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Q. A circular disc of radius R is rolling on a horizontal surface. Find the distance travelled by a point P lying on the circumference of the cirle in one complete rotation.

Come on goiitians, try this!!!

Q. A uniform circular disc of mass M and radius R is suspended vertically from a
horizontal axis AB fixed at a distance R/2 above the centre C of the disc. The disc can rotate freelly about the axis AB. A particle of mass m moving horizontally with
velocity v strikes the point 'P' lying vertically below the centre and on the edge of the disc.Find the minimum value of v so that the disc can make full rotation about the axis AB. [Take (M/m)=3 and e=0.5].

SALUTES ASSURED TO ALL CORRECT ANSWERS.

Q. The condition for the two tangents drawn from a point to the parabola y²=4ax,

to become normals to the parabola x²=4by is that a²>8b^2.prove this.

log _X2 . log _2x2. log ₂4x > 1

= 1 1 (log ₂4 + log₂x) >1

------------------ -------------

log ₂x log ₂2x

log ₂2x= (log ₂2 + log ₂x)= (log ₂x + 1)

Substitute

log₂ x=y and solve the equation.

The answer is ⁿ⁺¹C_r+1.

Q. ⁿC_r + ^n-1C_r + ^n-2C_r+ ........ ^rC_r=

Salutes assured for all correct answers

come on, goiitians!!!try this.rates assured

come on, goiitians!!!try this.rates assured

come on, goiitians!!!try this.rates assured

As

/16 + 7

/16=

/2

tan ² 7

/16 = cot²pi/16

The required sum reduces to

(tan²pi/16 + cot²pi/16) + (tan²2pi/16+cot²2pi/16)......+ 1 {because tan²4pi/16=1}

= (tan pi/16 + cot pi/16)²+(tan2pi/16+cot2pi/16)²+.............+1-2-2-2

= 4 4

------------------------- + ----------------------------- + .............-5

4sin²pi/16cos²pi/16 4sin²2pi/16cos²2pi/16

= 4 4 4

------------ + ----------------+ --------------------- - 5

sin²pi/8 sin²pi/4 sin²3pi/8

= 4{ 1 1 } + 8 - 5

------------ + -------------

sin²pi/8 sin²3pi/8

On solving this we get

32{sin²pi/8 + sin²3pi/8} + 8 - 5

As sin 3pi/8=cospi/8

sin²pi/8 + sin²3pi/8=1

Therefore

= 32 + 8 - 5

=35

Hence Proved.

Nudge me for any doubt.

Q. If mod(cos

{sin

+(sin²theta + sin²alpha)}<=k for all theta, then find the value of k in terms of sin alpha

come on goiitians, try it.....

Q. Prove that _{[r=1 ]}

^{[k ]} (-3)^r-1 ³ⁿC_2r-1= 0 where k=3n/2 and n is even positive

integer.

Q. If modz<=1, mod w<=1,

show that mod(z-w)² <= (modz-modw)² + [arg (z) - arg(w)]²