“Explore the concepts of functions and limits in mathematics. Understand how functions map inputs to outputs and how limits describe the behavior of functions as they approach specific points.”
Solutions of Mathematics Class 12 Chapter 1
If f(x) = x sec x, then f(0): 0
f(x) = sin x + cos x is ———— function: Neither even nor odd
Derivative of x3with respect to x2is: 3/2 x
A function in which the variable appears as exponent (power), is called a/an _________ function: Exponential
Domain f-1= Range f and Range f-1=: Domain f
The domain of the function g(x)=?: (-
Let f(x) = cos x, then f(x) is an: Even function
f(x) = x3+ sin x, then f(x) is: Odd function
If y = ex, then y3=: ex
If a variable y depends on a variable x in such a way that each value of x determines exactly one value of y, then y is a ____________ of x: Function
f(x) = cos x is a/an _____________ function: Even
A function defined by f(x) = x2is: Even function
Domain of hyperbolic sine function is: The set of all real numbers
lim(1-x)1/x : e-1
d/dx logax: 1/x 1/ln a
If f(x) = ex, then f1 (x) =: lnx
A correspondence that assigns to each element x in X a unique element y is Yis called: Function
If f(x) = x2+ 1, then the value of fof is equal to: x4+ 2x2+ 2
A circle and a square have the same perimeter. Then: The area of the circle is larger
Range of hyperbolic cosine function is: The set of all members in the integral [1,+ infinity]
If f(x) = 2x + 5, then f(2) equals: 9
Let f(x) = 4 – x, g(x) =-2, then fog (x) =: 6
A rule that assigns to each element x in X a unique element y in Y is called a function from: X to Y
A symbolic way to write the statement ” y is a function of x” as y = f(x) invented Swiss mathematician: Euler
The symbol y = f(x) i.e. y is equal to f of x,invented by Swiss mathematician: Euler
x = at2, y = 2at are parametric equations: Parabola
Symbolically Imliplicit function can be written as: f(x,y)=0
The term function was recognized by German Mathematician: Leibniz
y = log10xis known as the ______ of x: Common logarithmic
Inverse hyperbola functions are expressed in terms of natural: Logarithms
If f(x)=x3-x/x2+1then f(x) is: Odd function
If x=Sec: Hyperbola
Domain of hyperbolic cosine function is: The set of all real numbers
The function f(x)=x3+x is: Odd function
Range of hyperbolic sine function is: The set of all real numbers
The inverse hyperbolic function are expressed in terms of: Natural logarithm
If f(-x) = f(x) for all x in the domain of f, then f is Even function
Let f(x) = 4 – x, g(x) = 2x + 1, then gof (x) =: 9 – 2x
f(x) = sinx is a a/an __________ function: Odd
If f(x)=?(x+4) then f(x-1)=: ?(x+3)
f(x) is even function. if and only if: f(-x) = f(x)
Sin h-1x =: ln(x+?x2+1)
If A = ( 1 , 2) the number of elements in A x A are: 4
If f(x) = x3– 2x2+ 4x – 1, then f(1) =: 2
If P is the perimeter of a square and A is its area then P=: 4?A
In a binary relation, the set consisting of all the first elements of the ordered pairs is called: Range
If y is an image of x under the function f, we denote it by: y = f(x)
If f(x)=?: 2
Which one is a constant function: f(x) = 14
Let f(x) = -2, g(x) = 2x + 1, then fog (x): -2
Which of the following is an odd function: sin hx
If y = f(x) is a function then a vertical line cut the graph of f(x): only once
A function in which the variable appears as exponent is called an: Exponential function
If(x)=3x/x2+1, then it is: Odd function
If f(x)=2x+1 and g(x)=x2-1 then fg(x)=: 2x2-1
If x=Cos: Ellipes
If f(x) is a function such that f(-x) = f(x), then f(x) is said to be: Even
If f(x)=x2/3+ 6 then f(x) is: Even function
If f(x) = x2, then the range of f is: Set of all non-negative real numbers
If x=a Cos t & y=a Sint then x2+y2: a2
Function play a central role in the study of: Calculas
lim sin3x/sin2x =: 2-Mar
If f(-x) = f(x), then f(x) is called: Even function
The term function was recognized by a German Mathematician: Leibniz
If f(x) = 2x + 1, then fof(x) equals: 4x + 3
Let f(x) = 4 – x, g(x) = 2x + 1, then fog(x) =: 3 – 2x
If f(x) = x3 -2x2+4x -1, then f(-2)=: -25
If f(x) = x3 -2x2+4x -1, then f(1+x) =: x3+ x2+ 3x +2
If x=ay then y=loga x and a=10 then its known as the: Common Logarithm
If(x)=Sinx + Cos x, then it is: Neither function
X = at2, y = 2at represents: Parabola
If the degree of a polynomial function is __________,then it is called a linear function: 1
lim sinx0/x equals: ?/180
If the degree of a polynomial function is 1, then it is called a: Linear function
Which one is an implicit function: y = f(u), u = g(x)
cos h2x + sin h2x =: cos h 2x
Let f(x) = x2+ 3, then domain of f is the: Set of real numbers
Area of circle of unit radius is: ?
lim 2x Sin (3/2x) =: sln2
sec h2x =: 1 – tan h2x
If x=at2 & y=2at represent the equation of: Parabola
Let f(x) = x2, then domain of f is the set of all: Real numbers
Let f(x) = x2, then range of f is the set of all: Non-negative real numbers
The function ? (x) = (x+1)2 is: neither even nor odd
If f(x) = x2– x, then f(-2) is equal to: 6
The function is said to be an even function if f(-x) =: f(x)
Lim ax-1/x = logae
If x=ay then y=loga x and a: General Logarithm
lim x3 – a3/x – a =: a2
If a variable y depends upon a variable x in such a way that each avlue of x determines exactly one value of y, then we say that: y is a function of x
f(x) = sin x + cos x is __________ function: Neither even nor odd function
Which one is an implicit function: xy + xy2+ x2+ y = 2
f(x) is odd function. if and only if: f(-x) = -f(x)
Let f(x) =4 – x, g(x) = 2x + 1, then gof (x) =: 9 – 2x
If f(x) = cos x, then f(0) = : 1
A function is a rule relating to: Sets
For any set X, a function 1 : X: Linear function
Let f(x) = x3+ sin x, then f(x) is: Neither even nor odd
If x = ey, then y = logeX= ln x, is known as the _____________ of x: Natural logarithmic
Parametric equations x = a cos t, y = a sin t represent the equation of: Circle
Important : Review all previous years’ 12 Class Past Papers for comprehensive practice and better exam preparation.