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Recent questions in CBSE XII
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CBSE XII
CBSE XII
Math
Physics
Chemistry
Biology
Find a vector of magnitude $5$ units, and parallel to the resultant of the vectors $\overrightarrow a = 2\hat i + 3 \hat j - \hat k$ and $\overrightarrow b = \hat i - 2\hat j + \hat k$
cbse
class12
bookproblem
ch10
misc
q6
p458
medium
sec-a
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
If $\overrightarrow a = \hat i + \hat j + \hat k, \overrightarrow b = 2\hat i - \hat j + 3\hat k$ and $\overrightarrow c = \hat i - 2\hat j + \hat k$, find a unit vector parallel to the vector $2\overrightarrow a - \overrightarrow b + 3\overrightarrow c$
cbse
class12
bookproblem
ch10
misc
q7
p458
easy
sec-a
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
Show that the points A(1, – 2, – 8), B (5, 0, – 2) and C (11, 3, 7) are collinear, and find the ratio in which B divides AC.
cbse
class12
bookproblem
ch10
misc
q8
p458
easy
sec-b
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are \((2\overrightarrow a + \overrightarrow b)\) and \((\overrightarrow a - 3\overrightarrow b)\) externally in the ratio 1 : 2. Also, show that P is the mid point of the line segment RQ
cbse
class12
bookproblem
ch10
misc
q9
p458
easy
sec-b
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
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
Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ are $ \frac{\large 1}{\large \sqrt 3}, \: \frac{\large 1}{\large \sqrt 3}, \: \frac{\large 1}{\large \sqrt 3} $
cbse
class12
bookproblem
ch10
misc
q11
p458
easy
sec-a
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
Let \(\overrightarrow a = \hat i + 4 \hat j + 2\hat k, \overrightarrow b = 3\hat i − 2 \hat j + 7\hat k \: and \: \overrightarrow c = 2\hat i − \hat j + 4\hat k \) . Find a vector \( \overrightarrow d\) which is perpendicular to both \(\overrightarrow a\) and \(\overrightarrow b\) , and \( \overrightarrow c ⋅ \overrightarrow d =15\)
cbse
class12
bookproblem
ch10
misc
q12
p348
difficult
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
If \( \overrightarrow a, \overrightarrow b, \overrightarrow c, \) are mutually perpendicular vectors of equal magnitudes, show that the vector \( \overrightarrow a + \overrightarrow b + \overrightarrow c\) is equally inclined to \( \overrightarrow a, \overrightarrow b and \overrightarrow c\).
cbse
class12
bookproblem
ch10
misc
q14
p458
difficult
sec-b
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
Prove that \( (\overrightarrow a + \overrightarrow b) ⋅ (\overrightarrow a + \overrightarrow b) =| \overrightarrow a |^2 + |\overrightarrow b |^2\), if and only if \(\overrightarrow a,\: \overrightarrow b\) are perpendicular, given \(\overrightarrow a ≠ 0, \overrightarrow b ≠ 0\).
cbse
class12
bookproblem
ch10
misc
q15
p459
easy
sec-b
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
Choose the correct answer in the following : let \( \overrightarrow a\) and \( \overrightarrow b\) be two unit vectors and θ is the angle between them. Then \( \overrightarrow a\ + \overrightarrow b\) is a unit vector if
cbse
class12
bookproblem
ch10
misc
q17
p459
easy
sec-b
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
Choose the correct answer if the value of $ \hat i.( \hat j\times \hat k)+ \hat j . (\hat i \times \hat k) +\hat k. (\hat i \times \hat j)$ is
cbse
class12
bookproblem
ch10
misc
q18
p459
easy
sec-a
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
Choose the correct answer if θ is the angle between any two vectors $\overrightarrow a$ and $\overrightarrow b$, then $| \overrightarrow a ⋅\overrightarrow b | \: = \: | \overrightarrow a \times\overrightarrow b |$ when θ is equal to
cbse
class12
bookproblem
ch10
misc
q19
p459
easy
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
If \(y = \begin{vmatrix} f(x) & g(x) & h(x) \\l & m &n \\ a & b & c \end{vmatrix}\), prove that \(\large\frac{dy}{dx}\normalsize = \begin{vmatrix} f'(x) & g'(x) & h'(x) \\l & m &n \\ a & b & c \end{vmatrix}\)
cbse
class12
bookproblem
ch5
misc
q22
p192
sec-a
easy
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
Integrate the rational functions\[\frac{1}{x(x^n+1)}\] \[Hint:multiply\;numerator\;and\;denominator\;by\;x^{n-1}and\;put\;x^n=t\]
cbse
class12
bookproblem
ch7
sec5
q16
p322
sec-c
difficult
math
asked
Dec 4, 2012
by
sreemathi.v
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
Integrate the rational functions $\frac{(x^2+1)(x^2+2)}{(x^2+3)(x^2+4)}$
cbse
class12
bookproblem
ch7
sec5
q18
p323
sec-b
difficult
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Integrate the rational functions\[\frac{2x}{(x^2+1)(x^2+3)}\]
cbse
class12
bookproblem
ch7
sec5
q19
p323
sec-c
difficult
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Integrate the rational functions\[\frac{1}{x(x^4-1)}\]
cbse
class12
bookproblem
ch7
sec5
q20
p323
sec-c
difficult
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Integrate the rational functions $\frac{1}{(e^x-1)} [Hint:Put\;e^x=\;t]$
cbse
class12
bookproblem
ch7
sec5
q21
p323
sec-b
difficult
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
Choose the correct answer in $\Large \int \normalsize\frac{\large dx}{\large x(x^2+1)}$equals
cbse
class12
bookproblem
ch7
sec5
q23
p323
sec-c
difficult
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Does there exist a function which is continuous everywhere but not differentiable at exactly two points? Justify your answer.
cbse
class12
bookproblem
ch5
misc
q21
p192
sec-a
easy
math
asked
Dec 4, 2012
by
thanvigandhi_1
1
answer
Using the fact that \(\sin (A + B) = \sin A \cos B + \cos A \sin B\) and the differentiation, obtain the sum formula for cosines.
cbse
class12
bookproblem
ch5
misc
q20
p192
sec-b
easy
math
asked
Dec 4, 2012
by
thanvigandhi_1
1
answer
Using mathematical induction prove that \( \large\frac{d}{dx}\normalsize (x^{\large n}) = nx^{\large{n-1}} \) for all positive integers \(n\).
cbse
class12
bookproblem
ch5
misc
q19
p192
sec-b
difficult
math
asked
Dec 4, 2012
by
thanvigandhi_1
1
answer
If \(f (x) = |\; x\; |^3\), show that \(f ″(x)\) exists for all real \(x\) and find it.
cbse
class12
bookproblem
ch5
misc
q18
p192
sec-a
easy
math
asked
Dec 4, 2012
by
thanvigandhi_1
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 $\;\int\;x\;sin\;x$
cbse
class12
bookproblem
ch7
sec6
q1
p327
sec-b
easy
math
asked
Dec 4, 2012
by
sreemathi.v
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\[x^2logx\]
cbse
class12
bookproblem
ch7
sec6
q6
p327
sec-b
easy
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 $(\sin^{-1}x)^2$
cbse
class12
bookproblem
ch7
sec6
q10
p327
sec-b
difficult
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\[x\;\sec^2x\]
cbse
class12
bookproblem
ch7
sec6
q12
p327
sec-a
easy
math
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 $\;\int\;(x^2+1)\;log\;x$
cbse
class12
bookproblem
ch7
sec6
q15
p327
sec-b
easy
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Integrate the function\[e^x(\sin x+\cos x)\]
cbse
class12
bookproblem
ch7
sec6
q16
p328
sec-a
easy
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Integrate the function $\;\int\;\frac{xe^x}{(1+x)^2}$
cbse
class12
bookproblem
ch7
sec6
q17
p328
sec-a
easy
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 $e^x \large($$ \large \frac{1}{x}$$-\large\frac{1}{x^2})$
cbse
class12
bookproblem
ch7
sec6
q19
p328
sec-a
easy
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
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