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CUET (UG)
List of top Questions asked in CUET (UG)
The area of the region bounded by |x| + |y| = 1, x ≥ 0 y ≥ 0 is :
CUET (UG) - 2023
CUET (UG)
Mathematics
Area of the region bounded
ABCD is a rhombus, whose diagonals intersect at E. Then
\(\overrightarrow{EA}+\overrightarrow{EB}+\overrightarrow{EC}+\overrightarrow{ED}\)
equals to :
CUET (UG) - 2023
CUET (UG)
Mathematics
Vector Algebra
The general solution of the differential equation xdy - ydx - 0 represents :
CUET (UG) - 2023
CUET (UG)
Mathematics
Solutions of Differential Equations
The value of the integral
\(\int\frac{1-\sin x}{\cos^2 x}dx\)
is :
CUET (UG) - 2023
CUET (UG)
Mathematics
Integration
Match List I with List II
List I
List II
A.
\(\frac{d^2y}{dx^2}+(\frac{dy}{dx})^{\frac{1}{2}}+x^{\frac{1}{2}}\)
I.
order 2, degree 1
B.
\(\frac{dy}{dx}=\frac{x^{\frac{1}{2}}}{y^{\frac{1}{2}}(1+x)^{\frac{1}{2}}}\)
II.
order 2, degree not defined
C.
\(\frac{d^2y}{dx^2}=\cos3x+\sin3x\)
III.
order 2, degree 4
D.
\(\frac{d^2y}{dx^2}+2\frac{dy}{dx}+y=\log(\frac{dy}{dx})\)
IV.
order 1, degree 2
Choose the correct answer from the options given below :
CUET (UG) - 2023
CUET (UG)
Mathematics
Differential Equations
If
\(f(x)=\begin{cases} \frac{1-\cos4x}{x^2} & x\ne0 \\ k & x=0 \end{cases}\)
is continuous at x = 0, then the value of k is :
CUET (UG) - 2023
CUET (UG)
Mathematics
Continuity and differentiability
The slope of the normal to the curve y = 2x
2
+ 3sinx at x = 0, is :
CUET (UG) - 2023
CUET (UG)
Mathematics
Slope of a line
If y = Asinx + Bcosx, Where A and B are constants, then
\(\frac{d^2y}{dx^2}\)
is equal to :
CUET (UG) - 2023
CUET (UG)
Mathematics
Derivatives
For fencing of flower bed with 100 cm long wire in the form of circular sector, the maximum area of the flower bed is :
CUET (UG) - 2023
CUET (UG)
Mathematics
Mensuration
Match List I with List II
List I
(Functions)
List II
(Derivatives)
A.
f(x)=sin
-1
x
I.
\(\frac{1}{1+x^2}\)
, x ∈ R
B.
f(x)=tan
-1
x
II.
\(\frac{1}{\sqrt{1-x^2}}\)
, x ∈ (-1, 1)
C.
f(x)=cos
-1
x
III.
\(-\frac{1}{\sqrt{1-x^2}}\)
, x ∈ (-1, 1)
D.
f(x)=sin
-1
x
IV.
\(-\frac{1}{1+x^2}\)
, x ∈ R
Choose the correct answer from the options given below :
CUET (UG) - 2023
CUET (UG)
Mathematics
Derivatives
Match List I with List II
List I
List II
A.
\(\int\limits^{\frac{\pi}{2}}_0\frac{\sin^{\frac{7}{2}}x}{\sin^{\frac{7}{2}}+\cos^{\frac{7}{2}}}dx\)
I.
\(\frac{\pi}{4}-\frac{1}{2}\)
B.
\(\int\limits_0^{\pi}\frac{x\sin x}{1+\cos^2x}dx\)
II.
0
C.
\(\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}}x\cos x\ dx\)
III.
\(\frac{\pi}{4}\)
D.
\(\int\limits_{-\frac{\pi}{4}}^{\frac{\pi}{4}}\sin^2x\ dx\)
IV.
\(\frac{\pi^2}{4}\)
Choose the correct answer from the options given below :
CUET (UG) - 2023
CUET (UG)
Mathematics
Definite Integral
The value of the determinant
\(\begin{vmatrix} x+y & y+z & z+x \\ z & x & y \\ 1 & 1 & 1 \end{vmatrix}\)
is :
CUET (UG) - 2023
CUET (UG)
Mathematics
Determinants
The determinant
\(\begin{vmatrix} x & \sin\theta & \cos\theta \\ -\sin\theta & -x & 1 \\ \cos\theta & 1 & x \end{vmatrix}\)
is :
CUET (UG) - 2023
CUET (UG)
Mathematics
Determinants
The value of λ for which the matrix
\(\begin{pmatrix} 1 & 0 & λ \\ 0 & 1 & 0 \\ 1 & 0 & 1 \end{pmatrix}\)
is a singular matrix is :
CUET (UG) - 2023
CUET (UG)
Mathematics
Types of Matrices
If A is an invertible matrix, such that A
2
- A + I = 0, then the inverse of A is :
CUET (UG) - 2023
CUET (UG)
Mathematics
Adjoint and Inverse of a Matrix
If the order of a matrix A is 2 × 3, the order of matrix B is 3 × 4 and the order of matrix C is 3 × 4, then the order of the matrix (A, B).C
T
is
CUET (UG) - 2023
CUET (UG)
Mathematics
Order of Matrix
The value of k for which the matrix
\(\begin{pmatrix} 0 & 2 & 4 \\ 2 & 0 & 5 \\ -3 & 5 & 0 \end{pmatrix}\)
is a symmetric matrix is given by :
CUET (UG) - 2023
CUET (UG)
Mathematics
Symmetric and Skew Symmetric Matrices
The relation R in the set A = {1, 2, 3, 4} is given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)} is :
CUET (UG) - 2023
CUET (UG)
Mathematics
Relations and Functions
If f(x) - 27x
3
and g(x) =
\((x)^{\frac{1}{3}}\)
, then gof(x) is :
CUET (UG) - 2023
CUET (UG)
Mathematics
Relations and Functions
If
\(P(A)=\frac{3}{10},P(B)=\frac{2}{5}\)
, and P(A ∪ B) =
\(\frac{3}{5}\)
, then
\(P(\frac{B}{A})+P(\frac{A}{B})\)
is equal to :
CUET (UG) - 2023
CUET (UG)
Mathematics
Probability
The corner points of feasible region determined by the system of linear constraints are (0, 3), (1, 1) and (3, 0). Let Z = px + qy where p, q > 0. The condition on p and q so that, minimum of Z occurs at (3, 0) and (1, 1) is :
CUET (UG) - 2023
CUET (UG)
Mathematics
Linear Programmig Problem
The principal value of
\(\sin^{-1}(\frac{1}{2})\)
is :
CUET (UG) - 2023
CUET (UG)
Mathematics
Inverse Trigonometric Functions
The mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces, and 5 on 1 face is :
CUET (UG) - 2023
CUET (UG)
Mathematics
Mean, median, mode and standard deviation
The tangent to the parabola, x
2
= 2y at the point
\((1,\frac{1}{2})\)
makes with the x-axis an angle of :
CUET (UG) - 2023
CUET (UG)
Mathematics
Parabola
If
\(f(x)=\begin{cases} 2x+8, & 1\le x\le2 \\ 6x, & 2\lt x \lt4\end{cases}\)
, then
\(\int_1^4f(x)\)
is :
CUET (UG) - 2023
CUET (UG)
Mathematics
Integration
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