List of top B.Ed. Mathematics Questions on Calculus asked in CUET (PG)

Arrange the following differential equations in increasing order on the basis of their order: 

CodeDifferential Equation
A.\(\dfrac{d^4y}{dx^4}+\sin\!\left(y'''\right)=0\)
B.\(\left(\dfrac{d^5s}{dt^5}\right)^4+3s\dfrac{d^2s}{dt^2}=0\)
C.\(y'''+2y''+y'=0\)
D.\(y''+y=e^x\)
Arrange the following in ascending order based on their values:
A. \(\displaystyle \int_0^{\frac{\pi}{2}}\frac{1}{1+\sin x}\,dx\),
B. \(\displaystyle \int_1^2 x^2\,dx\),
C. \(\displaystyle \int_0^{\frac{\pi}{2}}\sin x\,dx\),
D. \(\displaystyle \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\sin^3x\,dx\).
The function \(f(x)=|x-2|+|x|+|x+2|\) is not differentiable at which points?
Which of the following is the variance of the data? \[ 6,\ 8,\ 10,\ 12,\ 14,\ 16,\ 18,\ 20,\ 22,\ 24 \]
Arrange the following in increasing order as per the last digit:
A. \(2^{444}\),
B. \(17^{10}\),
C. \(13^{10}+2\),
D. \(1^1+2^2+3^3+\cdots+100^{100}\),
E. \(11!+2\).
Arrange the following in ascending order based on their values:
A. \(\displaystyle \int_0^{\frac{\pi}{2}}\frac{1}{1+\sin x}\,dx\),
B. \(\displaystyle \int_1^2 x^2\,dx\),
C. \(\displaystyle \int_0^{\frac{\pi}{2}}\sin x\,dx\),
D. \(\displaystyle \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\sin^3x\,dx\).
The function \(f(x)=|x-2|+|x|+|x+2|\) is not differentiable at which points?
Which of the following is equation of hyperbola with vertices \((\pm 2,0)\) and foci \((\pm 3,0)\)?
The normal at the point \((1,1)\) on the curve \(2y+x^2=3\) is?
Evaluate the determinant:
\[ \left| \begin{array}{ccc} b+c & a-b & a\\ c+a & b-c & b\\ a+b & c-a & c\\ \end{array} \right| \]
If \[ x=e^{\tan^{-1}\left(\frac{y-x^2}{x}\right)} \] then \(\dfrac{dy}{dx}=?\)
If \(y=e^{m\sin^{-1}x}\) and \(y_n\) indicates \(n^{th}\) derivative of \(y\) with respect to \(x\), then which of the following relation is true?