Physics CPP-FIITJEE

FTTT'CC I AlPr UR

cPP-1

Maths

CENT RE

Ghapter Practice prob lems

" ' 'Baircl,es-Xl(CTY

lf the.normals

at rwo points p and

ofordinates pand O is

G)qd 1

A tangent to

a

4

Jl = 4ar

;o,!2

intersect at a thfud point

]

G){zqz.Eq) ve

ex in

p,

3f +ly_6aag=g

from when 3 distinct normals can be drawn

6

The va lue

ofl

forwhich the equarion

ror j*

f

(D) None ofrhese

(sx- t2y+

tlf

is: (D) None ofrhese

l3

(l0r-5):+(l0y_7)2=D(5r+l2yr-7)2

G)-i*

given by:

is

28

(c)

3

Z.!ep =

@)+

ro{",}),,,

t2

(B)

''(+'?)

and S is the focus of the Parabola the

@;



zt=5+3i

Ji

point represented by z, w.,e,. o,I -----l _ - _o , ts -, when

"ro4

(c)

+

{D) none orthese

1c1l,i=z1t

then the maximum vatue ot lrz + z, I

@)

(D) an arc of a circte

otl,l=314

ts

$1-z

Gt

Ji +z

j

G)

it

(o)7

The value of tn(-1)

iA) does not

exist

(B) 2ln

(D)

O

ANSWER KEY

1.A2.83.C4.A5.D6.D 7. D 8. 8

FIIT.lCC

9. D

10.

A

11.D

12. C 5

t.

HEJCC IAIPUR,

Maths

CENTRE

GPP

Ghapter Practice Prdtlems

for JEE, 2Ol7

CPP-7

Class

COMPLEXNUMBER

't. 2,

Common roots

of

the equation z3

+Zl

-

Xl

+22+1 =Oandztes*21@+1=0is............

l.f points coresponding to the complex numbers zr, zz, 23 and zlarc lhe vertic€s of a rhombus, taken in ordei, then for a non-zero real number k {A) z1 -2.=ik(zz-z) (B)21-72=ik(4-41 (C)21 +7. =k(zr+41 lD) z, + 7, = k! zt +z.l

3. . 4.

lf z1 and zz are two comprex numbers such rhar (A) (B) -

nt4

rtz

'll f(x)

lzl-z2l=llal-lz2l lC) xtz

is equar

l, then argz, - argz2 1o1 o-

to

and g(x) are two potynomiats such that the potynomial h(x) = x f(x3) r x, g(xu) is divisible by x' +x +1 , then (A) f(1) =s(t) ,(B) f(1)+-s( i) (c)f(1)=s(1),a0 (D)f{l)= j(1) +0

5.

conside. a square oABC in the argand plane, where o'. is origin ind A A(ze). Then the equation of = the circle that can 'be inscribed in this square is; ( vertices oi squarb are gi-ven in antictockwile order)

(A)tz-a(l+Dt=tzot

zl,-a{'9=6r r"tf,-{-l=r.r

1e1

(D) none

of

these

For a complex number z, the minimum value of lzl + | z - coscr - isinol is

6.

(B)l

{A)0

The rcots of equalion 2n = (z +1)' (A) are vertices of regular polygon (C) are collinear

7

8,

Let

z

=l-t +i

+r+2, Wherb

{A) A hyperbola

{A) r

10.

-i+(2+Ji)

{4)(=)=

ellipse

(C) A straight

tine

maximum area that can be inscribed in the curve jz

-

(D)_1_(

2 il =2,1s 2 +2i

2_6)

k, then points A (21), B(22),c(3, o) and D(2, o) (taken in crockwise sense)

(A) lie on a circle only for k >

0

Let'z'be

a complex number

and ,a'be a real parameter such lhal z2 + az+

(A) locus

of z is a pair of srraight Ines

{c) lzl

:

(D) None of these.

1a;-r-qz*J3; (C)1+(2-Ji)

(C)lieonacircle Vk € R 11.

of

(B) lle on a circle (D) none of these

t is a real parameter. The locus of z in the Arq and plane is

(B)An

one .vertex of the triangre remaining vertices is / a.e

9.

{D) flone of these

2

i

-

3x + q

-

(B)a

g, s a R and a

{

4'-

(C)a>5

ar- a + 3 < o rs satisfied by atleast one real.r: (C)a (B) SP =

b > 1.

4.

Astraightline touc.fres both f + f = Sandtf = 16x. Show that its equation is y= 11y + i;.

5.

From a variable point P, on a fixed nomal to lhe parahla = qa*, two normah are drawn Show that the chord joining the feet of lhese two normals is paralbl to a ,i)€d lin€.

6.

lf the normal at any polnt P on th€ ellipse cuts the major and minor axis in Cr and G respoctively and C be the centre of theellipse then show a'zCCf + 6fo6'z= (." i,1,.

7

Consider the ellipse x2 +

=

ulz

- b int€irs€d in /ou, oi"tir.t

f

b

the parabda.

31 = 6and a pointPonitin lhe first quadrant at a distance of 2 units

centre. Find the eccentric angle of P.

I

I 10.

pon15

from the

The ellipse

is rotated through a right angle in its own plane about iB eenre which is fixed. 5-# =, Prove thatthe logy? I thg po,lnt of lntens€cti,on of the tang€nts to the elllpso ln [s origlnal ard in the rlew position ls (x' + \f) (t' + f a' g'l = \a' 42lxy. lf two @lnts are taken on lhe minor axb of an ellipse at lhe same disiance from the centre as ttle foci, prove that the sum of the squares of the perpendiculars fiom these polnts on any tangenl lo the eflipse is constant. Show that for all real p, the line Zgx + ellipse

y

rtl-f,

= 1 touches a fixed ellipse. Find the eccentricity ot this

ANSWERS Subroct : Mathematics

Topic : Parabola

&tllipse

Eatch : xl

OBJECTIVE

(B) 8. (8) 1s. (A) ?z.lcl 2e.(c) 1.

2

4.

10. (A)

(c) 11.(c)

5.{A)

s. (C)

12.(^)

13. (D)

16. (A)

14. {A)

17. (B)

18. (B)

1e. (B)

20. (8)

21. (Bl

23. (B)

24.(c)

25.

{c)

26.(c)

27. (Dl

28. (A)

(A)

6.

(c)

7.

(8)

,

30. (D)

SUBJECTIVE 2. syz - 1?ax + 8a2 = 0.

fIITJCC

3. (B)

7. nl4

3