List of top Mathematics Questions asked in IIT JAM BT

Consider a spherical epithelial cell (C1) of diameter \(20\ \mu m\) and a cubic shaped liver cell (C2) of side \(20\ \mu m\). The ratio of the surface areas of C1 : C2 is _ _ _. (round off to two decimal places)

The value of

In a geometric progression, the \(3^{rd}\) term is \(36\) and the \(5^{th}\) term is \(324\). The \(7^{th}\) term of the same progression will be _ _ _. (in integer)

Select the value(s) of \(x\) for which the determinants,

Which of the following is/are true for the data given below?

Consider the differential equation

Which one of the following is the correct graphical representation for functions, \(\sin(x)\) and \(\sin^2(x)\) for \(0\leq x\leq \pi\)?

The derivative of \(x\log_e(x)\) is

If \( y(x)=15\cos(x)-13\sin(x) \), then \( \dfrac{d^2y}{dx^2} \) will be

The value of $\lim_{𝑥→3}\frac{(𝑥^2 −9)}{(𝑥^2−4𝑥+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 $100 𝑐𝑚^2$ , then the area of its circumcircle is __________ $𝑐𝑚^2$ (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).

A random variable X and its probability distribution is given below. The value of P(X<5) is _______. (rounded off to one decimal place)

X	0	1	2	3	4	5
P(X)	0	K	2K	3K	4K	5K

Given the following sets:
𝐴 = {2, 4, 6, 8, 10, 12}
𝐵 = {8, 10, 12, 14, 16, 18}
𝐶 = {7, 8, 9, 10 11, 12, 13}
(𝐴 ∩ 𝐵) ∪ (𝐵 ∩ 𝐶) is

The order of differential equation $\frac{𝑑^3𝑦}{dx^3} + 2 \frac{𝑑^2𝑦}{dx^2} − 3 \frac{𝑑𝑦}{dx} + 6𝑥^4𝑦$ = 0 is _______.

The value of $\lim_{𝑥→−3}\frac{(2𝑥+6)}{(𝑥+3)}$ is

Given data consists of distinct values of $𝑥_𝑖$ occurring with frequencies $𝑓_𝑖.$ The mean value for the data is _____. (rounded off to one decimal place)

$X_i$	5	6	8	10
$F_i$	8	10	10	12

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).

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