List of top Mathematics Questions

Let A = {1, 3, 4, 6, 9} and B = {2, 4, 5, 8, 10}. Let R be a relation defined on A × B such that R = {(\((a_1, b_1),(a_2, b_2)\)) : \(a_1 ≤ b_2\) and \(b_1 ≤ a_2\)}. Then the number of elements in the set R is 

Let P be the plane passing through the points (5, 3, 0), (13, 3, –2) and (1, 6, 2). For α ∈ N, if the distances of the points A (3, 4, α) and B (2, α, a) from the plane P are 2 and 3 respectively, then the positive value of a is

The converse of ((~ p) ∧ q) ⇒ r is

If the radius of the largest circle with centre (2, 0) inscribed in the ellipse \(x^2 + 4y^2 = 36\) is r, then \(12r^2\) is equal to

Let the function f: [0,2] \(\rightarrow\) R be defined as \(f(x) =   \begin{cases}     e^{min}{x^2,x-[x]}       & \quad x \in[0,1]\\     e^{[x-log_ex]}  & \quad x\in[1,2]   \end{cases}\)
where [t] denotes the greatest integer less than or equal to t. Then the value of the integral \(\int^2_0xf(x)dx\) is 

The angle of elevation of the top P of a tower from the feet of one person standing due South of the tower is 45° and from the feet of another person standing due west of the tower is 30°. If the height of the tower is 5 meters, then the distance (in meters) between the two persons is equal to

If f : R \(\rightarrow\) R be a continuous function satisfying \(\int^{\frac{\pi}{2}}_0f(sin2x)sinxdx+\alpha\int^{\frac{\pi}{4}}_0f(cos2x)cosxdx=0\), then the value of \(\alpha\) is

Let f and g be two function defined by \(f(x) =   \begin{cases}     x+1       & \quad x<0\\    |x-1|,   & \quad x \geq0   \end{cases}\) and g(x) = \(f(n) =   \begin{cases}     x+1,       & \quad x<0 \\     1,  & \quad x\geq0   \end{cases}\) Then (gof)(x) is 

If Anil's salary is \(20\%\) less than that of Rama, then by what percent is Rama's salary more than that of Anil?

The value of a car depreciates every year by \( 10\%\) . What will be its value after \( 3\) years if its present value is \(₹6,25,000\)?

In how many years a sum placed on compound interest becomes 8 times of itself, if it becomes twice in 6 years?

If two squares X and Y have each side of 10 m and 20 m respectively, then the side of the square Z whose area is equal to the sum of the areas of square X and square Y is:

If the average of \(15, 25, 19, 20, 23, 18\) and\( (x-3)\) is \(20\). then Find the average of \(x, (x+6), (2x-1)\) and \(23\).

The average of a positive number, its square and 3 is 5. Find the number.

Which term of the A.P. \( 3, 7, 11,........ ,147 \) is its middle term?

The range of f(x) = \(4\sin^{-1}(\frac{x^2}{x^2+1})\) is 

Let \( R \) be a reflexive relation on the finite set \( A \) having 10 elements and if \( m \) is the number of ordered pairs in \( R \), then

The tangent to the hyperbola x²-y² = 3 are parallel to the straight line 2x + y +8=0 points are

The number of common tangents that can be drawn to the circle x²+y²-4x-6y-3=0 and x²+y²+2x+2y+1=0 is

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:

If an angle a is divided into two parts A and B such that A-B=x and tan A: tan B=k:1, then the value of sinx is

If α and β are the roots of a quadratic equation x²+αx + β=0 where β≠0, then what is the value of α + β?

Function f(x)=(x+1)^cotx is continuous at x = 0, then the value of f(0) is

The variance of a series of numbers 2, 3, 11 and x is 12.25. Find the value of x.

The area of region bounded by the curve y²=x, the y-axis and between y = 2 and y = 4 is