List of top Mathematics Questions

A loan of ₹200000 at the interest rate of 6% p.a. compounded monthly is to be amortized by equal payments at the end of each month for 5 years. The monthly payment is:
[Given (1.005)-60 = 0.74137220]
The sum of order and degree of the differential equation\[\frac{\{1+(\frac{dy}{dx})^2\}^\frac{5}{2}}{\frac{d^2y}{dx^2}}=p\]is:
If \(\frac{d}{dx}(2\frac{d^2y}{dx^2})^3= 7\), then the sum of order and degree of the differential equation is:
A 300 m long train is moving at a speed of 60 km/h. In what time will it cross a single pole?
A metallic sphere of radius 8 cm is melted to form a cone with radius same as that of sphere. What is the height of the cone (in cm) ?
\(f(x) = \begin{cases} 3x-8 & \text{if } x \leq 5 \\ 2k & \text{if } x > 5 \end{cases}\)
Let \(tan^{-1}y=tan^{-1}x+tan^{-1}(\frac{2x}{1-x^2})\). Then y is:
If \(\begin{bmatrix}        x+4 & 2x & 2x           \\[0.3em]        2x & x+4           & 2x\\[0.3em]        2x   & 2x & x+4      \end{bmatrix}=\lambda(4-x)^2\),then value of \(\lambda \) is
The value of \(sin^{-1} [cos(sin^{-1}\frac {\sqrt{3}}{2})]\) is:
If \(y=log[\frac{x^2}{e^2}]\) then value of \(\frac{d^2y}{dx^2}\) is:
The value of the sum of 10 term of the series
\(S_{10}=\frac{1}{2^2-1}+\frac{1}{4^2-1}+\frac{1}{6^2-1}+...\)
Simplify \(\sqrt{54-\sqrt{20+\sqrt{32-\sqrt{49}}}}\)
Let A and B be symmetric matrices of same order, then which of the following statement is true?
Find the area of an equilateral triangle each of whose sides measures 4 cm :
The area of the region bounded by the curve \(y=\sqrt{3x+10}\), x-axis and between the lines x = -3 and x = 2 is equal to :
The inverse of the function f: R→R given by f(x) = 2x +7 is:
The value of \(\lambda\), for which the projection of \(\vec{a} = \lambda \hat{i} + \hat{j} +4 \hat{k}\) on \(\vec{b} =2\hat{i} +6 \hat{j} +3\hat{k}\) is 4 units
A 180 m long train crosses a man standing on the platform in 6 seconds. What is the speed of the train?
Set A has elements and the set B has 6 elements, then the number of injective mappings that can be defined from A to B is :
What is emprical relationship between mean, median and mode ?
A. Mean - mode = 3(Mean - Median)
B. Mode = Mean - Median
C. Mode = 3 Median - 2 Mean
D. Median - Mode = 3 (Mean - Median)
E. Mode = 2 Mean + 3 Median
Choose the correct answer from the options given below
If, \(f(x) = \begin{bmatrix}0 & x-a & x-b \\[0.3em]x+a&o & x-c \\[0.3em]x+b & x+c & 0\\[0.3em] \end{bmatrix}\), then \(f(0)\) is:
A's month salary was ₹40000 and he used to save ₹10000 per month. His salary increased by 25% and expenditure increased by 15%. By what percent his savings increased ?
Match List I with List II
LIST I LIST II
A.\(\frac{d}{dx} [tan^{-1} (\frac{3x-x^3}{1-3x^2})]\)I.\(\frac{3}{1+x^2}\)
B.\(\frac{d}{dx}[cos^{-1}(\frac{1-x^2}{1+x^2})]\)II.\(\frac{-3}{1+x^2}\)
C.\(\frac{d}{dx}[cos^{-1} (\frac{2x}{1+x^2})]\)III.\(\frac{-2}{1+x^2}\)
D.\(\frac{d}{dx}[cot^{-1}(\frac{3x-x^3}{1-3x^2})]\)IV.\(\frac{2}{1+x^2}\)
Choose the correct answer from the options given below:
The differential equation whose solution is Ax2+By2=1 where A and B are arbitrary constant is of:
(A) first order and first degree
(B) second order and first degree
(C) second order and second degree
(D) second order
Choose the correct answer from the options given below:
If y = \(10^{10^x}\), then \(\frac{dy}{dx}\) is :