List of top Mathematics Questions

The regression analysis confined to the study of only two variables at a time, is called as

Any square matrix A can be expressed as:
1. The product of a symmetric and a skew-symmetric matrices. 
2. The division of a symmetric matrix by a skew-symmetric matrix. 
3. The sum of a symmetric and a skew-symmetric matrices. 
4. The subtraction of a symmetric from a skew-symmetric matrix.

The function F(x) = [x] at x = 0 is

If \(∫^{0.15}_{-0.15 }|100x^2-1|dx=\frac{k}{3000,}\)  then k is equal to____.

Let the plane x + 3y – 2z + 6 = 0 meet the co-ordinate axes at the points A,B,C. If the orthocentre of the triangle ABC is \((α,β,\frac{6}{7}),\) then 98(α + β)² is equal to___.

Two circles in the first quadrant of radii r₁ and r₂ touch the coordinate axes. Each of them cuts off an intercept of 2 units with the line x + y = 2. Then \(r^2_1+r_2^2– r_1r_2\) is equal to_____.

Let the digits a, b, c be in A.P. Nine-digit numbers are to be formed using each of these three digits thrice such that three consecutive digits are in A.P. at least once. How many such numbers can be formed?

(S1): (p⇒q)∧(p∧((~q)) is a contradiction and
(S2): (p∧q)v((~q)v((~p)∧ q)v (p∧(~q))v((~p)∧ (~q)) is a tautology

Match List I with List II

	List I		List II
A	Spring constant	I	[T-1]
B	Angular speed	II	[MT-2]
C	Angular momentum	III	[ML2]
D	Moment of Inertia	IV	[ML2T-1]

Choose the correct answer from the options given below:

If the point \((α ,\frac{7√3}{3} )\) lies on the curve traced by the mid-points of the line segments of the lines x cosθ + y sinθ=7,θ∈( \(0,\frac{π}{2}\) ) between the coordinates axes, then α is equal to 

Let P \((\frac{2√3}{√7},\frac{6}{√7} )\), Q,R and S be four points on the ellipse 9x² + 4y² = 36. Let PQ and RS be mutually perpendicular and pass through the origin. If  \(\frac{1}{ ( P Q )^2}  +\frac{ 1}{ ( R S ) ^2} =\frac{ P }{q}\),  where p and q are coprime, then p + q is equal to

Let a, b, c be three distinct real numbers, none equal to one. If the vectors \(a\hat{i}+\hat{j}+\hat{k},\hat{i}+b\hat{j}+\hat{k}\) and \(\hat{i}+\hat{j}+c\hat{k}\) are coplanar, then \(\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}\) is equal to 

The area of the region enclosed by the curve y = x³ and its tangent at the point (-1, -1) is

If the local maximum value of the function f( x )=\((\frac{√3e}{2 sin x} )^{ sin^2x}\) ,\(  x ∈ ( 0,\frac{π}{2} )\),  is \(\frac{k}{e}\), then \((\frac{k}{e})^8+\frac{k^8}{e^5}+k^8 \) is equal to

Let A=\(\begin{bmatrix} 1 & \frac{1}{51} \\ 0 & 1\end{bmatrix}\). If B=\(\begin{bmatrix} 1 & 2 \\ -1 & -1\end{bmatrix}\)A \(\begin{bmatrix} -1 & -2 \\ 1 & 1\end{bmatrix}\), then the sum of all the elements of the matrix \(\sum^{50}_{n=1}B^n\) is equal to

Find the value of
16÷4×4−3+2

Out of the three numbers, first number is twice of the second number and thrice of the third number. The average of their reciprocals is 1/6. The numbers are:

A fruit vendor bought apples for 6,000. He sold 40% stock with 25% profit, another 40% stock with 15% profit and the rest with 10% profit. Find his profit percentage.

A cardboard box of dimensions 80 cm x 60 cm x 75 cm is to be constructed. Find the cardboard required (in m^2) for the box.

Two natural numbers are in the ratio 3:5 and their product is 2160. The smaller of the numbers is

If an article is sold at 300 percent profit, then the ratio of its cost price to its selling price will be

How much time will it take for an amount of Rs.450 to yield Rs.81 as interest at 4.5% per annum of simple interest?

Process of indicating addition [3+2=5] at number system

Choose the correct answer from the options given below:

The set of all values of $a^2$ for which the line $x+y=0$ bisects two distinct chords drawn from a point $P \left(\frac{1+a}{2}, \frac{1-a}{2}\right)$ on the circle $2 x^2+2 y^2-(1+a) x-(1-a) y=0$, is equal to :