If the roots of the quadratic equation x2 + px +q = 0 are tan30° and tan15°, respectively then what is the value of 2 + q – p?
If the equation anxn + an-1xn-1 + ... + a1x = 0, a1 
0, n ≥ 2, has a positive root x = a, then the equation nanxn-1 + (n – 1)an-1xn-2 + ... + a1 = 0 has a positive root, which is
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, w2 then the roots of the equation (x – 1)3 + 8 = 0, are
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 x2 + px + 12 = 0 is 4, while the equation x2 + px + q = 0 has equal roots, then the value of 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 x2 + 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 x2 – 3|x| + 2 = 0 is
If the sum of the roots of the quadratic equation ax2 + 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 a2 + b2 + c2 = 1 then what is the value of ab + bc + ca ?
The value of a for which one root of the quadratic equation (a2 – 5a + 3)x2 + (3a – 1)x + 2 = 0 is twice as large as the other is
If p and q are the roots of the equation x2 + px + q = 0, then
Product of real roots of the equation x2 + |x| + 9 = 0
Difference between the corresponding roots of x2 + ax + b = 0 and x2 + bx + a = 0 is same and a 
b, then
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 a2 + b2 + c2 + 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 A2 = 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 |A2| = 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 A2 – B2 = (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 a2 + b2 + c2 = – 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 A2 – A + I = 0, then the inverse of A is
If a1, a2, a3, ...., an, ... 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 A2 = 
, 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 z1 and z2 are two nonzero complex numbers such that |z1 + z2| = |z1| + |z2|, then argz1 – argz2 is equal to
If |z2 – 1| = |z|2 + 1, then z lies on
If z = x – iy and z1/3 = p + iq, then when will value of 
?