List of top Mathematics Questions

△ABC∼△DEF, the area of △ABC=9 cm2 and the area of △DEF = 16 cm2. If BC=2.1 cm, then EF=
If \( \alpha,\,\beta,\,\gamma \) are the roots of the equation \[ \begin{vmatrix} x & 2 & 2\\ 2 & x & 2\\ 2 & 2 & x \end{vmatrix} = 0 \]
In \(△ABC\), \(DE || BC\), \(\frac {AD}{DB}=\frac 35\) and \(AC=5.6\) cm, then \(AE =\)\(?\)
If the slope of the line joining the points (4,2) and (3,-k) is -2, then the value of k is
If tan 48°.tan 23°.tan 42°.tan 67°=tan(A+30°), then the value of A is
If the area of a rectangle is \(112\ m^2\) and its length is \(6\ m\) more than the breadth, then the breadth of the rectangle is
2 cards of hearts and 4 cards of spades are missing from a pack of 52 cards. A card is drawn at random from the remaining pack. What is the probability of getting a black card?
Which of the following is a polynomial?
Nimra went to a bank to withdraw ₹2,000. She asked the cashier to give her ₹50 and ₹100 notes only and she got 30 notes in all. How many notes of ₹50 and ₹100 respectively that she received?
The equation of the circle whose diameter is the common chord of the circles \(x^2 + y^2 - 6x - 7 = 0\) and \(x^2 + y^2 - 10x + 16 = 0\) is:
If \( A(1,2) \), \( B(2,1) \) are two vertices of an acute angled triangle and \( S(0,0) \) is its circumcenter, then the angle subtended by \( AB \) at the third vertex is
Two dice are thrown at the same time. What is the probability that the sum of the two numbers appearing on the top of the dice is more than 10?
The area of the shaded region in the given figure is
The area of the shaded region in the given figure is
The power of a point \( (2,0) \) with respect to a circle \( S \) is \(-4\) and the length of the tangent drawn from the point \( (1,1) \) to \( S \) is \( 2 \). If the circle \( S \) passes through the point \( (-1,-1) \), then the radius of the circle \( S \) is:
In the following figure, if DE || BC, then x =
In the following figure, if DE || BC, then x
If \(sinα+sinβ+sinγ=3\), then \(cosα+cosβ+cosγ =\)
Let a relation \( R \) on the set of natural numbers be defined by \( (x, y) \in R \) if and only if \( x^2 - 4xy + 3y^2 = 0 \) for all \( x, y \in \mathbb{N} \). Then the relation is:

$$ \begin{vmatrix} x-2 & 3x-3 & 5x-5 \\ x-4 & 3x-9 & 5x-25 \\ x-8 & 3x-27 & 5x-125 \end{vmatrix} = 0 $$

The real valued function \( f: \mathbb{R} \to \left[ \frac{5}{2}, \infty \right) \) defined by \( f(x) = \left| 2x + 1 \right| + \left| x - 2 \right| \) is:
If \(\alpha, \beta, \gamma\) are the roots of the equation \(2x^3 - 3x^2 + 5x - 7 = 0\), then \(\Sigma \alpha^2 \beta^2\) is:
If \( y = a \cos 3x + b e^{-x} \), then \( y'(3\sin 3x - \cos 3x) = \):
If \( f(x) = \int_0^{x^3} (t + 4)^2 \, dt \), then \( f'(2) \) is equal to:

Given the Linear Programming Problem: 
Maximize \( z = 11x + 7y \) subject to the constraints: \( x \leq 3 \), \( y \leq 2 \), \( x, y \geq 0 \). 
Then the optimal solution of the problem is:

Length of the common chord of the circles \(x^2 + y^2 - 6x + 5 = 0\) and \(x^2 + y^2 + 4y - 5 = 0\) is:
The lengths of two equal sides of an isosceles triangle are given by \(L_1 = 2x + y - 3 = 0\) and \(L_2 = ax + by + c = 0\). If \(L_3 = x + 2y + 1 = 0\) is the third side of this triangle and \((5, 1)\) is a point on \(L_2\), then \(b^2/|ac|\) is: