List of top Mathematics Questions

Solve for $y : 2y^{2}+6y+\frac{17}{2}=0$.

Prove that the function f(x) = 5x-3 is continuous at x = 0, at x = -3 and at x = 5.

Factorise: 27x3+y3+z3–9xy.

State whether the following statements are true or false. Justify. 
(i) For an arbitrary binary operation * on a set N, a * a=a ∀ a * N. 
(ii) If * is a commutative binary operation on N, then a * (b * c)= (a * b)* a

Find the equation of the parabola that satisfies the following conditions: Vertex \((0, 0) \)passing through \((2, 3) \)and the axis is along the x-axis

Find the equation of the circle passing through the points \((4, 1) \)and \((6, 5)\) and whose center is on line \(4x + y = 16.\)
The length, breadth and height of a room are 825 cm, 675 cm and 450 cm respectively. Find the longest tape which can measure the three dimensions of the room exactly.
A = {2,4,6,8}, B = {3,7,6,9}. R: A × B → A × B such that (a1, b1) R (a2, b2) ⇔ a1 + a2 = b1 + b2 where (a1, b1) ∈ A, (a2, b2) ∈ B. Find the number of elements in the relation.2)= 4, then find (a2 + b2 + c2).
If A is 3 x 3 matrix, det(3adj (2 adj A)) = 2-13. 3-10 and det(3adj (2A)) = 2-m. 3-n, then find 2m + 2n.d by 21?
A, B and C are given as
A = αî + 4j + 5k
B = 2î + 5j + 6k
C=A+B
|C| = | A - B |
Find the value of α and |C|2 is:
A circle passes through (0, 0) and (1, 0) and touches the circle x2 + y2 = 9. Then the locus of the centre of the circle is:
Tetrahedral dice having outcomes (1, 2, 3, 4) has 3 outcomes a, b, c (which are visible). Probability that ax2 + bx + c = 0 has real roots is m/n (m, n are coprime), then m + n =?
If solution of differential equation xdy - ydx = xy(xdy - ydx) and y(1) = 1 is α|y| = |x|e(xy - β) then (α + β) is equal to
A triangle is drawn inside a bounded region of y2 = 2x and x = 24. Then maximum area of triangle is
Bag X contains five one-rupee coins, four five rupee coins. Bag Y contains 4 one rupee and 5 five rupees. Bag Z contains 3 one-rupee coins and 6 five rupee coins. If 1 rupee coin is selected at random, what is the probability it is drawn from bag Y?
A circle x2 + y2 = 8 and a parabola y2 = 2x are given. Find area bounded by these two curves in first quadrant which lie inside the circle and outside the parabola.
Two points (5, 2) and (2, a). Line passes through these points makes an angle of π/4 at origin. The product of all values of a is equal to
sum of elements of 10th row,Then the sum of elements of 10th row.
Number of 5 letters words made from the word “MATHEMATICS” is equal to
3 blue balls and 4 yellow balls are in a box. 3 balls are drawn at random. Let variance and mean be X & Y respectively then value of 3X + 4Y is:
The area bounded by y = min{sin x, cos x} and x-axis in -π ≤ x ≤ π interval is equal to (in sq. units):
if \(y=\int\frac{e^{\tan x}dx}{\cos^2x(1+e^{2\tan x})}\) and y(0)=6 then y\(\frac{\pi}{4}\) is equal to
If C1: (x-α)2 +(y-β)2 =r12, c2: (x-6)2+ (y - 15/2)2 = r22 touches each other at (6, 6). If line joining centres of c1 & C2 is divided by (6, 6) in 2: 1 internally, then (α + β) + 4(r12 +r22) is equal to:
Let f(x) = cosx - x + 1, x ∈ [0,π], then
Integrate the function: \(\frac{sin^8x-cos^8x}{1-2sin^2xcos^2x}\)