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Recent questions tagged medium
Questions
The two adjacent sides of a parallelogram are \(2\hat i - 4\hat j + 5\hat k\) and \( \hat i - 2\hat j - 3\hat k\) . Find the unit vector parallel to its diagonal. Also, find its area.
cbse
class12
bookproblem
ch10
misc
q10
p458
medium
sec-b
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
The scalar product of the vector \(\hat i + \hat j + \hat k\) with a unit vector along the sum of vectors \(2\hat i + 4 \hat j − 5\hat k\) and \(λ\hat i + 2 \hat j + 3\hat k\) is equal to one. Find the value of \( λ.\)
cbse
class12
bookproblem
ch10
misc
q13
p458
sec-b
medium
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
Choose the correct answer if θ is the angle between two vectors $\overrightarrow a$ and $ \overrightarrow b$, then $ \overrightarrow a \: . \: \overrightarrow b\ \: \geq 0$ only when
cbse
class12
bookproblem
ch10
misc
q16
p459
medium
sec-a
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
If \( y = e^{\large a \: cos^{-1}x}, -1 \leq x \leq 1\), show that \((1- x^2)\large\frac{d^2y}{dx^2}-\normalsize x\large\frac{dy}{dx} -\normalsize a^2y \; = \; 0.\)
cbse
class12
bookproblem
ch5
misc
q23
p192
sec-a
medium
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
Integrate the rational functions $\frac{\cos x}{(1-\sin x)(2-\sin x)}\qquad[Hint:Put\;\sin x=t]$
cbse
class12
bookproblem
ch7
sec5
q17
p322
sec-c
medium
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Choose the correct answer in $\Large \int \normalsize\frac{\large xdx}{\large (x-1)(x-2)}$ equals\begin{array}{1 1}(A)\;log\mid\frac{(x-1)^2}{x-2}\mid+\: C & (B)\;log\mid\frac{(x-2)^2}{x-1}\mid+\: C\\(C)\;log\mid\bigg(\frac{x-1}{x-2}\bigg)^2\mid+\: C & (D)\;log\mid(x-1)(x-2)\mid+ \: C\end{array}
cbse
class12
bookproblem
ch7
sec5
q22
p323
sec-b
medium
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
If \(x = a (\cos t + t\sin t)\) and \(y = a (\sin t - t \cos\: t)\), find \( \large\frac{d^2y}{dx^2}\)
cbse
class12
bookproblem
ch5
misc
q17
p192
sec-b
medium
math
asked
Dec 4, 2012
by
thanvigandhi_1
1
answer
If \(cos\: y = x \cos (a + y)\), with $\cos$ \(a \neq \pm 1\), prove that \( \large\frac{dy}{dx}=\frac{\cos^2(a + y)}{\sin \: a}\)
cbse
class12
bookproblem
ch5
misc
q16
p192
sec-b
medium
modelpaper-2014
q21
math
asked
Dec 4, 2012
by
thanvigandhi_1
1
answer
Integrate the function\[x\;\sin3x\]
cbse
class12
bookproblem
ch7
sec6
q2
p327
sec-b
medium
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Integrate the function\[x^2e^x\]
cbse
class12
bookproblem
ch7
sec6
q3
p327
sec-c
medium
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Integrate the function $x\;\log x$
cbse
class12
bookproblem
ch7
sec6
q4
p327
sec-a
medium
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Integrate the function $x\; \log2x $
cbse
class12
bookproblem
ch7
sec6
q5
p327
sec-a
medium
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Integrate the function\[x\;\sin^{-1}x\]
cbse
class12
bookproblem
ch7
sec6
q7
p327
sec-b
medium
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Integrate the function $\;\int\;x\;\tan^{-x}$
cbse
class12
bookproblem
ch7
sec6
q8
p327
sec-b
medium
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Integrate the function\[x\;\cos^{-1}x\]
cbse
class12
bookproblem
ch7
sec6
q9
p327
sec-b
medium
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Integrate the function $\frac{x\cos^{-1}x}{\sqrt{1-x^2}}$
cbse
class12
bookproblem
ch7
sec6
q11
p327
sec-b
medium
math
modelpaper-2014
p18-a
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Integrate the function $\tan^{-1}x$
cbse
class12
bookproblem
ch7
sec6
q13
p327
sec-b
medium
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Integrate the function $x(\log x)^2$
cbse
class12
bookproblem
ch7
sec6
q14
p327
sec-b
medium
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Integrate the function $e^x\bigg(\frac{1+\sin x}{1+\cos x}\bigg)$
cbse
class12
bookproblem
ch7
sec6
q18
p328
sec-b
medium
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Integrate the function $\frac{(x-3)e^x}{(x-1)^3}$
cbse
class12
bookproblem
ch7
sec6
q20
p328
sec-a
medium
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Integrate the function $\sin^{-1}\bigg(\large\frac{2x}{1+x^2}\bigg)$
cbse
class12
bookproblem
ch7
sec6
q22
p328
sec-b
medium
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Find the area of the circle $4x^2 + 4y^2 = 9$ which is interior to the parabola $x^2 = 4y$.
cbse
class12
bookproblem
ch8
sec2
q1
p371
sec-c
medium
math
asked
Dec 4, 2012
by
thanvigandhi_1
1
answer
Find the area bounded by curves $(x - 1)^2 + y^2 = 1$ and $x^2 + y^2 = 1$.
cbse
class12
bookproblem
ch8
sec2
q2
p371
sec-c
medium
math
asked
Dec 4, 2012
by
thanvigandhi_1
1
answer
Choose the correct answer in the smaller area enclosed by the circle \(x^2 + y^2 = 4\) and the line \(x + y = 2\) is \[ \begin{array}{1} (A)\;2(\pi - 2) \qquad & (B)\;\pi - 2 \qquad &(C)\;2\pi - 1 \qquad & (D)\;2 ( \pi + 2) \end{array} \]
cbse
class12
bookproblem
ch8
sec2
q6
p372
sec-b
medium
math
asked
Dec 4, 2012
by
thanvigandhi_1
1
answer
Choose the correct answer in the area lying between the curves \(y^2 = 4x\) and \(y = 2x\) is
cbse
class12
bookproblem
ch8
sec2
q7
p372
sec-b
medium
math
asked
Dec 4, 2012
by
thanvigandhi_1
1
answer
Find the area of the region lying in the first quadrant and bounded by $y = 4x^2, x = 0, y = 1$ and $y = 4$.
cbse
class12
bookproblem
ch8
misc
q3
p375
sec-a
medium
math
aims-12-math
asked
Dec 4, 2012
by
thanvigandhi_1
1
answer
Find the area of the smaller region bounded by the ellipse \(\Large { \frac{ x^2}{ a^2}}+\Large { \frac{ y^2}{ b^2}} =\normalsize 1\) and the line \(\Large { \frac{ x}{ a}}+\Large { \frac{y}{ b}} =\normalsize1\)
cbse
class12
bookproblem
ch8
misc
q9
p375
sec-b
medium
math
asked
Dec 4, 2012
by
thanvigandhi_1
1
answer
Find the area of the region enclosed by the parabola \(x^2 = y\), the line \(y = x + 2\) and the \(x\) - axis.
cbse
class12
bookproblem
ch8
misc
q10
p375
sec-b
medium
math
asked
Dec 4, 2012
by
thanvigandhi_1
1
answer
Using the method of integration find the area of the triangle ABC, coordinates of whose vertices are A(2, 0), B(4, 5) and C(6, 3).
cbse
class12
bookproblem
ch8
misc
q13
p376
sec-b
medium
math
asked
Dec 4, 2012
by
thanvigandhi_1
1
answer
Using the method of integration find the area of the region bounded by lines: \(2x + y = 4, 3x - 2y = 6\) and \(x - 3y + 5 = 0\)
cbse
class12
bookproblem
ch8
misc
q14
p376
sec-c
medium
math
asked
Dec 4, 2012
by
thanvigandhi_1
1
answer
Choose the correct answer in the the area bounded by the curve $y = x |\; x\; | ,\; x$ - axis and the ordinates $x = -1$ and $x = 1$ is given by [Hint : $y = x^2$ if $x > 0$ and $y = -x^2$ if $x < 0$].
cbse
class12
bookproblem
ch8
misc
q17
p376
sec-a
medium
math
asked
Dec 4, 2012
by
thanvigandhi_1
1
answer
Choose the correct answer in the the area of the circle \(x^2 + y^2 = 16\) exterior to the parabola \(y^2 = 6x\) is \[\begin{array} (A) \frac{4}{3} (4\pi - \sqrt 3) \quad &(B) \frac{4}{3} (4\pi + \sqrt 3) \quad & (C) \frac{4}{3} (8\pi - \sqrt 3) \quad & (D) \frac{4}{3} (8\pi + \sqrt 3) \end{array}\]
cbse
class12
bookproblem
ch8
misc
q18
p376
sec-b
medium
math
asked
Dec 4, 2012
by
thanvigandhi_1
1
answer
Integrate the function $\sqrt{x^2+4x+6}$
cbse
class12
bookproblem
ch7
sec7
q3
p330
sec-a
medium
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Integrate the function $\sqrt{x^2+4x+1}$
cbse
class12
bookproblem
ch7
sec7
q4
p330
sec-a
medium
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Integrate the function $\sqrt{1-4x-x^2}$
cbse
class12
bookproblem
ch7
sec7
q5
p330
sec-a
medium
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Integrate the function $\sqrt{x^2+4x-5}$
cbse
class12
bookproblem
ch7
sec7
q6
p330
sec-a
medium
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Integrate the function $\sqrt{1+3x-x^2}$
cbse
class12
bookproblem
ch7
sec7
q7
p330
sec-a
medium
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Integrate the function $\sqrt{x^2+3x}$
cbse
class12
bookproblem
ch7
sec7
q8
p330
sec-a
medium
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Evaluate the definite integral as limits of sums $\displaystyle\int\limits_a^bx\;dx$
cbse
class12
bookproblem
ch7
sec8
q1
p334
sec-b
medium
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Evaluate the definite integral as limits of sums $\displaystyle\int\limits_0^5(x+1)dx$
cbse
class12
bookproblem
ch7
sec8
q2
p334
sec-b
medium
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Evaluate the definite integral as limits of sums $\begin{align*}\int\limits_2^3x^2dx \end{align*}$
cbse
class12
bookproblem
ch7
sec8
q3
p334
sec-b
medium
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Evaluate the definite integral as limits of sums\[\int\limits_1^4(x^2-x)dx\]
cbse
class12
bookproblem
ch7
sec8
q4
p334
sec-c
medium
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Evaluate the definite integral as limits of sums $\displaystyle\int\limits_0^4(x+e^{2x})dx$
cbse
class12
bookproblem
ch7
sec8
q6
p334
sec-c
medium
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Evaluate the definite integral $\begin{align*}\int\limits_0^\frac{\Large \pi}{2}\cos^2xdx \end{align*}$
cbse
class12
bookproblem
ch7
sec9
q12
p338
sec-a
medium
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Evaluate the definite integral $\begin{align*}\int\limits_2^3\frac{xdx}{x^2+1} \end{align*}$
cbse
class12
bookproblem
ch7
sec9
q13
p338
sec-a
medium
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Evaluate the definite integral $\begin{align*}\int\limits_0^1\frac{2x+3}{5x^2+1}dx \end{align*}$
cbse
class12
bookproblem
ch7
sec9
q14
p338
sec-a
medium
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Find the area bounded by the curve $x^2 = 4y$ and the line $x = 4y - 2$.
cbse
class12
bookproblem
ch8
sec1
q10
p366
sec-c
medium
math
asked
Dec 4, 2012
by
thanvigandhi_1
1
answer
Evaluate the definite integral $\displaystyle\int\limits_0^2\frac{6x+3}{x^2+4}dx$
cbse
class12
bookproblem
ch7
sec9
q19
p338
sec-b
medium
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Evaluate the definite integral $\displaystyle\int\limits_0^1(xe^x+\sin\frac{\pi\;x}{4})dx$
cbse
class12
bookproblem
ch7
sec9
q20
p338
sec-b
medium
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
The area between $x = y^2$ and $x = 4$ is divided into two equal parts by the line $x = a$, find the value of $a$.
cbse
class12
bookproblem
ch8
sec1
q8
p366
sec-b
medium
math
asked
Dec 4, 2012
by
thanvigandhi_1
1
answer
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