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?

A ball is dropped from high rise platform at t =0 starting from rest.After 6 second another ball is thrown downwards from same platform with speed v.The two ball meets at t = 18s .find thee value of v (g = 10 m/s*s)

A uniform rope of length 'L' is hanging off the edge of a rough table having coefficient of static friction u.What should be minimum length of hanging part so that the rope starts sliding down?

Two particles of masses m1,m2 and charges q1,q2 placed r0 distance apart on a smooth horizontal surface.Due to electrostatic repulsion they move away from each other.Ratio of their kinetic energy at a later time is

A body is projected horizontally from the top of tower 100m high with a velocity at 9.8 m/s.Find the velocity with which hits the ground?

The quadratic equations *x ^{2} – 6x + a = 0* and

*x*have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then what is the common root?

^{2}– cx + 6 = 0

If the difference between the roots of the equation *x ^{2} + ax + 1 = 0* is less than , then the set of possible values of a is

All the values of *m* for which both roots of the equation *x ^{2} – 2mx + m2 – 1 = 0* are greater than –2 but less than 4, lie in the interval

If the roots of the quadratic equation *x ^{2} + px +q = 0* are tan30° and tan15°, respectively then what is the value of

*2 + q – p?*

If the equation *a _{n}x^{n} + a_{n-1}x^{n-1} + ... + a_{1}x = 0*,

*a*,

_{1 }0*n ≥ 2*, has a positive root

*x = a*, then the equation

*na*has a positive root, which is

_{n}x^{n-1}+ (n – 1)a_{n-1}x^{n-2}+ ... + a_{1}= 0

A projectile is fired from the ground level with a velocity of 500m/s at 30 degree to horizontal range and greatest hight to which it rises.What is the least speed with which could be projected in order to achieve the same

A projectile is fired from the level with velocity 150 m/s at 30 degree to the horizontal.Find its horizontal range. What will be the least speed to achieve some horizontal range?

From a flying aeroplane a body should be dropped in advance to hit the target why?

If the cube roots of unity are *1, w, w ^{2}* then the roots of the equation

*(x – 1)*, are

^{3}+ 8 = 0

Two simple pendulum have lengths l and 25l/16 . At t = 0 they are in same phase. After how many oscillations of smaller pendulum will they be again in phase for first time ?

A 0.1 kg mass is suspended from a wire of negligible mass. The length of the wire is 1 m and its cross- sectional area is 4.9 × 10–7 m2. If the mass is pulled a little in the vertically downward direction and released, it performs simple harmonic motion of angular frequency 140 rad s–1. If the Young's modulus of the material of the wire is n × 109 Nm–2, the value of n is

Time period of a simple pendulum of length 95 and amplitude 1 cm is 4 s. If amplitude is made 2 cm, then time period is

A spring pendulum is taken from pole to equator. Its time period

If one root of the equation *x ^{2} + px + 12 = 0* is 4, while the equation

*x*has equal roots, then the value of

^{2}+ px + q = 0*q*is

A hollow spherical ball is filled up with sand. Sand comes out through a hole at the bottom. Time period of oscillation?

If *(1 – p)* is a root of quadratic equation *x ^{2} + px + (1 – p) = 0* then its roots are

Let two numbers have an arithmetic mean 9 and geometric mean 4. Then the roots of the quadratic equation are