Hence option A is correct

Acceleration=force/mass , in above mentioned case gravity is acting continuously on the object hence acceleration with be non zero, and at the highest point object will be in momentarily rest hence velocity will be zero. Hence the correct option is A

Correct answer is B. In velocity time graph , velocity is plotted against time . If two curve coincide then they will share same co-ordinates I.e same velocity at a time instant . These two curves may have different slope at that point i.e they can have different acceleration (slope of v-t curve is acceleration) , hence option B is correct

Option B is correct because dv/dt = acceleration

For constant speed there won't be any tangential acceleration. So there will be only centripetal acceleration and it can be given by a=v^2/r =6*6/.3 = 120m/s^2

Pi/6

For a safe turning centripetal acceleration must be equal to acceleration due to friction. .1*g=v^2/r .1*10=v^2/400 V=20

Option D

Fictitious force stands for pseudo force , it is applied when observer is in non inertial frame. When observer is in circular motion then it apply a pseudo force to study the motion of other objects, it is known as centrifugal force

False , option C It acts towards center

Option D ,it happens because friction coefficient reduces

For maximum velocity mv^2/r = maximum tension 5*v^2/10= 160 V=√320 = 17.88 Option A

Option C Impulse(P)=m*v For a given object m is constant dP/dt= mdv/dt =ma = force

dP=fdt Hence unit of momentum is Newton second

Option C Inertia

Option C This happens due to decrease in friction coefficient

C , same height because deceleration and initial velocity is same for both objects

Option A Because direction is continuously changing is circular motion hence velocity will change continuously

SOQ=2*70=140 SOR=2*60=120 HENCE , OQR =360-140-120=100

Answer is Zero, since friction force depends on normal between surfaces in touch, above mentioned case is an example of free fall motion so normal force will be zero hence friction is Zero.

Let E1 =Neither blue nor green ,means ball should be yellow P(E1) = number of favorable ways/total number of ways =7/18 Let E2= ball should not be blue , Means it should be either yellow or green P(E2) = favorable ways /total number of ways = 12/18 =2/3

Answer is 12

Number of students good at mathematics= 25*72/100=18 Hence number of students not good at mathematics=25-18=7

Answer is 60

Probability of ace =no of favorable ways/total number of ways = 4/52=1/13 Probability of not red =1-probability of red =1-26/52 = 1/2

Using AA similarity (COA=BOD , OCA=ODB) OCA and ODB are similar triangles Hence area(OCA)/area (ODB) =( OC/OD)^2 60/area(ODB)=( 5/8)^2 area(ODB) = 153.6 cm^2

Refer to the image

Refer to image

Correct answer is A 8

Correct answer is D

Refer the image attached for explanation

Option B is correct

Refer the picture

Answer is D

Answer is D

Area of shaded region=22/7(R^2-14^2)=770 R^2=441 R=21

Side of square=4+6+2=12cm The area of circle = 22/7*r^2 Where r is 3 So 22/7*3*3 28.29cm^2 of square is (side)^2 =12*12=144 Areas of shaded region=144-28.29 =115.71

Option D is correct:- (201.14 cm^2) area = pi*(R^2 - r^2)

Refer to the picture

Option D

Correct answer is A

Correct answer is B

Option C is correct I.e 47.32 m Distance between the feet of tower and building = 30/√3 m = 10√3 m = 17.32 m . So, the extra height of tower than the building = 17.32 m . So total height of the tower = (30 + 17.32) m = 47.32 m .

correct answer is (17.94 cm), volume is assumed to be constant while melting and forming another object, so using this logic Volume of the hollow cylinder = Volume of the cone pi*(81^2 - 80^2)*200 = (1/3)*pi*r^2*300 . => r^2 = 322 . Hence, r = √322 = 17.94 cm

Let slant height of cone =L L =√(3.5^2 + 12^2) cm = 12.5 cm . Total surface area of the figure = CSA of the conical part +CSA of the hemispherical part = pi*3.5*12.5 + 2pi*3.5^2 = pi*(43.75 + 7) cm^2 = 159.5 cm^2

Volume of cone=1/3*pi*r^2*h =1/3 *pi*3*3*3 Volume of pipe =pi*r^2*h = Pi*3.5*3.5*10 Number of cone= 3.5*3.5*10*3/3*3*3 = 13

Option C

X=120/2=60 Y=180-60=120 2Y-3X =2*120-3*60 = 60deg

a=6x+r, where, r = 0,1,2,3,4,5; and a is an integer . a' is an odd number r= 1,3,5. Hence number is 6x+1', '6x+3' and '6x+5'.

Look for point of intersection between curve and X axis . a=3,b=1, c=2 , d=0

√2 = 1.414... √3 = 1.732. Hence select any 10 terminating decimals between these two Like 1.5,1.51,1.52,1.53,1.54,1.55,1.56,1.57,1.58,1.59

For zero we need (5*2) pairs. But in case of 6^ it's prime factorisation is 2*3 hence (2*3)^n cannot end with zero

Make sure that in p/q p and q are co primes , once verified look for prime factors of q , if it contains 2^m*2^n where m and n both are not zero and m,n are non negative integer

Try to deduce this reasoning practically , then you will realize that lcm is the answer hence Lcm=(18,12)= 36 min so they will after 36 minute.

As per question , then number will be factor of 33-3=30, 45-5=40, 64-4=60 ,ie the greatest factor is 10

Follow the pic

mean = (5+ 3+ 7+ 5+ 4+ 3+ 2+ 1+ 3+ 9+ 3+3)/12 =48/12= 4 For median arrange data in increasing order 1,2,3,3,3,3,3,4,5,5,7,9 number of terms = 12 (even) ,so, median = average of 6th and 7 th term =(3+3)/2 = 3

New average= (m*n +n*p)/n = m+p

Even numbers between 21 and 43 are: 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42 Thus, Median = 6th number ,i.e middle number of standard sequence. = 32

It is 11 because of it's end with 1 so cube root also ends with 1.

Let no of matches be x Then x *40/100= 10 => x=25 matches

Using formula (i) ( 51+49)(51-49)=100×2=200 (ii) (1.02+0.98)(1.02-0.98) =2×.04=.08 (iii) (153+147)(153-147) =300×6 =1800 (iv) (12.1+7.9)(12.1-7.9) =20×4.2=84

11.4*5-10*4 = 57-40=17

Let the digits are 1,2,97 So median is 2