) 0 None of these y vii) The trnsverse is of hyperbol = is long (vii) b - is (b) y = y is z is viii) If f() = sin then lim f( ) = (viii) 0 0 (b) Undefined dy y i) Degree of homogenious eqution = d + y is (i) (b) Zero None of these d ) ( ) =... () d log e (b) log e log e None The stndrd form of n ellipse with centre t origin length of semi mjor nd minor is re i) (i) nd b is given by; + = (b) = = 0 + = ii) If l y = then y =.. (ii) X (b) y e
iii) Rdius of circle + y + = 0 is ; (iii) (b) iv) If f() = e m then f () =... (iv) e m (b) m e m me m m n e m v) If A(,), B(, 6) then AB = (v) (b) 0 d vi) (sin ) =. (vi) d cos (b) 9 9 9 vii) The eccentricity e e = c of conic is hyperbol if ; (vii) e < A (b) e = e > e = viii) ( + )d =... (viii) (b) 6 0 i) In prbol = Py if P = thn it will be open ; (i) To left (b) To right Upwrd Downwrd ) Slope of line psses through two point A(, y ) B(, y ) is given by ; () yy (b)