# maths svkm

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Q.18 If a: I -logr2 and b: r"rr(+) thenthe value of (49)u +5b equals 2t (A), 23 (B) t 25 (C) T 29 @z Q.19 Let E :logr(logr3) + logz0og:4) + logr(lo eoSl +lo9r(lo916) + logr(logu7) + logr(logrg), then gE is equalto (A)4 (B) s (c)27 (D) 36 Q.38 Theexactvalueof (A)12 96sin80osin 65osin 35o sin20"+sin50o+sin1 (B)24 sin 80 .cos 0 - sin 60 .cos 30 cos 20.cos 0 - sin 30.sin 40 @) z-Jl (c)-12 when 0 :7.5o is (c)Ji+r is equal to 100 Q.39 The value of (t)Ji - r (D)48 @) 2+J1 Q.4 Thesumtontermsoftheseries, + .+ *1 *3+......isequalto ).4 816""'' (A)2'-n-l (B) 1 - z-' (C) Z-" + n -'l (D) 2n - I a.B There is aformtrlathat says that sin 7x =A sidx + B sin6x + C sin5x + D sinax + E sin3x + F sin2x + G sin x + H. The value ofthe sum (A +B + C + D + E + F + G + H), is (c)-1 @) not possible to determine (A) 0 (B) I Q.4 The real values of 'a'for which the quadratic equation, 2x2 - 1as + ga _ l) x + * _ 4a:0 possesses roots ofopposite signs is givenby : (A) a>5 (B) 0 <a<4 (C) a>0 @) a>7 Q.11 Letcr,Bberealrootsofthequadraticequation x2+kx +(k2+Zk_4):0,tlienthemaximumvalue of (c2 + pz) is equal to (A) e (B) r0 (c) ll (D) 12 Q.15 The 3'dterm ofanarithmetic progressionis 7 andits Tmterm is 2 Thesum ofits first 20 te,rmsequals (A)470 (B)740 (c)704 more than thrice of its 3td term. (D)770 The maximum value of the sum ofthe A.p. 50, 4g, 46, 44,............ is (A)32s (B) 64s (c) 6so (D)6s2 Q.16 InatriangleABc, a: b :c :4 : 5: 6.Then 3.{+g: (A) 4C (B) 2n (c) n _ C @)r

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• Q.18 If a: I -logr2 and b: r"rr(+) thenthe value of (49)u +5b equals

2t(A), 23(B) t 25(C) T [email protected] Let E :logr(logr3) + logz0og:4) + logr(lo eoSl +lo9r(lo916) + logr(logu7) + logr(logrg), then gE is

equalto(A)4 (B) s (c)27 (D) 36

Q.38 Theexactvalueof(A)12

96sin80osin 65osin 35osin20"+sin50o+sin1

(B)24

sin 80 .cos 0 -

sin 60 .cos 30cos 20.cos 0

- sin 30.sin 40

@) z-Jl

(c)-12

when 0 :7.5o is

(c)Ji+r

is equal to100

Q.39 The value of

(t)Ji -

r

(D)48

@) 2+J1

Q.4 Thesumtontermsoftheseries, + .+ *1 *3+......isequalto).4 816""''(A)2'-n-l (B) 1 -

z-' (C) Z-" + n -'l (D) 2n - I

a.B There is aformtrlathat says thatsin 7x =A sidx + B sin6x + C sin5x + D sinax + E sin3x + F sin2x + G sin x + H.

The value ofthe sum (A +B + C + D + E + F + G + H), is(c)-1 @) not possible to determine(A) 0 (B) I

Q.4 The real values of 'a'for which the quadratic equation, 2x2 - 1as + ga _ l) x + * _ 4a:0 possesses

roots ofopposite signs is givenby :(A) a>5 (B) 0 7

Q.11 Letcr,Bberealrootsofthequadraticequation x2+kx +(k2+Zk_4):0,tlienthemaximumvalueof (c2 + pz) is equal to(A) e (B) r0 (c) ll (D) 12

Q.15 The 3'dterm ofanarithmetic progressionis 7 andits Tmterm is 2Thesum ofits first 20 te,rmsequals(A)470 (B)740 (c)704

more than thrice of its 3td term.

(D)770The maximum value of the sum ofthe A.p. 50, 4g, 46, 44,............ is(A)32s (B) 64s (c) 6so (D)6s2

Q.16 InatriangleABc, a: b :c :4 : 5: 6.Then 3.{+g:(A) 4C (B) 2n (c) n _ C @)r

• Q. I I The line through point (m, -

9) and (7 ,m) has slope z. The y-intercept of this line, is(A)- 18 (B)-6 (c) 6 (D) 18Q. 12 A line passes through (2, 2) and cuts a triangle ofarea 9 square units from the first quadrant. The sum of

all possible values forthe slope of such a line, is(A)

-2.s (B) - 2 (c) - 1.5 (D) _ IQ.13 A variable straight line passes through the points of intersection of the lines, x+ 2y: 1 and

Zx-y: l andmeetstheco-ordinateaxesinAandB.ThelocusofthemiddlepointofABis:(A) x +3y- 10xy:0 (B) x

-3y+ 10xy:0(C) x+3y+ l0xy:0 @) noneQ.l4 Locus of a point which is equidistant from the point (3,4) and (5,

-2) is a straight line whosex-intercept is(A) 1/3 (B)2t3 (c) 1 (D)_ 1/3

Q.l5 A line with gradient 2 intersects a line with gradient 6 at the point (40, 30). The distance betweenx-intercepts ofthese lines, is(A) 6 (B) 8 (c) l0 (D) 12

Q. 1 6 The diagonals of a parallelogram PQRS are along the lines x + 3y : 4 and, 6x -

2y: 7 . Then PQRSmustbe a(A) rectangle (B) square (c) cyclic quadrilateral @) rhombus

Q.17 ThesidesofatriangleABClieonthelines 3x*4y:0; 4x+3y:0andx:3.Let(h,k)bethecentreof the circle inscribed in AABC. The value of (h + k) equals(A) 0 (B) U4 (c)_ t/4 (D)U2

Q.18 The co-ordinates of the orthocentre of the triangle bounded by the lines,4x -7y+ 10:0;

x+y:5 and 7x+4y:15 is:(A) (2, 1) (B) (- 1,2) (c) (1,2) (D) (1, _2)

Q. l9 Ifthe x intercept ofthe line y: mx * 2 is greate rthan l/Zthen the gradient ofthe line lies in the interval(A) (-1, 0) (B) (-1l4, 0) (C) (- *,

- 4) (D) (- 4, 0)

Q.20 Let the co-ordinates of the two points A and B be ( I , 2) and (7, 5) respectively . The line AB is rotatedthrough 45o in anti clockwise direction about the point of trisection ofAB which is nearer to B . Theequation ofthe line in newposition is :(1t) 2x-y-6:0 (B) x-y-1:0 (C) 3x-y-11:0 (D) noneofthese

Q'15 ltt \,,k2 (kr 'kz) be two values of k for which the expression x2 -y2 + kx + I can befactorised into two real linear factors, then (k, -

k1) is equal to(^)2 @)_2 -(cj0 (D)4Q.16 The true solution set ofthe inequality logr(?L !) , ,, ,,

-'\zx-l )r", (- *,;) re) (4, "o) r.r (-*, j) ro) (7, *)

• Q.9 Thesumoftheflrstptermsofasequenceisp(p+ 1)(p+2). The l0thtefmofthesequenceis(A) 3e6 (B) 600 (c) 114 (D) 330Q.5 The general solution of sin x + sin 5x: sin 2x + sin 4x is(n) Znn (B) nn (C) nn/3 (D) 2nn/3

where n e I

Q.14 AnglesA, B and c of a triangleABC are inAp. ,r: : fi ,n", z. A isequar to :(A) nl6 (B) n/4 (C) 5n/12 (D) n/2Q.4 The four points whose co-ordinates are (2, l), (I, 4), (4, 5),(5, 2) form :(A) a rectangle which is not a square @) atrapezium which is not a parallelogram(C) a square (D) a rhombus which is not a square.Q.5 FindtheareaofthequadrilateralABCDwithverticesA(-2,0),B(0,4),C.(4,-2),and,De,2).(A)l2sq.units (B) l6sq.units

(C)20 sq. units @)32sq. unitsQ.6 If the two vertices of a triangle are (7 ,2) and( I , 6) and its centroid is (4, 6) then the coordinate ofthe

third vertex are (a, b). The value of (a + b), is(A) 13 (B) 14 (c) ls (D) 16

Q'7 A stick of length 10 units rests against the floor and a wall of a room . Ifthe stick begins to slide on thefloor then the locus of its middle point is :(A) x2 tyz:2.5 (B) *2 *y2:25 (C) x2+y2:100 @) none