CUET Mathematics MCQs Differential Equations

Question : The general solution of a differential equation is (y + c)² = cx where c is an arbitrary constant. The order and degree of the differential equation are respectively   
(a) 1, 2                                 
(b) 2, 2                                 
(c) 1, 1                                  
(d) 2, 1

Answer : A

Question :

(a) 16                                    
(b) 63                                   
(c) 64                                    
(d) 15

Answer : C

Question : The degree of the differential equation 

(a) one                                                
(b) two                                
(c) half                                 
(d) four 

Answer : B

Question : The order and degree of the differential equation of the family of circles touching the x-axis at the origin, are respectively

(a) 1, 1                                 
(b) 1, 2                                 
(c) 2, 1                                  
(d) 2, 2

Answer : A

Question : The general solution of the equation

Answer : A

Question : The differential equation Φf(x)dy = y {fΦ'(x) – y}dx is changed in the form df(x, y) = 0. Then f(x, y) is           

(a) 1/2Φ(x)+y
(b) 1/yΦ(x)-x
(c)1/yΦ(x)+x
(d) Φ(x)/y

Answer : B

Question : The differential equation of the family of curves y = e^x(A cos x + B sin x), where A, B are arbitrary constants, has the degree n and order m. Then  
(a) n = 2, m = 1                 
(b) n = 2, m = 2                 
(c) n = 1, m = 2                  
(d) n = 1, m = 1 

Answer : C

Question : The order and degree of the differential equation of the fami&*aving the same foci, are respectively
(a) 1, 1                                 
(b) 2, 1                                 
(c) 2, 2                                  
(d) 1, 2

Answer : D

Question :

Answer : A

Question : The order the differential equation 

(a) one                               
(b) two                                              
(c) four                               
(d) zero

Answer : B

Question : If y(t) is a solution of the equation 

(a) -1/2   
(b) e+1/2         
(c) e-1/2 
(d) 1/2 

Answer : A

Question : The solution of primitive integral equation (x² + y²)dy = xy . dx is y = y(x). If y(1) = 1 and y(x₀) = e then x₀ is

Answer : C

Question : The number of arbitrary constants in the general solution of differential equation of fourth order is
(a) 4
(b) 3
(c) 2
(d) 0

Answer : A

Question : The general solution of a differential equation is y = ae^bx+c where a, b, c are arbitrary constants. The order of the differential equation is               
(a) 3                                      
(b) 2                                      
(c) 1                                      
(d) none of these

Answer : B

Question : The solution of (x + logy)dy + y dx = 0 when y(0) = 1 is
(a) y(x – 1) + ylog y = 0  
(b) y(x – 1 + logy) + 1= 0               
(c) xy + ylogy + 1 = 0       
(d) none of these

Answer : B

Question : The order of the differential equation of all the circles of given radius 4 is
(a) 2
(b) 3
(c) 4
(d) 5

Answer : A

Question : The degree and order of the differential equation of the family of all parabolas whose axis is the x-axis, are respectively   
(a) 1, 2                                 
(b) 3, 2                                 
(c) 2, 3                                  
(d) 2, 1

Answer : A