List of top Questions asked in Assam CEE

Which of the following functions is differentiable on the set of real numbers?
Which of the following functions is not continuous on the set of real numbers?
\(f(x)\) is a polynomial of degree \(3\) such that \[ f(0)=f(3)=f(-3)=0 \] \[ f(1)=-8 \] The maximum and minimum values of \(f(x)\) are respectively
The function \[ y=\frac{\sin x+2\cos x}{3\sin x+4\cos x} \] is
The value of \[ \sin\left[\cos^{-1}\left(\frac{3}{5}\right)+\tan^{-1}(-2)\right] \] is
If \[ 1+\cos2\theta+\cos4\theta+\cos6\theta=0, \qquad 0\le\theta\le180^\circ, \] then
If \[ (1+x)^n=C_0+C_1x+C_2x^2+\cdots+C_nx^n \] where \[ C_i={}^{n}C_i, \] then \[ (C_0+C_1)(C_1+C_2)\cdots(C_{n-1}+C_n) \] equals
If \(A=[-1,1)\) and \(B=(0,\infty)\), then the complement of \(A\cup B\) is
If a set \(A\) contains \(3\) elements and another set \(B\) contains \(4\) elements, then the number of functions from \(A\) to \(B\), which are not injective, is
If a set \(A\) contains \(5\) elements, then the number of reflexive relations on \(A\) is
The direction cosines of the vector \[ \vec a=a_1\hat i+a_2\hat j+a_3\hat k \] are
The differential equation of all circles in a plane of radius \(r\) is \[ \text{where } y_1=\frac{dy}{dx}, \qquad y_2=\frac{d^2y}{dx^2} \]
The number of arbitrary constants in the general solution and in the particular solution of a differential equation of fourth order are respectively
The sum to \(n\) terms of the series \[ 1+3+7+15+\cdots \] is
In an election, the number of candidates is one more than the number of seats. If a voter can cast his vote in 30 ways, find the number of candidates (when a voter can cast his vote for one or more seats).
20 delegates from 20 countries sit in a circle such that two particular delegates never sit together. In how many ways can they be seated?
Two motorcyclists \(A\) and \(B\) leave a place at 12 noon. \(A\) travels north at \(60\) km/hr and \(B\) travels east at \(80\) km/hr. At 2 PM, they are separating at the rate
In a class XII of a school, \(40\%\) of the students study Mathematics, \(30\%\) study Physics and \(20\%\) study Chemistry. \(20\%\) of the class study both Mathematics and Physics, \(10\%\) study both Mathematics and Chemistry and \(10\%\) study both Physics and Chemistry. \(5\%\) of the class study all the three subjects. If a student is selected at random from the class, find the probability that he studies neither Mathematics nor Physics nor Chemistry.
If \(f\) is a subset of \(Z\times Z\), then which of the following is a function from \(Z\) to \(Z\)?
The mean of 5 observations is \(4.4\) and their variance is \(8.24\). If three of the observations are \(1, 2\) and \(6\), then the other two observations are
If \(A\) is a square matrix of order 3 such that \(|A| = 4\), then the value of \(|\text{adj}(\text{adj } A)|\) is:
A box contains \(5\) red and \(4\) black balls. Two balls are drawn one by one without replacement. What is the probability that the second ball is red, given that the first ball drawn was black?
The angle between the lines whose direction cosines satisfy the equations \(l + m + n = 0\) and \(l^2 = m^2 + n^2\) is:
The value of the definite integral \(\int_0^{\pi/2} \frac{\sin x}{\sin x + \cos x} dx\) is:
Which of the following noble gases is the most reactive and forms the maximum number of compounds?