List of top Mathematics Questions asked in IIT JAM BT

If a coin is tossed three times, what is the probability that NO two successive tosses show the same face?
The curve \( y = x^4 - 4x^3 + 4x^2 - 4 \) has tangents parallel to the x-axis at the following points \( (x, y) \)
The solution to the limit \( \lim_{x \to 0} \frac{2 - \sqrt{4 - x}}{x} \) is ...........
Let \( \mathbf{a} = 4i - 2j + 6k \) and \( \mathbf{b} = 7i + j - 12k \). If \( \mathbf{a} \times \mathbf{b} = \alpha i + \beta j + \gamma k \), then the value of \( \alpha + \beta + \gamma \) equals .............

Let \( \mathbb{N} \) be the set of natural numbers and \( f : \mathbb{N} \to \mathbb{N} \) be defined by 

Let \( f^n(x) \) denote the \( n \)-fold composition of \( f(x) \). What is the smallest integer \( n \) such that \( f^n(13) = 1 \)? 
 

The value of \( \int_0^\pi x \sin x \, dx \) is .......
Let XYZ be an equilateral triangle and let P, Q, R be the midpoints of YZ, XZ, and XY, respectively.
Let \( r = \frac{\text{Area of } \Delta PQR}{\text{Area of } \Delta XYZ} \).
Let \( U = \{1, 2, \dots, 15\} \). Let \( P \subseteq U \) consist of all prime numbers, \( Q \subseteq U \) consist of all even numbers and \( R \subseteq U \) consist of all multiples of 3. Let \( T = P - Q \). Then, which of the following is/are CORRECT?
Let \( f(x) = (x - 1)(x - 2)(x - 3)(x - 4) \) and let \( \alpha = f\left( \frac{3}{2} \right) \), \( \beta = f\left( \frac{5}{2} \right) \) and \( \gamma = f\left( \frac{7}{2} \right) \). Which of the following is/are CORRECT?
Simplify \( \frac{\sin A}{1 + \cos A} + \frac{1 + \cos A}{\sin A} \).
Let \( a = \frac{\sqrt{5}+1}{2} \) and \( b = \frac{\sqrt{5}-1}{2} \). Then, \( \lim_{n \to \infty} \frac{a^n + b^n}{a^n - b^n} \) is ________
In how many ways can one write the elements 1, 2, 3, 4 in a sequence \( x_1, x_2, x_3, x_4 \) with \( x_i \neq i \) for all \( i \)?
Which one of the points P = \(\left(\frac{3}{2}, \frac{1}{2}\right)\), Q = \(\left(\frac{1}{2}, \frac{3}{2}\right)\), R = \(\left(\frac{3}{2}, \frac{11}{2}\right)\) and S = \(\left(\frac{11}{2}, \frac{3}{2}\right)\) lies ABOVE the parabola \(y = 2x^2\) and INSIDE the circle \(x^2 + y^2 = 4\)?
Let \( U = \{1, 2, 3, 4, 5\} \). A subset \( S \) is chosen uniformly at random from the non-empty subsets of \( U \). What is the probability that \( S \) does NOT have two consecutive elements?

The value of \[ \lim_{n \to \infty} \frac{3n^2 + 5n + 4}{4 + 2n^2} \] is 
 

If \( \varphi(x) = x^2 \) and \( \psi(x) = 2^x \), then \( \psi(\varphi(x)) \) is
Consider the equation \( x^3 - 1 = 0 \). If one of the solutions to this equation is 1, the other solution(s) is/are
The value of \( \log_n 4^{16} = -32 \). The value of \( n \) is ................

The determinant of the matrix \[ \left[ \begin{array}{ccc} 1 & 3 & 0 \\ 2 & 6 & 4 \\ -1 & -1 & 2 \end{array} \right] \] is ........... 
 

For \( a = \) ..............., the following simultaneous equations have an infinite number of solutions: \[ 10x + 13y = 6 \] \[ ax + 32.5y = 15 \]
If A and B are events such that \( P(A) = 0.3, P(B) = 0.2 \) and \( P(A \cup B) = 0.45 \), the value of \( P(A \cap B) \) is .............

What is the solution of \( \int x^2 \ln x \, dx \)? Given \( C \) is an arbitrary constant. 
 

The number of three-letter words, with or without meaning, which can be formed using letters of the word 'VIRUS' without repetition of letters is
The area of an equilateral triangle with sides of length \( \alpha \) is
Three vectors are as follows: \[ \mathbf{a} = 3\hat{i} - 10\hat{j} + 7\hat{k}, \mathbf{b} = -9\hat{i} + 6\hat{j} - 47\hat{k}, \mathbf{c} = 11\hat{i} - 17\hat{k} \] The value of \((\mathbf{a} + \mathbf{b}) \cdot \mathbf{c}\) is