List of top Mathematics Questions on types of differential equations asked in WBJEE JENPAS UG

The population \( p(t) \) of a certain mouse species follows \[ \frac{dp}{dt} = 0.5p - 450. \] If \( p(0)=850 \), then the time at which population becomes zero is:}

If \[ x = \int_0^y \frac{1}{\sqrt{1+9t^2}} \, dt \quad \text{and} \quad \frac{d^2 y}{dx^2} = ay, \] then \( a \) is equal to:

If \(0.2\bar{45}=\frac{p}{q}\) , where p, q are integers and q ≠ 0, then \(\frac{p}{q}\) = ?

If \(∠A+ ∠B = 90°\), then \(1+ \frac{tan A}{tan B}=\) 

If \(\frac{bz-cy}{b-c}=\frac{cx-az}{c-a}\) , a, b, c ≠ 0, then their equivalent ratio is / are

If θ+Φ=90°,θ-Φ=30°,then sin θ+sin Φ=

If \(f(x)=ax^2+bx+c\) and \(f(0)=3\), \(f(1)=1\), \(3f(2)=5\) then \(a:b:c=\)

A tower stands vertically on the ground and on the same ground there is a house of height 10 m and the distance between the house and the tower is 15 m. If the angle of elevation of the top of the tower is found to be 45° from the roof of the house, then what is the height of the tower ?

If x⁴+y⁴=18x²y², then which of the following is/are correct?

Consider two triangles △ABC and △DEF, where \(\frac{AB}{DF}=\frac{BC}{FE}=\frac{CA}{ED}\). Then which is correct?

If tan \(A =\frac{2}{3}\)  then cos² A-sin² A = ?

The value of \(\frac{x+\sqrt{x²-1}}{x-\sqrt{x²+1}} +\frac{x+\sqrt{x²+1}}{x-\sqrt{x²-1}}\) is

The inner and outer radius of a ring-shaped iron sheet of thickness 1 cm is 8 cm and 10 cm respectively. When it is melted to make a solid iron ball, its diameter will be 1 cm

If three times of a number is, 3 less than three times of its square, then the number will be

ABCD is a square whose diagonal AC is 4√2 cm. Then the circumference of its inscribed circle is

If a ∞ b and b ∞o c, then which of the following is/are correct?

Which of the following is/are correct?

If 0<θ≤90°, then the minimum value of 4cot2θ +9 tan2 θ is

If sin θ=\(\frac{8}{17}\), then tan θ+secθ = 

log₄ log₃, log₂ x = 1, then x =

If a² + b² = 14ab, then log (\(\frac{a+b}{4}\))=