MOCK TEST PAPER 2019
JEE (Main and Advanced).
(Complex number, Quadratic Equation, Trigonometry, Co-ordinate geometry-2D).
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Section -1
(single option correct)
( 3 marks for correct answer
and -1 for wrong answer)
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1) value of (1+cosπ/8 +isinπ/8)⁸
(1+cosπ/8 -isinπ/8)⁸
a) 1+i b) 1-i c) 1 d) -1
2) If |z+1/z| = 3 then the greatest
value of |z| is.
a) 3+√3 b) 3+√13 c) √13 -3 d) N
3) Let 3 - i and 2+i affixes of two
points A and B in Argand plane
and P represent the complex
number z=x+iy such that |z-3+i|
= |z-2-i|. Then the locus of P is
a) a circle on AB as diametre
b) the line AB
c) the perpendicular bisector of
AB.
d) none.
4) The quadratic equation
x²-6x+a =0 and x²-cx+6=0 has
one root in common. The other
roots of the first and second
equation are integers in the ratio
4 : 3. Then the common root is
a) 2 b) 1 c) 4 d) 3
5) If the roots of the equation
a(b-c)x²+b(c-a)x+c(a-b)=0 are
equal then a,b ,c are in
a) A P b) G.P c) H.P d)none
6) In a triangle with one angle
2π/3, the length if the side
forms an A.P. If the length of the
greatest side is 7 cm. then the
radius of the circumcircle of the
triangle is
a)7√3/3 b) 5√3/3
c) 2√3/3 . d) 7√3.
7) The most general solution of
2ˢⁱⁿˣ +2ᶜᵒˢˣ = 2¹⁻ ¹/√² are
a) nπ -π/4 b) nπ+π/4
c) nπ + (-1)ⁿπ/4 d) 2nπ±7π/4
8) The perpedicular bisector of the
line segment joining P(1,4)and
Q(k,3)has y-intercept is -4.
Then a possible value of k is
a) -4 . b) 1 c) 2. d) -2
9) Through the point (13,31), a
straight line is drawn to meet
the axes of x and y at Q and S
respectively. If the rectangle
OQRS is completed then the
locus R(h,k) is
a) 13/x +31/y = 1
b) 31/x +13/y =1
c) 31/x - 13/y =1
d) 13/x -31/y =1
10) If the lines ax +ky+10=0,
bx+(k+1)y+10=0 and
cx+(k+2)y+10 =0 are
concurrent. then
a)a,b,c are in G.P
b)a,b,c are H. P
c)a,b,c are in A.P d) a+b=c
Section -II
(Multiple correct option)
(4marks for correct and -1
for incorrect answer)
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11) If in ∆ABC,
a⁴ + b⁴+c⁴=2a²(b²+c²),
then angle A is
a) 45º b) 60º c) 90º d)135º.
12) If (1-tanx)(1+sin2x)=1+tanx,
then x is equal to
a) nπ. b) (2n+1)π
c) nπ-π/4 . d) 2nπ± π/8
13) The equation
x² -6x +8+α(x²-4x+3)=0,
α ∈ R has
a)real and distinct root ∀ α
b) real roots ∀ α ≺ 0
c) real roots ∀ α ≻ 0
d) real and distinct roots for α =0
14) The value of
∑⁶ⱼ₌₀(Sin 2jπ/7 - iCos 2jπ/7) =
a) -i b) 0 c) i d) -i⁻³⁷
15) The lines 2x-y+1=0,
(m-4)x- (2m-1)y=0 and
4mx+ (m-6)y+1=0 are
a) cocurrent for two values of m.
b) concurrent for one value of m
c) concurrent for no value of m
d) parallel for m=2
Section- III
(Assertion and Reason Type)
(This section contains 5 questions. Each question contains Statement-1(Assertiin) and Statement-2(Reason). Each question has 4 choices a,b ,c and d out of which ONLY ONE is correct.
In each of the following questions two statements are given as Assertion (A) and Reason(R). Examine the statements carefully and answer the questions according to the instruction given below.
a) if both A and R is correct and R is the proper reason of A.
b) if both A and R is correct and R is not the proper reason of A.
c) if A is correct and R is wrong.
d) if A is wrong and R is correct.
16) Statement-1 )
Consider the point A(0,1)and
B(2,0) and P be a point on the
line 4x+3y+9=0, then the
coordinates of P such that
|PA - PB| is maximum
is (-84/5, 13/5)
Statement-2 ) If A and B are two
fixed points and P is any point in
a plane then |PA - PB| ≤ AB.
17) Let z be a moving point in a
complex plane such that
amp((z-1)/(z-2)) =π/4.
Statement-1) The locus of z will be
a circle.
Statement-2) If a point is miving
such that its distance from the
fixed point is always constant
then the locus of the point is a
circle.
18) Statement -1)
Incentre of a triangle formed
by the lines 3x+4y=0,
5x-12y=0and y-15=0 is the
point P whose coordinates are
(1,8).
Statement -2)
Point P is equidistant from the
3 lines forming the triangle.
19) Statement-1)
if a,b,c ∈ R and equations
ax²+bx+c=0 and x²+ 5x+7=0 has
a common root then
(a+c)/b=7/5.
Statement-2) If both roots of
a₁x²₁+ b₁x + c₁=0 and
a₂x²+b₂x+c₂=0 are identical,
then a₁/a₂ =b₁/b₂ = c₁/c₂,
where a₁, b₁c₁ and a₂, b₂, c₂ ∈ R.
20. Statement -1)
If ∆ABC is equilateral, then
tanA + tan B + tan C= 3√3.
Statement -2) In ∆ABC,
tanA + tanB+tanC= tanAtanBtanC.
Section IV
(Integer Answer type)
4 marks for correct and -1
for incorrect answer.
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21) The smallest value of k for
which both the roots if the
equation x²-8xk+16(k²-k+1)=0
are real, distinct and have values
at least 4 is.
22) Let w=Cos 2π/3 +iSin 2π/3.
Then the number of distinct
complex number z satisfying
Determinant
z+1 w w²
w z+w² 1 . = 0 is equal to
w² 1 z+w
23) Consider a ∆ABC. suppose
BC=6, CA=10 and area of the
triangle is 15√3. If angle
ACB> 90º and r denotes the
radius of the incircle of the
triangle, then r² is equal to
24) if z is a complex number
satisfying |z-3-2i| ≤2, then the
minimum value of
|2z -6 +5i| ≤2 is
25) The number if values if x in
(0, 2π) such that
1+ sin⁴2x= cos²6x is.
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