List of top Mathematics Questions on types of differential equations asked in JEE Main

Let s₁, s₂, s₃,…..,s₁₀ respectively be the sum to 12 terms of 10 A.P.s whose first terms are 1,2,3, …. ,10 and the common differences are 1, 3, 5, …. , 19 respectively. Then \(10∑^{10}_{i=1} s_i\) is

\((S1) : lim_{n→∞}\frac{1}{ n ^2} ( 2 + 4 + 6 + . . . . + 2n) = 1\)
\((S2): lim_n→∞\frac{1}{n^{16}}( 1^15 +2^15 +3^15 + . . . . + n^15 ) = \frac{1}{16} \)

\(max\\{0≤x≤π}\) \(\{x−2\,\, sin. x \,\,cos+\frac{1}{3} sin\,\, 3x \}=\)

The negation of the statement \(((A\land(B\lor C)) ⇒ (A\lor B)) ⇒ A\) is

If the system of equations
x + y + az = b
2x + 5y + 2z = 6
x + 2y + 3z = 3
Has infinitely many solutions, then 2a + 3b is equal to

if \(2x^y+3y^x=20\) then \(\frac{dy}{dx}\) at (2,2) is equal to:

If the point \((α ,\frac{7√3}{3}) \)lies on the curve traced by the mid-points of the line segments of the lines x cosθ + y sinθ = 7, θ ∈ (0 , \(\frac{π}{2}\) ) between the coordinates axes, then α is equal to

Two dice A and B are rolled, Let the numbers obtained on A and B be α and β respectively. If the variance of α - β is \(\frac{p}{q}\), where p and q are coprime, then the sum of the positive divisors of p is equal to

Among the two statements
(S1) : (p ⇒ q)∧(q ∧(~q)) is a contradiction and
(S2) : (p∧q) v ((~p)∧q) v (p ∧ (~q)) v ((~p) ∧ (~q)) is a tautology

Let S = {\( x∈(−\frac{ π}{ 2} , \frac{π}{2} )\) : 9^1−tan2 x + 9^tan2 x=10 } and \(β=∑_{ x∈s} t a n ^2 (\frac{ x}{ 3} )\) , then \(\frac{1}{6}\) ( β − 14 )² is equal to

Let s={\(z=x+ry:\frac{2z-3i}{4z+2i}\) is a real number}. Then which of the following is not correct?

Let g(x) = f(x) + f(1 - x) and f''(x) > 0, x ∈ (0,1). If g is decreasing in the interval (0, α) and increasing in the interval (α, 1), then tan-1 (2α) + tan^-1 (\(\frac{1}{α}\)) + tan^-1\((\frac{α+1}{α})\) is equal to

For, α, β, γ, δ ∈ \(\mathbb{N},\) if \(∫\left((\frac{x}{e})^{2x}+(\frac{e}{x})^{2x}\right)log_e\,xdx=\) \(\frac{1}{\alpha}(\frac{x}{e})^{βx}-\frac{1}{γ}(\frac{e}{x})^{δx}+c,\) Where \(e=\displaystyle\sum_{n=10}^{∞}\frac{1}{n!}\) and C is constant of integration, then α + 2β + 3γ - 4δ is equal to

the points P and Q are respectively the circumcentre and the orthocentre of a ΔABC, then \( \overrightarrow{PA}+ \overrightarrow{PB}+ \overrightarrow{PC}\) is

The statement ~[p v (~(p ∧ q))] is equivalent to

Let y = y(x), y>0, be a solution curve of the differential equation (1 + x²) dy=y (x–y)dx. If y(0)=1 and y(2√2) , = b then

If the point \((α ,\frac{7√3}{3} )\) lies on the curve traced by the mid-points of the line segments of the lines x cosθ + y sinθ=7,θ∈( \(0,\frac{π}{2}\) ) between the coordinates axes, then α is equal to

Let the lines l₁: \(\frac{x+5}{3} =\frac{y+4}{1}=\frac{z−α}{−2}\) and l₂:3x+2y+z–2=0=x–3y+2z-13 be coplanar. If the point P(a, b, c) on l₁ is nearest to the point Q(-4,-3, 2), then |a| + |b|+|c| is equal to

(S1): (p⇒q)∧(p∧((~q)) is a contradiction and
(S2): (p∧q)v((~q)v((~p)∧ q)v (p∧(~q))v((~p)∧ (~q)) is a tautology

Match List I with List II

	List I		List II
A	Spring constant	I	[T^-1]
B	Angular speed	II	[MT^-2]
C	Angular momentum	III	[ML²]
D	Moment of Inertia	IV	[ML²T^-1]

Choose the correct answer from the options given below:

Let f (x) = \(\frac{x}{ (1+x ^n )^{\frac{1}{n} }}\), x∈R-{-1}, n∈N. n>2.
If fⁿ(x) = (fofof____upto n times) (x), then \(lim ∫^1_ {n→∞ 0} x^{n-2}\)( fⁿ(x))dx is equal to ___.

If the lines \(\frac{x−1}{2}=\frac{2−y }{−3} =\frac{ z−3 }{α}\) and \( \frac{x−4 }{5} =\frac{y−1}{ 2}= \frac{z}{ β}\) intersect, then the magnitude of the minimum value of 8αβ is ___.