A swimmer wants to reach to a point just opposite on the other bank of the river. How should he swim and why?

A ball is dropped gently from the top of tower and another ball is thrown horizontally at same time.Which ball will hit the ground first?

A stone is projected horizontally with 20 m/s from top of a tall building. Calculate its position and velocity after 3 sec neglecting the air resistance?

A stone is projected horizontally with 20 m/s from top of a tall building. Calculate its position and velocity after 3 sec neglecting the air resistance?

If the displacement of a body is proportional of square of time, state whether the body is moving with uniform velocity or uniform acceleration?

Two stones P and Q of different masses m and 2m respectively are dropped simultaneously from top of a tower and reach the ground with different energies . Which one is faster?

Can an object with constant acceleration reverse its direction of travel ? Explain

If the constant of gravitation (G), Planck's constant (h) and the velocity of light (c) be chosen as fundamental units. The dimensions of the radius of gyration is

The magnitude of any physical quantity

What is the relationship between dyne and newton of force?

Wavelength of ray of light is 0.00006 m. It is equal to

X = 3YZ*Z find dimensions of Y in (MKSA) system, if X and Z are the dimensions of capacity and magnetic field respectively

Number of particles crossing unit area perpendicular to X-axis in unit time is given by

n =

are number of particles per unit volume in the position x1 and x2. Find dimensions of D called as diffusion constant

If L, C and R represent inductance, capacitance and resistance respectively, then which of the following does not represent dimensions of frequency?

A projectile is launched with an initial velocity of 30 m/s at angle of 60 degree above the horizontal. Calculate the magnitude and direction of its velocity 5s after launch?

An object is dropped from the top of the tower of height 156.8 m and the same time another object is thrown vertically upward with velocity of 78.1 mm/s from the foot of the tower, find when and where two object meet?

A cannon fires successively two shells from the same point with velocity v0 = 250m/s ; the first at the angle =60° and the second at the angle =45° to the horizontal, the azimuth being the same. Neglecting the air drag, find the approximate time interval between firings leading to the collision of the shells (g = 9.8 m/s2.)

A block of mass m is pulled on an incline surface having coefficient of friction = 1 & angle of inclination = 30°, with the horizontal, such that required external force is minimum. The angle made by this force with the incline is :

A particle is projected with speed 30m/s at angle 22.5° with horizontal from ground as shown. AB and CD are parallel to y-axis and B is highest point of trajectory of particle. CD/AB is

Each of the two block shown in the figure has mass m. The pulley is smooth and the coefficient of friction for all surfaces in contact is . A constant horizontal force P applied in two cases shown in such a way that block A start just sliding then the value of minimum force P in case-I and case-II is :

Let T_{r} be the *r ^{th}* term of an A.P. whose first term is

*a*and common difference is

*d*. If for some positive integers

*m, n, m n, Tm = 1/n*and

*Tn = 1/m,*then

*a – d*equals

Let *R _{1}* and

*R*respectively be the maximum ranges up and down on an inclined plane and R be the maximum range on the horizontal plane. Then,

_{2}*R*,R,

_{1}*R*are in

_{2}

If *x _{1} , x_{2} , x_{3}* and

*y*are both in G.P. with the same common ratio, then the points

_{1}, y_{2}, y_{3}*(x*and

_{1},y_{1}), (x_{2},y_{2})*(x*

_{3}, y_{3})

The sum of the series is equal to

Let *f(x)* be a polynomial function of second degree. If *f(1) = f(–1)* and *a, b, c* are in A.P., then and are in

If the system of linear equations *x + 2ay + az = 0*,* x + 3by + bz = 0*, *x + 4cy + cz = 0* has a nonzero solution, then *a, b, c*

Fifth term of an GP is 2, then the product of its 9 terms is

What is the value of 2^{1/4 }**. **4^{1/8} **.** 8^{1/6 }... ?

Sum of infinite number of terms in GP is 20 and sum of their square is 100. The common ratio of GP is

1^{3} – 2^{3} + 3^{3} – 4^{3} + ... + 9^{3} =

If 1, log_{9}(3^{1-x }+ 2), log_{3}[4.3^{x}– 1] are in AP. then x equals

**Statement1 :**

**Statement2 :**

What is the correct choice between Statement1 (Assertion) and Statement2 (Reason)?

In the binomial expansion of *(a – b) ^{n}, n ≥ 5*, the sum of 5

^{th}and 6

^{th}terms is zero, then

*a/b*equals

For natural numbers *m, n* if *(1 – y) ^{m}(1 + y)^{n }= 1 + a_{1}y + a_{2}y^{2} + ...,* and

*a*then what is

_{1}= a_{2}= 10,*(m, n)*?

If the expansion in powers of x of the function is a_{0} + a_{1}x + a_{2}x^{2} + a_{3}x^{3} + ..., then what is a_{n}?

The sum of the series

If *x* is so small that *x ^{3}* and higher powers of x may be neglected, then may be approximated

If the coefficient of *x ^{7}* in equals the coefficient of

*x*in then what is the relation between

^{-7}*a*and

*b?*

If *s _{n} =* and

*t*, then

_{n}=*t*is equal to

_{n}/ s_{n}

What is the coefficient of x^{n }in the expansion of (1 + x)(1 – x)^{n}?

The coefficient of the middle term in the binomial expansion in powers of x of *(1 + ax) ^{4}* and of

*(1 – ax)*is the same if a equals

^{6}

What is the number of integral terms in the expansion of ?

If *x* is positive, what is the first negative term in the expansion of *(1 + x) ^{27/5}*?

If the sum of the coefficients in the expansion of *(a + b) ^{n}* is 4096, then what is the greatest coefficient in the expansion?

The coefficients of *x ^{p}* and

*x*in the expansion of

^{q}*(1 + x)*are

^{p+q}

The coefficients of *x ^{p}* and

*x*in the expansion of

^{q}*(1 + x)*are

^{p+q}

*r* and *n* are positive integers *r > 1, n > 2* and coefficient of *(r + 2) ^{th}* term and 3r

^{th}term in the expansion of (1 + x)

^{2n }are equal, then n equals

The positive integer just greater than (1 + .0001)^{10000} is

A body falls freely from the top of a tower and during the last second of its fall it falls through 25 m. Find the height of tower?

A ball is thrown velocity with a velocity V at an angle theta with the horizontal .Can an another angle of projection achieve the some horizontal range.Justify your answer?