List of top Mathematics Questions

An open box with a square base is to be made out of a given quantity of a cardboard of area $c^2$ square units. The maximum volume of the box is (in cubic units)
An equilateral triangle is inscribed in the parabola $y^2 = 4x.$ If one vertex of this triangle is the vertex of the parabola, then the length of a side of this triangle is ...........
An equation of the plane passing through the points $(3, 2, -1)$, $(3, 4, 2)$ and $(7, 0, 6)$ is $5x + 3y - 2z = \lambda$, where $\lambda$ is
An edge of a variable cube is increasing at the rate of 10cm/sec. How fast the volume of the cube will increase when the edge is 5 cm long ?
An anti-aircraft gun takes a maximum of four shots at an enemy plane moving away from it. The probability of hitting the plane at the first, second, third and fourth shot are 0.4, 0.3, 0.2 and 0.1 respectively. The probability that the gun hits the plane is:
An A.P., a G.P. and a H.P. have the same first and last terms and the same odd numbers of terms, the middle terms of the three series are in
Amongst all pairs of positive numbers with product $256$, find those whose sum is the least.
All the letters of the word are arranged in different possible ways. The number of such arrangements in which no two vowels are adjacent to each other is
After simplification, what is the number of terms in the expansion of $[(3x + y)^5]^4 - [(3x-y)^4]^5$ ?
ABCD is a convex quadrilateral. 3, 4, 5 and 6 points are marked on the sides AB, BC, CD and DA respectively . The number of triangles with vertices on different sides is
ABC is a triangle and AD is the median. If the coordinates of A are ( 4, 7, - 8)and the coordinates of centroid of the triangle ABC are (1, 1, 1), what are the coordinates of D?
A wire of length $36 \,m$ is to be cut into two pieces. One of the pieces is to be made into a square and the other into a circle. What should be the lengths of the two pieces, so that the combined area of the square and the circle is minimum?
A vertical lamp-post 6 m height stands at a distance of 2 m from a wall, 4 m high. A 1 -5 m tall man starts to walk away from the wall on the other side of the wall in line with the lamp-post. The maximum distance to which the man can walk, remains in the shadow is
A variable plane which remains at a constant distance 3p from the origin cut the coordinate axes at A, B and C. The locus of the centroid of triangle ABC is
A urn contains 9 red, 7 white and 4 black balls. Out of them, one is drawn at random. The probability that the ball drawn will be a red or black, is
A tree is broken by wind and its upper part touches the ground at a point 10 metres from the foot of the tree and makes an angle of 45$^\circ$ with the ground. The entire length of the tree is
A town has total population $25000$, out of which $13000$ read ??he Hindustan Times and $10500$ read ??he Indian Express?
A tower subtends an angle of 30$^\circ$ at a point on the same level as the foot of the tower. At a second point h metres above the first, the depression of the foot of the tower is 60$^\circ$. The horizontal distance of the tower from the point is.
A teaparty is arranged for 16 people along two sides of a large table with 8 chairs on each side. Four men want to sit on one particular side and two on the other side. The number of ways in which they can be seated is
A student has to answer $10$ questions, choosing atleast $4$ from each of parts $A$ and $B$. If there are $6$ questions in Part $A$ and $7$ in Part $B$, in how many ways can the student choose 10 questions ?
A student is allowed to select at most $n$ books from a collection of $(2n + 1)$ books. If the total number of ways in which be can select a book is $255$, then the value of $n$ equals to
A straight line is such that the sum of the reciprocals of its intercepts on the axes is K.Then it passes through the fixed point with co-ordinates
A straight line through the point A (3, 4) is such that its intercept between the axes is bisected at A. Its equation is
A square piece of tin of side $24\, cm$ is to be made into a box without top by cutting a square from each corner and folding up the flaps to form a box. What should be the side of the square to be cut off so that the volume of the box is maximum?
A square of side a lies above the x-axis and has one vertex at the origin. The side passing through the origin makes an angle $\alpha\left(0 < \alpha < \frac{\pi}{4}\right)$ with the positive direction of x-axis. The equation of its diagonal not passing through the origin :