List of top Mathematics Questions

Consider the adjoining diagram: What is the minimum number of different colours required to paint the figure such that no two adjacent regions have same colour?
Consider the adjoining diagram:
Given below are two statements :
Statement I: If the roots of the quadratic equation \(x^2-4x-log_3a=0\) are real, then the least value of a is 1/81.
Statement II: The harmonic mean of the roots of the equation \((5+ \sqrt2)x^2 - (4+\sqrt5)x + (8+2\sqrt5) = 0\) is 2.
In the light of the above statements, choose the correct answer from the options given below:
If f and g are differentiable functions in (0, 1) satisfying f(0) = 2 = g(1), g(0) = 0 and f(1) = 6, then for some c ∈]0, 1[
Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
3 Assertion A: \(\int\limits_{-x}^{3}(x^3+5)dx=30\)
Reason R: f(x) = x3 +5 is an odd function
In the light of the above statements, choose the correct answer from the options given below:
Ankit owes ₹ 42,580 on his credit cards, but he could pay only ₹ 12,580. If the annual rate of compound interest is 10%, then how much will he owe after 4 years?
The mean deviation from the mean of the AP a, a+d, a+2d,..... a + 2nd is
The order of the permutation\(\begin{pmatrix} 1 & 2 & 3 & 4 & 5 & 6 \\   2 & 4 & 6 & 5 & 1 & 3 \end{pmatrix}\)is
The order of the given permutation \(\begin{pmatrix} 1 & 2 & 3 & 4 & 5 & 6& 7&8&9 \\2 &4& 6 &1 &7&3& 8&9 &5  \end{pmatrix}\) is:
Function f(x)=(x+1)cotx is continuous at x = 0, then the value of f(0) is
If \(\overrightarrow F=y^2\hat{i}+xy\hat{j}+xz\hat{k}\) and C is the bounding curve of the hemisphere x2+y2+z2=9,z>0, oriented in the positive direction, then value of \(\int\limits_C \overrightarrow F\cdot d\hat{r}\) is
If \(f(z)=\frac{1}{z^2-3z+2}\)is expanded in the region |z|<1, then
If the solution of \(x\frac{dy}{dx}+y=x^3y^6\) is \(\frac{1}{y^\alpha x^\beta}=\frac{\gamma}{2x^2}+C\), then value of \(\alpha+\beta+\gamma\) is
Let f(z) = u + iv be an analytic function, where u = x3-3xy2 +3x2 -3y2, then the imaginary part v of f(z) is
A beam is supported at its ends by supporters which are 12 meters apart. Since the load is concentrated at its centre, there is a deflection of 3 cm at the centre and the deflected beam is in the shape of a parabola. How far from the centre is the deflection 1 cm?
The average of 5 consecutive odd positive integers is 9. Then sum of smallest and greatest number is
The point (-1, 2, 7, 6) lies in which of the following half spaces corresponding to hyperplane 2x1+3x2+4x3+5x4 = 6
If A, G, H be respectively, the A.M., G.M., and H.M. of three positive numbers a, b, c; then the equation whose roots are these numbers is given by
The Value of \(lim_{n\rightarrow \infty }\bigg[\frac{2}{1}\bigg(\frac{3}{2}\bigg)^2\bigg(\frac{4}{3}\bigg)^3.....\bigg(\frac{n+1}{n}\bigg)^n\bigg]^{\frac{1}{n}}is\)
The general solution of \((D^2+6D+9)y=\frac{e^{-3x}}{x^2}\), where \(D\equiv \frac{d}{dx}\) is
(given that c1 and c2 are arbitrary constants)
The area of the region bounded by the curve x2=4y and the straight line x = 4y - 2 is
The given series \(\frac{x}{1.3}+\frac{x^2}{2.4}+\frac{x^3}{3.5}+......,(x\gt0)\)is convergent in the interval
The area of region bounded by the curve y2=x, the y-axis and between y = 2 and y = 4 is
If f(x) satisfies the conditions of Rolle's theorem in [1, 2] and f(x) is continuous in [1, 2], then \(\int_1^2f'(x)dx\) is equal to
Which of the following is incorrect?
The volume generated by the revolution of the cardiod r = a(1-cosθ) about x-axis is