KEAM
Mathematics

KEAM Mathematics

KEAM Maths Mock Test 1 Mock Test

KEAM Mathematics Mock Test Questions 2025

KEAM Mathematics Mock Test Question Paper 2025 - Practice Free Online KEAM (Mathematics) Quiz MCQs

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KEAM Mathematics Quiz - Practice Online

If \( \int_0^1 (3x^2 + 2x + 1)\, dx \) is evaluated, the result is:
  • 2
  • 3.5
  • 4
  • 2.5
Evaluate \( \sum_{k=1}^{n} k \cdot (k+1) \):
  • \( \frac{n(n+1)}{2} \)
  • \( \frac{n(n+1)(n+2)}{6} \)
  • \( \frac{n(n+1)(2n+1)}{6} + \frac{n(n+1)}{2} \)
  • \( \frac{n(n+1)^2}{2} \)
The general solution of \( \frac{dy}{dx} = y \tan x \) is:
  • \( y = \sin x + C \)
  • \( y = C \sec x \)
  • \( y = C \sec x \)
  • \( y = C \cos x \)
Evaluate \( \lim_{x \to 0} \frac{\sin 3x}{x} \):
  • 1
  • 3
  • 0
  • Undefined
The determinant of the matrix \( \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \) is:
  • 6
  • -2
  • 1
  • 2
If \( \vec{a} = \hat{i} + 2\hat{j} \), \( \vec{b} = 3\hat{i} - \hat{j} \), then \( \vec{a} \cdot \vec{b} \) is:
  • 1
  • 1
  • 0
  • 5
The value of \( \sum_{r=1}^5 r^2 \) is:
  • 50
  • 45
  • 55
  • 60
Find the area under the curve \( y = x^2 \) from \( x = 1 \) to \( x = 3 \):
  • 7
  • \(\frac{26}{3}\)
  • \( \frac{9}{2} \)
  • 8
If \( y = e^{3x} \), then \( \frac{dy}{dx} \) is:
  • \( 3e^{3x} \)
  • \( e^x \)
  • \( x e^x \)
  • \( 3e^x \)
Which of the following series is convergent?
  • \( \sum \frac{1}{n} \)
  • \( \sum \frac{1}{n^2} \)
  • \( \sum \frac{n}{n+1} \)
  • \( \sum n \)
If \( \vec{a} = 2\hat{i} - \hat{j} \), \( \vec{b} = \hat{i} + \hat{j} \), find \( |\vec{a} \times \vec{b}| \):
  • 2
  • 1
  • 3
  • 0
If \( \int \frac{dx}{x^2 + 1} = \theta \), then \( \theta = \):
  • \( \ln |x^2 + 1| + C \)
  • \( \tan^{-1} x + C \)
  • \( \tan^{-1} x + C \)
  • \( \frac{1}{x^2 + 1} + C \)
The value of \( \lim_{x \to \infty} \left(1 + \frac{1}{x}\right)^x \) is:
  • 1
  • \( \infty \)
  • \( e \)
  • 0
Find the sum: \( \sum_{k=1}^{n} k = ? \)
  • \( \frac{n(n+2)}{2} \)
  • \( \frac{n^2}{2} \)
  • \( \frac{n(n-1)}{2} \)
  • \( \frac{n(n+1)}{2} \)
If \( A = \begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix} \), find \( \text{Tr}(A) \):
  • 5
  • 6
  • 7
  • 8
Which of the following is a solution to \( \frac{dy}{dx} = -ky \) ?
  • \( y = kx^2 \)
  • \( y = Ae^{-kx} \)
  • \( y = kx + A \)
  • \( y = \frac{1}{x^k} \)
Evaluate \( \int \ln x \, dx \):
  • \( \frac{1}{x} + C \)
  • \( x \ln x - x + C \)
  • \( \ln(x^2) + C \)
  • \( x^2 \ln x + C \)
If \( \vec{a} \cdot \vec{b} = 0 \), the vectors are:
  • Collinear
  • Perpendicular
  • Equal
  • Parallel
The determinant of a 3x3 identity matrix is:
  • 0
  • 1
  • -1
  • 3
The sum to \( n \) terms of the series \( 5 + 10 + 15 + \ldots \) is:
  • \( \frac{5n(n-1)}{2} \)
  • \( \frac{5n(n+1)}{2} \)
  • \( 5n \)
  • \( 10n \)