If 'm' and 'n' are the order and degree of the differential equation $(y^{\prime \prime }{)}^5+4\cdot \frac{(y^{\prime \prime }{)}^3}{y^{\prime \prime \prime }}+y^{\prime \prime \prime }$.

Q. If m and n are the order and degree of the differential equation ${\left(y_2\right)}^5+\frac{4{\left(y_2\right)}^3}{y_3}+y_3=x^2-1$, then
(a) m = 3, n = 3
(b) m = 3, n = 2
(c) m = 3, n = 5
(d) m = 3, n = 1

Q.

If ‘m’ and ‘n’ are the order and degree of the differential equation $(y^{\prime \prime }{)}^5+\frac{4(y^{\prime \prime }{)}^3}{y^{\prime \prime \prime }}+y^{\prime \prime \prime }=sinx$, then

Q. Find the angles between each of the following pairs of straight lines:
(i) 3x + y + 12 = 0 and x + 2y − 1 = 0
(ii) 3x − y + 5 = 0 and x − 3y + 1 = 0
(iii) 3x + 4y − 7 = 0 and 4x − 3y + 5 = 0
(iv) x − 4y = 3 and 6x − y = 11
(v) (m² − mn) y = (mn + n²) x + n³ and (mn + m²) y = (mn − n²) x + m³.

Q.

Add:

(i) 3mn, − 5mn, 8mn, −4mn

(ii) t − 8tz, 3tz − z, z − t

(iii) − 7mn + 5, 12mn + 2, 9mn − 8, − 2mn − 3

(iv) a + b − 3, b − a + 3, a − b + 3

(v) 14x + 10y − 12xy − 13, 18 − 7x − 10y + 8xy, 4xy

(vi) 5m − 7n, 3n − 4m + 2, 2m − 3mn − 5

(vii) 4x²y, − 3xy², − 5xy², 5x²y

(viii) 3p²q² − 4pq + 5, − 10p²q², 15 + 9pq + 7p²q²

(ix) ab − 4a, 4b − ab, 4a − 4b

(x) x² − y² − 1 , y² − 1 − x², 1− x² − y²