List of top Mathematics Questions

Let \(\overrightarrow V\) be a vector field and f be a scalar point function, then curl \((f\overrightarrow V)\) is equivalent to________.

Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R):
Assertion (A): Sum of n terms of series 1²+3²+5²+... to n terms is \(\frac{n}{3}(4n^2-1)\).
Reasons (R): Sum of the squares of first a natural numbers 1², 2², 3²,....,n² is \(\frac{n(n+1)(2n+1)}6\).
In the light of the above Statements, choose the correct answer from the options given below:

Given below are two statements:
Statement I: The locus of the middle points of chords of the circle x²+ y² = a² which are parallel to the line y=mx is x-my = 0.
Statement II: The two tangents drawn from (4, 2) to x² + y² = 10 are perpendicular.
In the light of the above Statements, choose the most appropriate answer from the options given below :

Given below are two statements:
Statement I: The sum of the series 2{7^-1+3^-17^-3 +5^-1.7^-5 +....} is log_e(\(\frac{4}{3}\)).
Statement II: The value of e always lies between 2 and 3.
In the light of the above Statements, choose the most appropriate answer from the options given below :

A, B, C and D entered into a partnership. 'A' contributed one-third of the capital, 'B' contributed one-fourth, 'C' contributed one-fifth and 'D' contributed the rest. All four of them agreed to share profit in the ratio of their capital. What is the share of 'D' when total profit is ₹6000?

A point P(7,9) is reflected about line x = y. The new point P¹ after reflection is:

If tanα=1/3, tanβ=1/7 and 2α + β = m, then sin 2m is equal.

What is the volume of a 6m deep tank having rectangular shaped top 6mx4m and bottom 4mx2m (compound through the use of prismoidal formula)

The system matrix of a linear time invariant continuous time system is given by \(A= \begin{bmatrix} 0 & 1 \\ -4 & -5 \end{bmatrix}\)
What are the roots of characteristics equation.

Let f (x) be defined on [0, 3] by \(f(x) =   \begin{cases}     x,\text{if x is a rational number}       \\  3-x\text{, if x is an irrational number}   \end{cases}\) Then f(x) is continuous in the interval at:

Let f: G→H be a group homomorphism from group G into group H with kernel K. If the order of G, H and K are 50, 25 and 10 respectively then the order of f(G) is

Find the sum of following hexadecimal numbers (7CA)₁₆+ (4B2)₁₆ =?

Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R):
Assertion (A): If the equation x²+ px+q=0 has rational roots and p and q are integers, then the roots are integers.
Reasons (R): A quadratic equation has rational roots if and only if its discriminant is a perfect square of a rational number.
In the light of the above Statements, choose the most appropriate answer from the options given below :

Values of \(K\) for which the quadratic equation \(2x^2 - Kx + K=0\) has equal roots are:

A solar photovoltaic system feeds power to a motor of 1hp at the shaft. The motor has an efficiency of 85%. Each module has 40 multi crestline Silicone solar cells arranged in 9x5 matrix? The cell is 130 mm×130 mm and the cell efficiency is 13%. Calculate the number of photovoltaic modules required, assuming global radiation incident to the panel as 1kW/m²

The all values of z, such that
√2 sin z = coshβ + isinħβ, where β is real, are

For Matrix \(A = \begin{vmatrix} 1 & 1 & 3 \\ 1 & 5 & 1 \\ 3 & 1 & 1  \end {vmatrix}\), the sum and differences of maximum & minimum 1 eight value of Matrix are 4 and 8, then the eigen values for the Matrix A are. 

Given below are two statements:
Statement I: The gradient of a straight line is constant i.e. it does not change.
Statement II: The gradient of a straight line can be calculated by considering the coordinates of any two different points on the line.
In the light of the above Statements, choose the most appropriate answer from the options given below :

The mathematical statement regarding Divergence theorem which is true:

If the cost function and revenue of x unit of an item are given by C(x)=25x²-x and R(x)=4x. Then the number of item to be produced to have maximum profit is,

Let the point $P(\alpha, \beta)$ be at a unit distance from each of the two lines $L _1: 3 x -4 y +12=0$, and $L _2: 8 x +6 y +11=0$ If $P$ lies below $L _1$ and above $L _2$, then $100(\alpha+\beta)$ is equal to

The number of elements in the set \(\{n ∈ Z : n^2-10n+19| < 6\}\) is __.

If P, R, T are the areas of parallelogram. a rhombus and a triangle standing on the same base and between the same parallel lines, then which of the following is true?

For the two positive numbers \(a, b\), if \(a, b\) and \(\frac{1}{18}\) are in a geometric progression, while \(\frac{1}{a}, 10\) and \(\frac{1}{b}\) are in an arithmetic progression, then \(16 a+12 b\) is equal to