Class 12 Mathematics - Chapter Integrals NCERT Solutions | \begin{align} \int\left(2x - 3Cosx + e^x
\begin{align} \int\left(2x - 3Cosx + e^x\right).dx\end{align}
\begin{align} \int\left(2x - 3Cosx + e^x\right).dx\end{align}
\begin{align} =2\int x .dx - 3\int Cosx .dx + \int e^x.dx\end{align}
\begin{align} =\frac{2x^2}{2} - 3(Sinx) + e^x + C\end{align}
\begin{align} =x^2 - 3Sinx + e^x + C\end{align}
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Popular Questions of Class 12 Mathematics
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Prove that the function f(x) = 5x – 3 is continuous at x = 0, at x = – 3 and at x = 5.
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Determine order and degree(if defined) of differential equation \begin{align} \frac{d^4y}{dx^4}\;+\;\sin(y^m)\;=0\end{align}
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Represent graphically a displacement of 40 km, 30° east of north.
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If a line makes angles 90°, 135°, 45° with x, y and z-axes respectively, find its direction cosines.
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Maximise Z = 3x + 4y
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Find the area of the region bounded by the curve y2 = x and the lines x = 1, x = 4 and the x-axis.
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\begin{vmatrix} \mathbf{2} & \mathbf{4} \\ \mathbf{-5} & \mathbf{-1} \end{vmatrix} - Q:- Determine whether each of the following relations are reflexive, symmetric and transitive:
(i) Relation R in the set A = {1, 2, 3,13, 14} defined as
R = {(x, y): 3x − y = 0}
(ii) Relation R in the set N of natural numbers defined as
R = {(x, y): y = x + 5 and x < 4}
(iii) Relation R in the set A = {1, 2, 3, 4, 5, 6} as
R = {(x, y): y is divisible by x}
(iv) Relation R in the set Z of all integers defined as
R = {(x, y): x − y is as integer}
(v) Relation R in the set A of human beings in a town at a particular time given by
(a) R = {(x, y): x and y work at the same place}
(b) R = {(x, y): x and y live in the same locality}
(c) R = {(x, y): x is exactly 7 cm taller than y}
(d) R = {(x, y): x is wife of y}
(e) R = {(x, y): x is father of y} - Q:- Find the rate of change of the area of a circle with respect to its radius r when
(a) r = 3 cm
(b) r = 4 cm - Q:-
Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.2, find P (E|F) and P(F|E).
Recently Viewed Questions of Class 12 Mathematics
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Find gof and fog, if
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(ii) f(x) = 8x3 and g(x) = x1/3 . - Q:-
The radius of a circle is increasing at the rate of 0.7 cm/s. What is the rate of increase of its circumference?
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In Figure, identify the following vectors.
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y = Ax : xy' = y (x ≠ 0)
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(i) Symmetric but neither reflexive nor transitive.
(ii) Transitive but neither reflexive nor symmetric.
(iii) Reflexive and symmetric but not transitive.
(iv) Reflexive and transitive but not symmetric.
(v) Symmetric and transitive but not reflexive. - Q:-
Let A = R – {3} and B = R – {1}. Consider the function f : A → B defined by
. Is f one-one and onto? Justify your answer. - Q:-
Let A and B be sets. Show that f : A × B → B × A such that f(a, b) = (b, a) is bijective function.
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Determine order and degree(if defined) of differential equation \begin{align}\frac{d^2y}{dx^2}=\cos3x + sin3x\end{align}
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