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Limits — BITSAT Mathematics PYQs

24 previous year questions from Limits with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

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Limits — BITSAT Mathematics PYQs

Given a real valued function ' f ' such that f(x)= array cc ^2 x x^2-[x]^2 & for x 0 1 & for x=0 x x & for x 0 array . then

Let f(x)= x, g(x)= x, h(x)=x^2 then _ x 1 f(g(h(x)))-f(g(h(1))) x-1 =

If f(x)= array l x^2-1,0 < x < 2 2 x+3,2 x < 3 array . , then the quadratic equation whose roots are _ x 2⁻ f(x) and _ x 2⁺ f(x) is

_ x 0 | x| x is equal to

The value of _ x 0 1- (1- x) x^4 is

The value of _ x 0 (1+x)^ 1 x -e+ 1 2 e x x^2 is

Value of _ x 0 a^ x -1 x is

_ x 0 2 ² 3 x x² is equal to

_ x 0 x- x x+ ² x is equal to

The value of lim x → 3 π 4 4 sin 2 x cos x - cos x + sin x sin x + cos x is

The value of a , so that lim x → 0 1 x 2 e a x - e x - x = 3 2 , is

lim n → ∞ sin π n 2 + 1 is equal to

If lim n → ∞ a n - 1 + n 2 1 + n = b , where a is finite number, then

_ n a^ n +b^ n a^ n -b^ n , where a>b>1, is equal to

_ x ₀^ 2 x x e^ x² d x e^ 4 x² equals

If _ x x ( 1 x )=A and _ x 0 x ( 1 x )=B , then which one of the following is correct?

_ x 0 ( cosec x)^ 1 / x is equal to :

Let f(x)= (x⁵-1 ) (x³+1 ), g(x)= (x²-1 ) (x²-x+1 ) and let h ( x ) be such that f ( x )= g ( x ) h ( x ) . Then limh _ x 1 ~h ( x ) is

If f(x)= array cl x²+3 x-10 x²+2 x-15 & , when x -5 a , & when x=-5 array . is continuous at x=-5 , then the value of 'a' will be

_ x / 2 (1- ( x 2 ) )(1- x) (1+ ( x 2 ) )( -2 x)³ =?

Evaluate ( _ x 1+ 3 x -1 (1+ 2 x) );

Find the equation of chord of the circle (x^2+y^2=8 x ) bisected at the point ((4,3) )

The minimum value of ( x^4+y^4+z^2 x y z ) for positive real number (x, y, z ) is

Two tangents (P Q ) and (P R ) drawn to the circle (x^2+y^2-2 x-4 y-20=0 ) from point (P(16,7) ). Ifthe centre of the circle is (C ) then the area of quadrilateral ( PQCR ) is

Limits — BITSAT Mathematics PYQs

Given a real valued function ' f ' such that f(x)= array cc ^2 x x^2-[x]^2 & for x 0 1 & for x=0 x x & for x 0 array . then

Let f(x)= x, g(x)= x, h(x)=x^2 then _ x 1 f(g(h(x)))-f(g(h(1))) x-1 =

If f(x)= array l x^2-1,0 < x < 2 2 x+3,2 x < 3 array . , then the quadratic equation whose roots are _ x 2⁻ f(x) and _ x 2⁺ f(x) is

_ x 0 | x| x is equal to

The value of _ x 0 1- (1- x) x^4 is

The value of _ x 0 (1+x)^ 1 x -e+ 1 2 e x x^2 is

Value of _ x 0 a^ x -1 x is

_ x 0 2 ² 3 x x² is equal to

_ x 0 x- x x+ ² x is equal to

The value of lim x &#8594; 3 &#960; 4 4 sin 2 x cos x - cos x + sin x sin x + cos x is

The value of a , so that lim x &#8594; 0 1 x 2 e a x - e x - x = 3 2 , is

lim n &#8594; &#8734; sin &#960; n 2 + 1 is equal to

If lim n &#8594; &#8734; a n - 1 + n 2 1 + n = b , where a is finite number, then

_ n a^ n +b^ n a^ n -b^ n , where a>b>1, is equal to

_ x ₀^ 2 x x e^ x² d x e^ 4 x² equals

If _ x x ( 1 x )=A and _ x 0 x ( 1 x )=B , then which one of the following is correct?

_ x 0 ( cosec x)^ 1 / x is equal to :

Let f(x)= (x⁵-1 ) (x³+1 ), g(x)= (x²-1 ) (x²-x+1 ) and let h ( x ) be such that f ( x )= g ( x ) h ( x ) . Then limh _ x 1 ~h ( x ) is

If f(x)= array cl x²+3 x-10 x²+2 x-15 & , when x -5 a , & when x=-5 array . is continuous at x=-5 , then the value of 'a' will be

_ x / 2 (1- ( x 2 ) )(1- x) (1+ ( x 2 ) )( -2 x)³ =?

Evaluate ( _ x 1+ 3 x -1 (1+ 2 x) );

Find the equation of chord of the circle (x^2+y^2=8 x ) bisected at the point ((4,3) )

The minimum value of ( x^4+y^4+z^2 x y z ) for positive real number (x, y, z ) is

Two tangents (P Q ) and (P R ) drawn to the circle (x^2+y^2-2 x-4 y-20=0 ) from point (P(16,7) ). Ifthe centre of the circle is (C ) then the area of quadrilateral ( PQCR ) is

The value of lim x → 3 π 4 4 sin 2 x cos x - cos x + sin x sin x + cos x is

The value of a , so that lim x → 0 1 x 2 e a x - e x - x = 3 2 , is

lim n → ∞ sin π n 2 + 1 is equal to

If lim n → ∞ a n - 1 + n 2 1 + n = b , where a is finite number, then