Mathematics Questions

Let f be a polynomial function such that , x > 0 , f(6) = 37then

Consider the circle C : x2 + y2 – 6x – 8y – 11 = 0. Let a variable chord AB of the circle C subtend a right angle at the origin. If the locus of the foot of the perpendicular drawn from the origin on the chord AB is the circle x2 + y2 – αx – βy – γ =

Let a line L1 pass through the origin and be perpendicular to the linesis the point on L3 at a distance of 17 from the point of intersection of L1 and L2 , then (a + b + c)2 is equal to _______.

If then 9α is equal to_____.

The sum of squares of all real solution of the equationis equal to _______.

Let represent an ellipse with major axis along the y-axis, where f is a strictly decreasing positive function on R. If the set of all possible values of a is R-, then is equal to:

Let If f is continuous at , then the value of is:

Let be defined by , where , for , then the area of the region bounded by the curves y=g(x), 2y=2x-3, y=0, x=4 is:

Let y = y(x) be the solution of the differential equation +, where ,, . Then is equal to:

The value of the integral is equal to:

Let the foot of the perpendicular from the point (λ,2,3) on the line be the point (1,μ,2). Then the distance between the lines and is equal to:

Let , and a vector be such that . If , then is equal to:

For the function , consider the following statements: Statement I : f is differentiable for all x ∈ R. Statement II : f is increasing in . In the light of the above statements, choose the correct answer from the options given below:

Let and , where inverse trigonometric functions take only the principal values. Given below are two statements:Statement I : cos(α + β) > 0Statement II : cos(α) < 0In the light of the above statements, choose the correct answer from the options given

Let O be the vertex of the parabola y2=4x and its chords OP and OQ are perpendicular to each other. If the locus of the midpoint of the line segment PQ is a conic C, then the length of its latus rectum is:

If a straight line drawn through the point of intersection of the lines 4x+3y-1=0 and 3x+4y-1=0, meets the coordinate axes at the points P and Q, then the locus of the midpoint of PQ is:

A person has three different bags and four different books. The number of ways, in which he can put these books in the bags so that no bag is empty, is:

If then \alpha is equal to:

A set of four observations has mean 1 and variance 13. Another set of six observations has mean 2 and variance 1. Then, the variance of all these 10 observations is equal to:

A candidate has to go to the examination centre to appear in an examination. The candidate uses only one means of transportation for the entire distance out of bus, scooter and car. The probabilities of the candidate going by bus, scooter and car are

Let . If is a root of the equation , , then is equal to:

Let and then equals:

If the system of linear equations: x + y + z = 6, x + 2y + 5z = 10, 2x + 3y + , has infinitely many solutions, then the value of equals.

The number of values of z ∈ ℂ, satisfying the equations |z-(4+8i)| = √10 and |z-(3+5i)| + |z-(5+11i)| = 4√5 is:

Consider the relation R on the set {-2,-1,0,1,2} defined by (a,b) ∈ R if and only if 1+ab>0. Then among the statements: I. The number of elements in R is 17 II. R is an equivalence relation