List of top Mathematics Questions

If a→,b→,c→ are non-coplanar vectors and λ is a real number, then[λ(a→+b→)λ2b→λc→]=[a→b→+c→b→] for
Draw a rough figure of a quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measure.
Differentiate w.r.t. x the function:\(x^x+x^a+a^x+a^a\), for some fixed \(a>0\) and \(x>0\)

The equation $e ^{4 x}+8 e ^{3 x}+13 e ^{2 x}-8 e ^x+1=0, x \in R$ has :

For any two statements p and q, the negation of the expression p∨(∼p∧q) is:

If ABCD is a parallelogram, vector AB = 2i + 4j - 5k and vector AD = i + 2j + 3k, then the unit vector in the direction of BD is

If A = {1, 2, 3, 4, 6} and R is a relation on A such that R = {(a, b) : a, b ∈ A and b is exactly divisible by a} then find the number of elements present in the range of R?
Find the sum of the roots of the quadratic equation \( 2x^2 - 3x - 5 = 0 \).
Find the value of \( x \) that satisfies the equation \( \frac{3x - 4}{2} = 5 \).
Find the value of \( x \) in the quadratic equation \( x^2 - 5x + 6 = 0 \).
Solve for \( x \) in the equation \( 3x + 5 = 2x + 7 \).
Write all the factors of the following numbers:
  1. 24
  2. 15
  3. 21
  4. 27
  5. 12
  6. 20
  7. 18
  8. 23
  9. 36
Explain the concept of a limit. Why is it important in calculus?
Find the equation of the tangent line to the curve \( y = x^2 - 3x + 2 \) at the point \( (1, 0) \).
You are given a sequence of numbers: 2, 5, 10, 17, ... Identify the pattern and find the next three terms in the sequence. Can you express the nth term of this sequence in a general formula?
The value of \[ \int_1^4 \log(\lfloor x \rfloor) \, dx \] where \( \lfloor x \rfloor \) is the greatest integer less than or equal to \( x \), is:
Some pictures (a) to (c) are given below. Tell which of them show:
\((a)\)

\((b)\)

\((c)\)

(i) 3 × \(\frac{1}{5}\) =\(\frac{3}{5}\)
(ii) 2 × \(\frac{1}{3}\) =\(\frac{2}{3}\)
(iii) 3 × \(\frac{3}{4}\) = \(\frac{21}{4}\)
Solve and check result: \(8x + 4 = 3(x - 1) + 7\)
If y=2x3x,then \(\frac{dy}{dx}\) at x=1 is
Solve the equation: \[ x + \log_{15}(5 + 3x) = x \log_{15} 5 + \log_{15} 24 \]
If the angle \( \theta \) between the line \[ \frac{2t + 1}{1} = \frac{y - 1}{2} = \frac{z}{2} \] and the plane \( 2x - y\sqrt{7} + z + 4 = 0 \) is such that \( \sin \theta = \frac{8}{\sqrt{3}} \), then the value of the expression is:
If \( y = y(x) \) satisfies \[ \left( \frac{2 + \sin x}{1 + y} \right) \frac{dy}{dx} = -\cos x, \] such that \( y(0) = 2 \), then the value of \( y\left( \frac{\pi}{2} \right) \) is:
Evaluate the integral: \[ \int_{-1}^{1} \log\left(\frac{2 - x}{2 + x}\right) dx \]
(i) For any integer a, what is (–1) × a equal to?
(ii) Determine the integer whose product with (–1) is
(a) –22
(b) 37
(c) 0
If \[ f(x) = 2 \left( \cos x + i \sin x \right) \left( \cos 3x + i \sin 3x \right) \cdots \left( \cos (2n-1)x + i \sin (2n-1)x \right) \] where \( n \in \mathbb{N} \), then what is the value of \( f''(x) \) ?