List of top Mathematics Questions asked in IIT JAM BT

The value of $\lim_{π‘₯β†’3}\frac{(π‘₯^2 βˆ’9)}{(π‘₯^2βˆ’4π‘₯+3 )} $ is (rounded off to the nearest integer).
If a variable 𝑧 shows a standard normal distribution, then the percent probability that $0 ≀ 𝑧^2 ≀ 1$ is ________ (rounded off to the nearest integer).
For a given square, if the area of its incircle is $100 π‘π‘š^2$ , then the area of its circumcircle is __________ $π‘π‘š^2$ (rounded off to the nearest integer).
If a fair coin is tossed two times, the probability that the first or the second toss will be heads is ________ (rounded off to two decimal places).
Given the following sets:
𝐴 = {2, 4, 6, 8, 10, 12}
𝐡 = {8, 10, 12, 14, 16, 18}
𝐢 = {7, 8, 9, 10 11, 12, 13}
(𝐴 ∩ 𝐡) βˆͺ (𝐡 ∩ 𝐢) is
A random variable X and its probability distribution is given below. The value of P(X<5) is _______. (rounded off to one decimal place)
X012345
P(X)0K2K3K4K5K
The order of differential equation $\frac{𝑑^3𝑦}{dx^3} + 2 \frac{𝑑^2𝑦}{dx^2} βˆ’ 3 \frac{𝑑𝑦}{dx} + 6π‘₯^4𝑦$ = 0 is _______.
The value of $\lim_{π‘₯β†’βˆ’3}\frac{(2π‘₯+6)}{(π‘₯+3)}$ is
Given data consists of distinct values of $π‘₯_𝑖$ occurring with frequencies $𝑓_𝑖.$ The mean value for the data is _____. (rounded off to one decimal place)
$X_i$56810
$F_i$8101012
A deck of ten cards is given to you as shown below in the figure. One card is drawn at random from this deck. The probability of selecting a number less than 9 is__ (to one decimal place).
A deck of ten cards
The average of all positive even integers less than or equal to 40 is___.
The smallest positive (non-zero) integer "n" for which the expression \((\frac{1+i}{1-i})^n\) = 1 holds true, is ___.
Given that A=\( (sin\theta cos\theta tan\theta + sin\theta cos\theta cot\theta)\), the value of A is
The equation $\sin \frac{\theta}{2}\, (\sin \frac{\theta}{2} + \cos \frac{\theta}{2}) = \beta$ has a solution, where $\beta$ is a natural number. Then $\beta$ is ______.
A function $f : D \to \mathbb{R}$ is defined as $f(x) = \dfrac{x^2 + 1}{x^2 + x + 1}$ where $D \subseteq \mathbb{R}$ is the domain. The domain(s) on which the function $f(x)$ is one-to-one is/are

The value of the integral $\int_0^4 (x - f(x))\,dx$, where 
 

is:
 

If $x + \dfrac{1}{x} = 1$, then the value of $x^6 + \dfrac{1}{x^6}$ is
The distance between the parallel lines $2x + 5y = 7$ and $2x + 5y = 15$ is ______ (rounded off to 2 decimals).
A stationary enemy ship is docked in the sea at a distance of 10 km from the coastline. A gun located at the sea level on the coastline can fire projectiles at a velocity of 120 m/s. What is the angle (in degrees) above the horizontal at which the gun must fire to hit the ship? [g = 9.8 m/s$^2$]
A bouncing ball is dropped from an initial height of \( h \) meters above a flat surface. Each time the ball hits the surface, it rebounds a distance \( r \times h \) meters and it bounces indefinitely. Consider the value of \( h = 5 \) meters and \( r = \frac{1}{3} \). The total vertical distance (up and down) travelled (in meters) by the ball is ...........

The average value of function \( f(x) = \sqrt{9 - x^2} \) on \([-3, 3]\), rounded off to TWO decimal places, is ............ 
 

The length of transverse and conjugate axes in a hyperbola are 6 and 8, respectively. The eccentricity of the hyperbola, rounded off to TWO decimal places, is .......

The median of Y in the following data is ............. 
\[ \begin{array}{|c|c|c|c|c|c|c|} \hline \text{Serial number} & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline Y & 22 & 12 & 10 & 14 & 16 & 20 \\ \hline \end{array} \]

The solution to the integral \( \int_0^1 2y\sqrt{1 + y^2} \, dy \), rounded off to TWO decimal places, is ............ 
 

Which of the following curve/straight line equations will pass through the origin when plotted on a graph?