TargetIIT Full Test before JEE

Q7 Let x,y be the real numbers satisfying the equation x2+2x+y2+2y-47=0
If the maximum and minimum values of x2+y2-4x-6y+13 are M and m respectively, then the numerical value of M-m is
Your Answer: 14
Correct Answer: none of these
Score: -1
Explaination :
x2+y2-4x-6y+13=(x-2)2+(y-3)2
P(2,3) lies inside the circle
let the distance between centre of circle and P be x
let M'=r+x and m'=r-x
M=M'2=r2+x2+2rx
m=m'2=r2+x2-2rx
M-m=4rx=4*7*5=140

x2+2x+y2+2y-47=0
(x+1)²+(y+1)²=49
This is a circle with centre (-1,-1) and radius 7

Now x²+y²-4x-6y+13=(x-2)²+(y-3)²
This is not an equation it is an expression
If you see this it is a distance of point (x,y) from (2,3)
As (x,y) always lie on the circle (x+1)²+(y+1)²=49 the expression (x-2)²+(y-3)² gives the (distance)² of any point on the circle from (2,3)

you have to find (x,y) on the circle which are at minimum and maximum distance from (2,3)

Q13 STATEMENT-I: The number of common tangents that can be drawn to the circle x2+y2=a2 and hyperbola x2-y2=a2 is two
STATEMENT-II: y=mx±a√(m2-1) is a tangent to the hyperbola. For common tangent |a√(m2-1)|/√(m2+1)=a.
Your Answer: d
Correct Answer: a
Score: -1
Explaination :
the tangents are x±a=0

i thought there were4 tangents vich could me drawn 4m a circle to a hyperbola
help me inm case of misconception

Here the circle touches the hyperbola
so no. of common tangents =2

(-pi to pi)∫ {sinx}dx :where {.} is the fractional part

Refer Prev Ques
Your Answer: d
Correct Answer: a
Score: 0

I DID
x=[x]+{x}

value daalien

mera to 0 aa raha tha and aa raha hai
please help in case of mistake!!!!!!

x=[x]+{x}
{sinx}=sinx-[sinx]
(-pi to pi)∫(sinx-[sinx])dx
(-pi to pi)∫sinxdx-(-pi to pi)∫[sinx]dx
0-(-pi to pi)∫[sinx]dx (sinx is odd function)
-(-pi to pi)∫[sinx]dx=-(-pi to 0)∫-1dx - (0 to pi)∫0dx
(-pi to 0)∫1dx=pi

explanation given in the result

-pi to 0){sinx}dx+(0 to pi){sinx}dx
(-pi to 0)(1+sinxdx+(0 to pi)sinxdx
(-pi to 0)1dx+(-pi to 0)sinxdx+(0 to pi)sinxdx
(-pi to 0)1dx+(-pi to pi)sinxdx
second is odd function so zero
(-pi to 0)1 dx=pi

For a triangle ABC with angles A, B and C, such that 6A=3B=2C Match the following

28) tan(B/2)tan(C/2)+tan(C/2)tan(A/2)+tan(A/2)tan(B/2)
29) 4sin(A/2)sin(B/2)sin(C/2)
30) 4cos(A/2)cos(B/2)cos(C/2)
31) cot(A/2)cot(B/2)cot(C/2)

A) (√3-1)/2
B) 1
C) (3+√3)/2
D) √3(2+√3)

A=30°, B=60° and C=90°
A/2=15° B/2=30° C/2=45°

you know tan 30 find tan15=2-√3, sin15 and cos 15 and put them here

As seen in the figure

The number of division on main scale in which 0 of vernier scale is between 37 and 38

so main scale division is 37

As seen in vernier scale division 23rd division of vernier coincides with 60th main scale division

main scale reading is 37 and of vernier it is 23

Q42 A dielectric slab of thickness d is inserted in a parallel plate capacitor whose negative plate is at x=0 and positive plate is at x=3d. The slab is equidistant from the plates. The capacitor is given some charge.
STATEMENT-I: The electric potential increases continuously
STATEMENT-II: The direction of electric field remains same
Your Answer: c
Correct Answer: a
Score: -1
Explaination :
As the direction remains same throughout
the potential will increase

. When a dielectric is present in a capacitor, polarization of the molecules that make up the dielectric gives rise to a reduced electric field between the plates

so i think the electric field gets reduced

Yes electric field will surely get reduced

but the direction of electric field remains same

Q73 Given reaction 2HI(g) [eq] H2(g)+I2(g)
Statement-I: Concentration of I2 can be increased by increasing the concentration of HI
Statement-II: degree of dissociation of HI is affected only by change of temperature
Your Answer: c
Correct Answer: b
Score: -1
Explaination :
both are true second one is not the correct reason

sir only by change of temperature
volume ya fir HI ko daalne se koi farak nahin padega ??????????/

2HI(g) [eq] H2(g)+I2(g)
1 0 0
1-2α α α
total moles at equilibrium=1, let pressure at equilibrium is P
Kp=(αP/1)(αP/1)/[(1-2α)P/1)]²=α²/(1-2α)²

so the degree of dissociation depends only on Kp and hence on temperature

Q14 STATEMENT-I: The closest point on the curve y2-4x-2y+9=0 from the line 12x-4y-27=0 is (19/9,5/3)
STATEMENT-II: The tangent at (19/9,5/3) has a slope same as the given line
Your Answer: a
Correct Answer: d
Score: -1
Explaination :
This point is not the closest as the line intersects the curve
so minimum distance=0
and point will be the intersection of line and curve
then how we define closest point?????????

closest point is the point whose distance is minimum from the given line

Your Answer: (CH3)3CCl + AlCl3
Correct Answer: (CH3)2CCH2 + AlCl3 + HCl And (CH3)3CCl + AlCl3 And (CH3)2CHCH2Cl + AlCl3 And CH3CH2CH2CH2Cl + AlCl3
Score: 0
Explaination :
all form the carbocation
(CH3)3C+

sir iss mein benzene kahan se aaega????????

hehe

hmm benzene likhna to bhool hi gaye

fir bhi options dekh ke samajh me aa jaana chahiye tha ke benzene hai chhupa hua kahin pe

thik hai question cancel kar dete hai

nahi volume aur pressure changes se farak nahi padega

Q34 Reasoning Type

An ideal black body at room temperature is thrown into a furnace. It is observed that
STATEMENT-I: it is the darkest body at all times
STATEMENT-II: black body absorbs all heat at highest rate
Your Answer: a
Correct Answer: d
Score: -1
Explaination :
initially it is darkest and then brightest

Here only first statement is false

It is darkest initially when it is absorbing heat, then after sometime it starts to radiate at highest rate and so is the brightest

No its not very important

but sometimes knowing it can help you in solving it easily

just know about some of them

As

dx+dy=d(x+y)

ydx+xdy=d(xy)

(ydx-xdy)/y²=d(x/y)

(ydx+xdy)/xy=d(logxy)