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

The number of real solutions of the equation *x ^{2} – 3|x| + 2 = 0* is

If the sum of the roots of the quadratic equation *ax ^{2} + bx + c = 0* is equal to the sum of the squares of their reciprocals, then

*a/c, b/a*and

*c/b*in

If *a, b, c* are distinct +ve real numbers and *a ^{2} + b^{2} + c^{2} = 1* then what is the value of

*ab + bc + ca*?

The value of *a* for which one root of the quadratic equation *(a ^{2} – 5a + 3)x^{2} + (3a – 1)x + 2 = 0* is twice as large as the other is

If *p* and *q* are the roots of the equation *x ^{2} + px + q = 0*, then

Product of real roots of the equation *x ^{2} + |x| + 9 = 0*

Difference between the corresponding roots of *x ^{2} + ax + b = 0* and

*x*is same and a b, then

^{2}+ bx + a = 0

A particle is thrown upward vertically with initial speed where g is acceleration due to gravity on earth's surface.What is the maximum height attain by the particle?

Find the free fall time of a test mass on an object of Mass M from a height 2R to R?

A Constant force f is applied on a particle of mass 'm' which is initially at rest. As the particle starts moving a resistive force -bv begins to act on it.Speed of the particle at any instant of time 't' is?

## Let A be a square matrix all of whose entries are integers. Then which one of the following is true?

Let A be a square matrix all of whose entries are integers. Then which one of the following is true?

Let *a, b, c* be any real numbers. Suppose that there are real numbers *x, y, z* not all zero such that *x = cy + bz, y = az + cx and z = bx + ay*. Then *a ^{2} + b^{2} + c^{2} + 2abc* is equal to

Let *A* be a 2 × 2 matrix with real entries. Let* I* be the 2 × 2 identity matrix. Denote by tr(*A*), the sum of diagonal entries of *A*. Assume that *A ^{2} = I*.

**Statement1 :** If *A I* and *A – I*, then det *A = –1*.

**Statement2 :** If *A I* and *A – I*, then tr(*A*) 0.

Let A = .

If *|A ^{2}| = 25* the |

*a|*quuals to

If D = for x 0, y 0 then D is

Let A = and B = , *a, b N*. Then

If A and B are square matrices of size n × n such that A^{2} – B^{2} = (A – B)(A + B), then what will be always true?

The system of equations *ax + y + z = a – 1, x + ay + z = a – 1, x + y + az = a – 1* has no solutions, if *a* is

If *a ^{2} + b^{2} + c^{2} = – 2* and

then what is *f(x)* is a polynomial of degree?

If A = and I = , then which one of the following holds for all n ≥ 1, by the principle of mathematical induction

If *A ^{2} – A + I = 0*, then the inverse of

*A*is

If a_{1}, a_{2}, a_{3}, ...., a_{n}, ... are G.P., then the value of the determinant

is

Let A = and 10(B) = .

If B is the inverse of matrix A, then what is the ?

Let A = Ì„

The only correct statement about the matrix A is

If A = and A^{2} = , then

A motor boat going down stream over came a raft at a point A, t = 60 min later it turned back and after some time passed the raft at a distance l = 6.0 km from the point A. Find the flow velocity assuming the duty of the engine to be constant?

A current carrying wire heats a metal rod. The wire provides a constant power (P) to the rod. The metal rod is enclosed in an insulated container. It is observed that the temperature (T) in the metal rod changes with time (t) as

Where is a constant with appropiate dimension with is a constant with dimension of temperature .

The heat capacity of the metal is?

Divide 64 into two parts such that sum of the cubes of two parts is minimum.

What is maximum acceleration so that so that two block move together?

Two particles of masses m1 and m2 are placed 'd' distance apart. Due to gravitational attraction they move towards each other.What is speed of m1 when their separation reduces to d/2.

What is the Value of ?

If *w = *[*z / z - *(1/3)*i*] -and *|w| = 1*, then *z* lies on

If *z _{1}* and

*z*are two nonzero complex numbers such that |

_{2}*z*+

_{1}*z*| = |

_{2}*z*| + |

_{1}*z*|, then argz

_{2}_{1}– argz

_{2}is equal to

If *|z ^{2} – 1| = |z|^{2} + 1,* then

*z*lies on

If *z = x – iy* and *z ^{1/3} = p + iq*, then when will value of ?