CADET COLLEGE KALLAR KAHAR ENTERANCE TEST FOR CLASS XI- MAY 2013

Time: 75 Min PAPER MATHEMATICS Marks: 60

QI . Define the following terms. (5 x 2 = 10) a. Radical Equation '-. .1 ,.'?''l[.,lS/~

., b. Binary Relation ~ !I "i1 C: - c. Direct common tangent (1'l,/ J/ ~!,J

d. Escrib~d circle ~!?cf.Lr~~ . e. Angle of Depression J.y.1:1----'!,I

Q2. Solve the f~lowing shmt questions. (10 x 3 = 30) a. Solve 2 ✓3x + 1 + 4 = 3 b. If a: b = 3 : 4, find 5a + 4b : 6a + 9b c. Factorize. x4 + 4 d. Eliminate 't' from x - y = 2t ; x2 + y2 = 3t2

e. Find mean proportional (x - 2), (x + 3)(x2 + x - 6) f Calculate arithmetic mean if U = (x - 120) / 5 , ~)U = 60 and If= 100 g. Prove that cos0 ( tan0 + cot0 ) = cosec0 / h. If ' x ' and 'y' varies inversely( (r _)'--' ) and k = 20, then find the value of

y, if X = 5 .J

1. Write down demerits ofMode. 0"21G~>L: J. Solve. x2

- 2x - 6 = 0

Q3. Solve the following questions. a. Solve by completing square method

ax2 + bx + c = 0, a i- 0

(5 X: 4 = 20)

b. I(.~ =6ab /(a -b) then ~m~ the value of (S - 3a)/(S: 3a~ .. + (S + 3"'J)/ (S - 3b) by using componendo-d1v1dendo theorem. ~ / ~ _, ~ /'

c. Simplify ( b + "b2 - a

2) / ( b - ✓ b2

- a2

)

d. A set of data contains the value as 148, 145, 160, 157, 156 and 160. Show that

Mode > Median> Mean.

e. If cos0 = 3 / 5, then find the remaining trigonometric ratios when 0 lies in the

first quadrant.

CADET COLLEGE KALLAR KAHAR ENTRANCE TEST CLASS XI - MAY 2014

PAPER MATH Time: 75 Minutes Total marks: 80

Q.No.1 Fill in the blanks. (2 X 11 = 22)

1. A root of an equation, which do not satisfy the ·equation is called ___ root.

2. If b2- 4ac = 0, then roots of ax:2+ bx +c = 0 are ___ and ___ _

3.· o.2 + B2 is equal to _____ _

4. If u/v=v/u = k, thenu= ____ _

5. Venn- diagram was first used by ____ _

6. Meart ( .b_...w ..J J ) is affected by change in

7. In decimal degree 25° 301 is equal to ____ _

8. If cosec0 > 0, Cos0 > 0 , then 0 lie in quadrant ( C:J ) ___ _ 9. The formula for area of sector is equal to _____ _

IO.A function f: A ~Bis called ifffunction f is one-one and onto. ------4)

II.Simplify ( 8 / 125) 3 = ___ _

Q.No.2 Give short answers of the followin2 questions (3 X 10 = 30)

1. Solve 5 x' - 30x by factorization ( (Ill!>/ ) .

2. Evaluate -13 -Ii

(I)+ (I).

3. Find third proportional ( '-,,Ao' I,;; 1/1/ ) t: ( x + y ) 2 , x' - xy -2y' .

4. Resolve into partial fraction ( / ~ ) x - 5 / · x2 +2x-3 .

5. Find a and b if ( 3- 2a, b-1 ) = ( a -7, 2b+ 5 ).

6. Find Harmonic mean of data

Q.No.3

·-

'i ., 7. Find r, when / = 52 cm , 0 = 45° .

8. Simplify and write in a+ bi form ( 2 - ~) ( 3 - ---✓--4). /

9. Verify the identities (f;'~L.:.) . Sec 0- cos O = tan 0 sin 0

1 O.Show that J 3 - sx/ 4 J

Solve the following questions. ( 4 x 7= 28) /

1. Derive quadratic formula by using completing square method ( C'.:-/ ~ ) ./

if ax2+ bx +c = 0 , a f. 0 .

2. If a , ~ are the roowof equation 4x2 -3x+6 =O , find the value of (u - ~) .

• I A: J . ~ I !' .> 3. Using theorem of Componendo- dividendo ( ~ ~,'~/ ~ ) ,

Solve

07 + jx - 3 4 ::::.-

~x +3 jx - 3 3

. 4. The length of a rectangle ( ~ ) is 4 m more than its breadth, if the

area of the rectangle is 45 m2 • Find its side.

5. Find the variance ( u V l ) for data 10 , 8 , 9 , 5 , 12 , 86 . 8 . 2 .

6. Prove 1 + cos e sin 0 = 2 coscc 0 . +

sin 0 + cos e . .. • . ... '41

7. A rocket is lunched and cl~mbs :It a cnnstant angh.· nf Xll'' . Find the- altitude l

( o 0 . ) of the rnckl·t atlcr it truvcls 5000 ml'l~·r.

\ . f

CADET COLLEGE KALLAR KAHAR

ENTRANCE TEST CLASS XI- MAY, 2015.

PAPER MATJ!

Time: 75 Minutes.

Q # 1 Solve the following short questions.

a. Express in the standard form a+bi

/ .. b. Factorize ( O' J (f,?. )

1

1 + 2i

25x2 - I Ox+ 1 - 36z2

Marks: 60

(8 X 3 = 24)

/ c. Evaluate( U/ (~) (2 +2w-2w2)(3-3w+3w2

)

/

d. Solve for x Ix + 21 - 3 = 5 - Ix + 21 (U'-:/d-9)

. I e. Solve the inequality( ~OJ~)

x-4 -3 <--<4 - -5

. . , .. f. If the given figure ABCD is a parallelogram ([Jftllcf(,I'

g. If x = 2 + -/3' find the value of x - ; and (x - ;) 2

A

~t~'((,~ (~{,:) h. The given triangle ABC is equilateral triangle and AD is bisector of anole A

then finds the value of unknowns x0,y° and z0 A b

P.T.O

B C

Q # 2 Solve the following long questions. (9 X 4 = 36)

a. Prove that 1 + sine 1 - sine 1 . - 1 + . e = 4tan0sece - sine sin

b. If a, pare the roots of the equation x2

- 3x + 6 = 0. Form equation whose 2 A2 roots are a , p .

h t . 2 )2 2 2 2 c. Show that t e equa ion x + (mx + c = a has equal roots, if c = a (I +m2) .

d. Solve by synthetic division x4 - 49x2 + 36x + 252 = 0 having roots -2 and 6.

e. Find Fourth proportional( ~t_;; I.Ar_,? ) of a3 - b3, a+ b and a

2 + ab + b2

f. Find the square root ( ) by factorization

1 2 1 2

( xz + x2) - 4 ( x + x) + 12 / ..

g. Resolve into partial fraction( ./ ~ ) llx + 3

(x - 3)(x 2 + 9)

-(cf;!)

. . d . . I(, l' lll ifthl' an~k at th1..' h. f md the area of the sector of a circle of ra iu~ ~

centre is 60°.

i. lf U= { I 2 3 2<)' X == ( I 17,9,15,l~.20l and Y:::. { I.3.5, ... . 17} th~n ' , , . . . . .. , J, .. ,

show that X - Y = XnYl:

liood l .ud.

·, (

• /

CADET COLLEGE-KALAR KAHAR ENTRANCE TEST CLASS XI MAY 2016

PAPER·MATH

Time: 75 minutes Marks: 60

Q: 1 Solve the following short questions. (8 x3=24)

a) Simplify (2x5y4) (-8x·\,2).

b) Use matrices, if possible solve equations by Cramer's rule 3x:-4y=4; x+2y=8.

c) Find value of x; iflogx 64 = 2

d) If x - ~ =4, then find value of x3 - 2- .

X x3

e) Factorize ( (!,} ) 9x4+36y4.

~ . t) Use factorization ( · (} _;?. ) to find the sq~ef root ( / P. ) of

(x2+ ~)+ 12(x +2:) +38 ; x * 0 X X • .

g) Solve inequalities ( 0 ~ V ,,J!) 3x-2< 2x + .1 < 4x + 17. . - L. .,, ;11 , ..,

h) Show that the points A(-2,l),B(2,l),C(3,3) and D(-1,3) form a paiallelogram(cJ,.,- ~/ ,Y )

Q:2 Solve the following long questions. (9x4=36)

sec8+1 sec0+1 a) Prove that 0 1

= -t 0 sec - an

b) Find-the sra_ndard deviation ( J,)/1 C} J ~ ) of 9,3,8,8,9,8,18.

c) IfU={l,2,3, . .. 10} ,A={l ,3,5,7,9}, B={2,3,4,5,8} ,prov,e (BnAt=AcuBc

d) Resolve x4

+ 1 into partial fraction ( 1,j}) x2(x-1) / c};;

e) If w varies inversely as t~e cube of u, and w=5 when u=3 find w, when u=6.

t) Convert 45.36° to D0 M' S" form.

g) Prove that the product of cube roots of unity is one.

h) Solve the equation ✓3x + 7 =2x+ 3 .

i) Form a quadratic equationvJ-'_L,.,iJ~)~] )with roots 3 and 4.