List of top Mathematics Questions

If a:b= 3:5, then (-a²+b²): (a²+b²) is :

The area of the circular round shown as 92 \(\pi\) m² then value of r is:

An article is marked for ₹200. A shopkeeper earns 25% profit even after allowing \(12\frac{1}{2}\)% discount on it. What is the cost price of the article (in ₹)?

\(\frac{8}{3}\) of \(40\%\) of \(\frac{18}{39}\) of 156 = _______ ?

If a % of a + b % of b = 2% of ab, then what percent of a is b ?

The monthly income and expenditure of a person were ₹10,000 and ₹6,000 respectively. Next year, his income increased by 15% and his expenditure increased by 8%. Then the percentage increase in his savings is:

Five men working 8 hours per day take 6 days to do a work. How many days will 12 men take to do the same work if they work for 10 hours per day?

Let f: [a, b]R be a continuous function on [a, b] and differentiable on (a, b), then there exists some e in (a, b) such that
\(f'(c) = \frac{f(b)-f(a)}{b-a}\)
This theorem in named

A water tank can be filled by two pipes P and Q in 60 minutes and 30 minutes respectively. How many minutes will it take to fill the empty tank if pipes P and Q are opened for first half of the time, after which only pipe Q is opened for next half of the time?

Calculate the mean of the following numbers: 100, 200, 600

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:

The point(s) at which function f is given by \(f(x)={\begin{Bmatrix}\frac{x}{|x|};x\lt0  \\ -1; x\geq0\end{Bmatrix}}\) is continuous is/are

If every pair from among the equation x² + px + qr = 0, x² + qx + rp = 0 and x² + rx + pq = 0 has a common root, then the product of three common roots is_______.

If f: R→R defined as of f(x) = x² + 1 then minimum value of f(x) is

Given below are two statements: One is lebelled as Assertion A and the other is labelled as Reason R.
Assertion A: If two circles interesect at two points, then the line joining their centres is prependicular to the common chord.
Reason R: The perpendicular bisectors of two chords of a circle intersect at its centre.
In the light of the above statements, choose the correct answer from the options given below:

If A, B and C are any three sets, then
A. A-(B∩C) = (A ∩ B) - (A∩C)
B. A-(B∪C) = (A - B) ∩ (A-C)
C. n (A-B) = n(A) -n (A ∩ B)
D. A∩(B - C) = (A∩B) ∩ (A-C)
Choose the most appropriate answer from the options given below :

Choose the correct sequence of the four statements given below, so that the phrase makes a complete sense:
A. Then the sets of equations connecting both are known as transformation of co-ordinates.
B. We can associate a unique set of co-ordinates.
C. Given a point P in rectangular co-ordinates.
D. Called the curvilinear co-ordinates of P.
Choose the correct answer from the options given below.

Match List-I and List-II

LIST I		LIST II
A.	No. of triangles formed using 5 points in a line and 3 points on parallel line is	I.	20
B.	No. of diagonals drawn using the vertices of an octagon	II.	10
C.	The no. of diagonals in a regular polygon of 100 sides is	III.	45
D.	A polygon with 35 diagonals has sides	IV.	4850

Choose the correct answer from the options given below:

A circle S passes through the point (0, 1) and is orthogonal to the circles (x-1)² + y² = 16 and x² + y² = 1. Then
A. Radius of S is 8
B. Radius of S is 7
C. Centre of S is (-7, 1)
D. Centre of S is (-8, 1)

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?

Which of the following functions is differentiable at x = 0?

If a Chord which is normal to the parabola y² = 4ax at one end subtends a right angle at the vertex, then its slope is -

Match List-I and List-II

LIST I		LIST II
A.	The angle between the straight lines, 2x2+ 3y2-7xy=0 is	I.	\(\tan^{-1}\frac{3}{5}\)
B.	The circles x2+y2+x+y=0 and x2+y2 +x-y=0 intersect at angle	II.	25π
C.	The area of circle centered at (1,2) and passing through (4,6) is	III.	π/4
D.	The parabola y2=4x and x2 =32y intersect at point (16,8) at angle	IV.	π/2

Choose the correct answer from the options given below:

A straight line has equation y=-x+6 which of the following line is parallel to it?

Match List-I and List-II

LIST I		LIST II
A.	Value of\(\lim\limits_{x\rightarrow0}\left(\frac{sinx}{x}\right)^{\frac{sinx}{x-sinx}}\)	I.	e3
B.	Value of \(\lim\limits_{x\rightarrow0}\int\limits_0^x\frac{sint^2dt}{x^2}\)is	II.	0
C.	Value of \(\lim\limits_{x\rightarrow0}(e^{2x}+x)^{\frac{1}{x}}\)is	III.	1
D.	Value \(\lim\limits_{x\rightarrow a}\frac{log(x-a)}{log(e^x-e^a)}\)of	IV.	e-1

Choose the correct answer from the options given below: