Consider a body as shown in figure, consisting of two identical bulls, each of mass M connected by a light rigid rod. If an impulse J=MV is imparted to the body at one of its ends, what would be its angular velocity. What is V ?

The sides of a triangle are $sin space alpha comma cos space alpha$ and $square root of 1 plus sin space alpha cos space alpha end root$ for some $0 less than alpha less than pi over 2$ .Then the greatest angle of the triangle is

The law of cosines generalizes the Pythagorean formula to all triangles. It says that c², the square of one side of the triangle, is equal to a² + b², the sum of the squares of the the other two sides, minus 2ab cos C, twice their product times the cosine of the opposite angle. When the angle C is right, it becomes the Pythagorean formula.

The sides of a triangle are $sin space alpha comma cos space alpha$ and $square root of 1 plus sin space alpha cos space alpha end root$ for some $0 less than alpha less than pi over 2$ .Then the greatest angle of the triangle is

A cubical block of side a is moving with velocity V on a horizontal smooth plane as shown in figure. It hits a ridge at point O. The angular speed of the block after it hits 0 is

A uniform rod of length 2 L is placed with one end in contact with horizontal and is then inclined at an angle $alpha$ to the horizontal and allowed to fall without slipping at contact point. When it becomes horizontal, its angular velocity will be.....

If the sides of a triangle are in the ratio $x colon y colon square root of x squared plus x y plus y squared end root$ then greatest angle is

A straight rod of length L has one of its ends at the origin and the other end at x=L If the mass per unit length of rod is given by Ax where A is constant where is its center of mass.

In $straight triangle A B C text , if end text c squared equals a squared plus b squared comma 2 s equals a plus b plus c$ then $4 s left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis equals$

s denotes the semi-perimeter of the triangle ABC, ∆ its area and R the radius of the circle circumscribing the triangle ABC i.e., R is the circum-radius.

In $straight triangle A B C text , if end text c squared equals a squared plus b squared comma 2 s equals a plus b plus c$ then $4 s left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis equals$

s denotes the semi-perimeter of the triangle ABC, ∆ its area and R the radius of the circle circumscribing the triangle ABC i.e., R is the circum-radius.

A small disc of radius 2 cm is cut from a disc of radius 6 cm. If the distance between their centrer is 3.2 cm, what is the shift in the center of mass of the disc...

Let be the moment of inertia of a uniform square plate about an axis AB that passes through its center and is parallel to two of its sides CD is a line in the plane of the plate that passes through the center of the plate and makes an angle of Q with AB. The moment of inertia of the plate about the axis CD is then equal to....

If $square root of 3 s i n invisible function application theta plus c o s invisible function application theta$ is positive, then $theta$ lies between

If $tan space A plus tan space B plus tan space C equals 3 square root of 3$ then the Δ^k is

If $A plus B plus C equals 720 to the power of ring operator end exponent$ then $Tan invisible function application A plus Tan invisible function application B plus Tan invisible function application C$ =

If $C o s invisible function application A equals negative 3 divided by 5 comma S i n invisible function application B equals fraction numerator 7 over denominator 25 end fraction$ and $90 to the power of ring operator end exponent less than A less than 180 to the power of ring operator end exponent$ , $0 to the power of ring operator end exponent less than B less than 90 to the power of ring operator end exponent$ then $T a n invisible function application left parenthesis A plus B right parenthesis equals$

In a $capital delta to the power of l e end exponent A B C$ If $T a n invisible function application fraction numerator A over denominator 2 end fraction equals fraction numerator 5 over denominator 6 end fraction comma T a n invisible function application fraction numerator B over denominator 2 end fraction equals fraction numerator 20 over denominator 37 end fraction$ then $T a n invisible function application fraction numerator C over denominator 2 end fraction equals$

Assertion (A): If $c o s invisible function application left parenthesis x minus y right parenthesis equals 3 c o s invisible function application left parenthesis x plus y right parenthesis$ then $cot invisible function application x coty equals 2$
Reason (R): If $fraction numerator a over denominator b end fraction equals fraction numerator c over denominator d end fraction$ then $fraction numerator a plus b over denominator a minus b end fraction equals fraction numerator c plus d over denominator c minus d end fraction$