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CBSE XI
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Math
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Principle of Mathematical Induction
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$f(x)=\left\{\begin{array}{1 1}mx^2+m,&x<0\\nx+m,&0 \leq x \leq 1 \\nx^3+m,&x>1 \end{array}\right.$ \[\] For what integers $m$ and $n$ does $ \lim\limits_{x \to 0} f(x)$ and $ \lim\limits_{x \to 1} f(x)$ exist?
math
cbse
class11
ch13
limits-and-derivatives
bookproblem
limits
exercise13-1
p301-303
q32
asked
Apr 7, 2014
by
thanvigandhi_1
1
answer
Show that $\large\frac{1\times2^2+2\times 3^2+........n\times (n+1)^2}{1^2\times 2+2^2\times 3+.........n^2\times (n+1)}=\frac{3n+5}{3n+1}$
cbse
class11
ch9
bookproblem
sequences-and-series
misc
sec-c
difficult
q26
math
asked
Apr 7, 2014
by
rvidyagovindarajan_1
1
answer
If the function $f(x)$ satisfies $ \lim\limits_{x \to 1} \large\frac{f(x)-2}{x^2-1}= \pi$ , evaluate $ \lim\limits_{x \to 1} f(x)$
math
cbse
class11
ch13
limits-and-derivatives
bookproblem
limits
exercise13-1
p301-303
q31
asked
Apr 7, 2014
by
thanvigandhi_1
1
answer
$f(x)=\left\{\begin{array}{1 1}|x|+1,&x<0\\0,&x=0 \\|x|-1,&x>0\end{array}\right.$ \[\] For what value(s) of a does $ \lim\limits_{x \to a}f(x)$ exists?
math
cbse
class11
ch13
limits-and-derivatives
bookproblem
limits
exercise13-1
p301-303
q30
asked
Apr 7, 2014
by
thanvigandhi_1
1
answer
Let $a_1, a_2, ....,a_n$ be fixed real numbers and define a function $f(x) = (x-a_1)(x-a_2)...(x-a_n)$ \[\] What is $ \lim\limits_{x \to a_1}f(x)$? For some $ a \neq a_1, a_2,...,a_n$. Compute $ \lim\limits_{x \to a}f(x)$.
math
cbse
class11
ch13
limits-and-derivatives
bookproblem
limits
exercise13-1
p301-303
q29
asked
Apr 7, 2014
by
thanvigandhi_1
1
answer
Suppose $f(x)=\left\{\begin{array}{1 1}a+bx,&x<1\\4,&x=1 \\b-ax,&x>1\end{array}\right.$ and if $ \lim\limits_{x \to 1} f(x) = f(1) $ what are possible values of $a$ and $b$?
math
cbse
class11
ch13
limits-and-derivatives
bookproblem
limits
exercise13-1
p301-303
q28
asked
Apr 7, 2014
by
thanvigandhi_1
1
answer
Find $ \lim\limits_{x \to 5}f(x)$ where, $ f(x) = |x|-5$
math
cbse
class11
ch13
limits-and-derivatives
bookproblem
limits
exercise13-1
p301-303
q27
asked
Apr 5, 2014
by
thanvigandhi_1
1
answer
Evaluate $\lim\limits_{x \to 0} f(x)$ where $f(x)=\left\{\begin{array}{1 1}\large\frac{x}{|x|},&x\neq 0\\0,&x=0\end{array}\right.$
math
cbse
class11
ch13
limits-and-derivatives
bookproblem
limits
exercise13-1
p301-303
q26
asked
Apr 5, 2014
by
thanvigandhi_1
1
answer
Evaluate $\lim\limits_{x \to 0} f(x)$ where $f(x)=\left\{\begin{array}{1 1}\large\frac{|x|}{x},&x\neq 0\\0,&x=0\end{array}\right.$
math
cbse
class11
ch13
limits-and-derivatives
bookproblem
limits
exercise13-1
p301-303
q25
asked
Apr 5, 2014
by
thanvigandhi_1
1
answer
Find $ \lim\limits_{ x \to 1} f(x)$, where $f(x)=\left\{\begin{array}{1 1}x^2-1, &x \leq 1\\-x^2-1, &x>1\end{array}\right.$
math
cbse
class11
ch13
limits-and-derivatives
bookproblem
limits
exercise13-1
p301-303
q24
asked
Apr 5, 2014
by
thanvigandhi_1
1
answer
Find $ \lim\limits_{x \to 0} f(x) $ and $ \lim\limits_{x \to 1} f(x) $ where $f(x)=\left\{\begin{array}{1 1}2x+3, &x \leq 0\\ 3(x+1),& x > o\end{array}\right.$
math
cbse
class11
ch13
limits-and-derivatives
bookproblem
limits
exercise13-1
p301-303
q23
asked
Apr 5, 2014
by
thanvigandhi_1
1
answer
Evaluate the given limit $ \lim\limits_{x \to \large\frac{\pi}{2}} \large\frac{\tan \: 2x}{ x - \Large\frac{\pi}{2}}$
math
cbse
class11
ch13
limits-and-derivatives
bookproblem
limits
exercise13-1
p301-303
q22
asked
Apr 5, 2014
by
thanvigandhi_1
1
answer
Evaluate the given limit $ \lim\limits_{ x \to 0} ( \text{cosec} \: x - \cot\: x)$
math
cbse
class11
ch13
limits-and-derivatives
bookproblem
limits
exercise13-1
p301-303
q21
asked
Apr 5, 2014
by
thanvigandhi_1
1
answer
Evaluate the given limit $ \lim\limits_{x \to 0} \large\frac{ \sin \: ax+bx}{ax+ \sin \: bx}$$a,b, a+b \neq0$
math
cbse
class11
ch13
limits-and-derivatives
bookproblem
limits
exercise13-1
p301-303
q20
asked
Apr 5, 2014
by
thanvigandhi_1
1
answer
Evaluate the given limit $ \lim\limits_{x \to 0} x\sec x$
math
cbse
class11
ch13
limits-and-derivatives
bookproblem
limits
exercise13-1
p301-303
q19
asked
Apr 4, 2014
by
thanvigandhi_1
1
answer
Evaluate the following limits $ \lim\limits_{ x \to 0} \large\frac{ ax + x\cos\: x}{b\sin \: x}$
math
cbse
class11
ch13
limits-and-derivatives
bookproblem
limits
exercise13-1
p301-303
q18
asked
Apr 3, 2014
by
thanvigandhi_1
1
answer
Evaluate the following limits $ \lim\limits_{ x \to 0} \large\frac{\cos\: 2x-1}{\cos\: x - 1}$
math
cbse
class11
ch13
limits-and-derivatives
bookproblem
limits
exercise13-1
p301-303
q17
asked
Apr 3, 2014
by
thanvigandhi_1
1
answer
Evaluate the following limits $ \lim\limits_{x \to 0} \large\frac{ \cos \: x}{ \pi - x}$
math
cbse
class11
ch13
limits-and-derivatives
bookproblem
limits
exercise13-1
p301-303
q16
asked
Apr 3, 2014
by
thanvigandhi_1
1
answer
Evaluate the following limits $ \lim\limits_{ x \to \pi} \large\frac{ \sin ( \pi - x)}{ \pi ( \pi - x)}$
math
cbse
class11
ch13
limits-and-derivatives
bookproblem
limits
exercise13-1
p301-303
q15
asked
Apr 3, 2014
by
thanvigandhi_1
1
answer
Evaluate the following limits \[\] $ \lim\limits_{ x \to 0} \large\frac{ \sin \: ax}{ \sin \: bx}, $$ a , b \neq 0$
math
cbse
class11
ch13
limits-and-derivatives
bookproblem
limits
exercise13-1
p301-303
q14
asked
Apr 3, 2014
by
thanvigandhi_1
1
answer
Evaluate the following limits: $ \lim\limits_{x \to 0} \large\frac{ \sin \: ax}{bx}$
math
cbse
class11
ch13
limits-and-derivatives
bookproblem
limits
exercise13-1
p301-303
q13
asked
Apr 3, 2014
by
thanvigandhi_1
1
answer
Evaluate the following limits: $ \lim\limits_{x \to -2} \Large\frac{ \Large\frac{1}{x}+ \Large\frac{1}{2}}{ \normalsize x +2}$
math
cbse
class11
ch13
limits-and-derivatives
bookproblem
limits
exercise13-1
p301-303
q12
asked
Apr 3, 2014
by
thanvigandhi_1
1
answer
Evaluate the following limits $ \lim\limits_{x \to 1} \large\frac{ax^2+bx+c}{cx^2+bx+a},$$ a+b+c \neq 0$
math
cbse
class11
ch13
limits-and-derivatives
bookproblem
limits
exercise13-1
p301-303
q11
asked
Apr 3, 2014
by
thanvigandhi_1
1
answer
Evaluate the following limits $ \lim\limits_{\large z \to 1} \large\frac{\large z^{\large\frac{1}{3}}-1}{z^{\large\frac{1}{6}}-1}$
math
cbse
class11
ch13
limits-and-derivatives
bookproblem
limits
exercise13-1
p301-303
q10
asked
Apr 3, 2014
by
thanvigandhi_1
1
answer
Evaluate the following limits $ \lim\limits_{x \to 0} \large\frac{ax+b}{cx+1}$
math
cbse
class11
ch13
limits-and-derivatives
bookproblem
limits
exercise13-1
p301-303
q9
asked
Apr 3, 2014
by
thanvigandhi_1
1
answer
Evaluate the following limits $ \lim\limits_{x \to 3} \large\frac{x^4-81}{2x^2-5x-3}$
math
cbse
class11
ch13
limits-and-derivatives
bookproblem
limits
exercise13-1
p301-303
q8
asked
Apr 3, 2014
by
thanvigandhi_1
1
answer
Evaluate the following limits $ \lim\limits_{x \to 2} \large\frac{3x^2-x-10}{x^2-4}$
math
cbse
class11
ch13
limits-and-derivatives
bookproblem
limits
exercise13-1
p301-303
q7
asked
Apr 3, 2014
by
thanvigandhi_1
1
answer
Evaluate the following limits $ \lim\limits_{x \to 0} \large\frac{(x+1)^5-1}{x}$
math
cbse
class11
ch13
limits-and-derivatives
bookproblem
limits
exercise13-1
p301-303
q6
asked
Apr 3, 2014
by
thanvigandhi_1
1
answer
Evaluate the following limits $ \lim\limits_{ x \to -1} \large\frac{x^{10}+x^5+1}{x-1}$
math
cbse
class11
ch13
limits-and-derivatives
bookproblem
limits
exercise13-1
p301-303
q5
asked
Apr 3, 2014
by
thanvigandhi_1
1
answer
Evaluate the following limits $ \lim\limits_{x \to 4} \large\frac{4x+3}{x-2}$
math
cbse
class11
ch13
limits-and-derivatives
bookproblem
limits
exercise13-1
p301-303
q4
asked
Apr 3, 2014
by
thanvigandhi_1
1
answer
Evaluate the following limits $ \lim\limits_{x \to 1} \pi r^2$
math
cbse
class11
ch13
limits-and-derivatives
bookproblem
limits
exercise13-1
p301-303
q3
asked
Apr 3, 2014
by
thanvigandhi_1
1
answer
Evaluate the following limits $\lim\limits_{x \to \pi} \bigg( x - \large\frac{22}{7} \bigg)$
math
cbse
class11
ch13
limits-and-derivatives
bookproblem
limits
exercise13-1
p301-303
q2
asked
Apr 3, 2014
by
thanvigandhi_1
1
answer
Evaluate the following limits $ \lim\limits_{x \to 3} x+3$
math
cbse
class11
ch13
limits-and-derivatives
bookproblem
limits
exercise13-1
p301-303
q1
asked
Apr 3, 2014
by
thanvigandhi_1
1
answer
Find the equation of an ellipse that satisfies the following conditions: Centre at $(0,0)$, major axis on y-axis and passes through $(3,2), \; (1,6)$
cl35719
cl35707
cl35701
cl35314
cl35310
cl35306
cl35304
math
cbse
class11
ch11
exercise11-3
conic-sections
ellipse
q19
easy
sec-b
asked
Apr 3, 2014
by
balaji.thirumalai
1
answer
Find the equation of an ellipse that satisfies the following conditions: Major axis on x-axis, passes through the points $(4,3)$ and $(6.2)$
cl35726
cl35717
math
cbse
class11
ch11
exercise11-3
conic-sections
ellipse
q20
easy
sec-a
asked
Apr 3, 2014
by
balaji.thirumalai
1
answer
Find the equation of an ellipse that satisfies the following conditions: $b=3, c=4$, centre at origin and foci on x-axis.
cl35717
math
cbse
class11
ch11
exercise11-3
conic-sections
ellipse
q18
easy
sec-a
asked
Apr 3, 2014
by
balaji.thirumalai
1
answer
Find the equation of an ellipse that satisfies the following conditions: $a = 4$ and Foci = $(\pm3,0)$
cl35717
cl35705
cl35703
cl35699
cl35697
cl35312
cl35308
cl35304
math
cbse
class11
ch11
exercise11-3
conic-sections
ellipse
q17-1
easy
sec-a
asked
Apr 3, 2014
by
balaji.thirumalai
1
answer
Find the equation of an ellipse that satisfies the following conditions: Length of minor axis $ = 16$ and Foci $ = (0,\pm6)$
cl35707
cl35701
cl35314
cl35310
cl35306
cl35304
math
cbse
class11
ch11
exercise11-3
conic-sections
ellipse
q16
easy
sec-b
asked
Apr 3, 2014
by
balaji.thirumalai
1
answer
Find the equation of an ellipse that satisfies the following conditions: Length of major axis is $26$ and Foci is $(\pm5,0)$
math
cbse
class11
ch11
exercise11-3
conic-sections
ellipse
q15
easy
sec-a
asked
Apr 3, 2014
by
balaji.thirumalai
1
answer
Find the sum of $n$ terms of the series $3+7+13+21+31+.............$
cbse
class11
ch9
bookproblem
misc
medium
sec-c
q23
math
sequences-and-series
asked
Apr 2, 2014
by
rvidyagovindarajan_1
1
answer
Find the equation of an ellipse that satisfies the following conditions: Ends of Major Axis $\;(0, \pm\sqrt 5)$, Ends of Minor Axis $\;(\pm 1,0)$
cl35701
cl35314
cl35310
cl35306
cl35304
math
cbse
class11
ch11
exercise11-3
conic-sections
ellipse
q14
easy
sec-b
asked
Apr 2, 2014
by
balaji.thirumalai
1
answer
Find the equation of an ellipse that satisfies the following conditions: Ends of Major axis $\;(\pm3,0)$, Ends of Minor Axis $\;(0, \pm 2)$
cl35703
cl35699
cl35697
cl35312
cl35308
cl35304
math
cbse
class11
ch11
exercise11-3
conic-sections
ellipse
q13
easy
sec-a
asked
Apr 2, 2014
by
balaji.thirumalai
1
answer
Find the equation of an ellipse that satisfies the following conditions: Vertices $\;(\pm6,0)$, Foci $\;(\pm4,0)$
cl35699
cl35697
cl35312
cl35308
cl35304
math
cbse
class11
ch11
exercise11-3
conic-sections
ellipse
q12
easy
sec-a
asked
Apr 2, 2014
by
balaji.thirumalai
1
answer
Find the equation of an ellipse that satisfies the following conditions: Vertices $\;(\pm 13,0)$, Foci $\;(\pm 5,0)$
cl35314
cl35310
cl35306
cl35304
math
cbse
class11
ch11
exercise11-3
conic-sections
ellipse
q11
easy
sec-b
asked
Apr 2, 2014
by
balaji.thirumalai
1
answer
Find the equation of an ellipse that satisfies the following conditions: Vertices $\;(\pm5,0)$, Foci $\;(\pm4,0)$
cl35697
cl35312
cl35308
cl35304
math
cbse
class11
ch11
exercise11-3
conic-sections
ellipse
q10
easy
sec-a
asked
Apr 2, 2014
by
balaji.thirumalai
1
answer
Find the coordinates of the foci, the vertices, the length of the major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse $4x^2+9y^2=36$
cl35312
cl35308
cl35304
math
cbse
class11
ch11
exercise11-3
conic-sections
ellipse
q9
easy
sec-b
asked
Apr 2, 2014
by
balaji.thirumalai
1
answer
Find the coordinates of the foci, the vertices, the length of the major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse $16x^2+y^2=16$
cl35693
cl35314
math
cbse
class11
ch11
exercise11-3
conic-sections
ellipse
q8
easy
sec-b
asked
Apr 2, 2014
by
balaji.thirumalai
1
answer
Find the coordinates of the foci, the vertices, the length of the major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse $36x^2+4y^2 = 144$
cl35314
math
cbse
class11
ch11
exercise11-3
conic-sections
ellipse
q7
easy
sec-b
asked
Apr 2, 2014
by
balaji.thirumalai
1
answer
Find the $20^{th}$ term of the series $2\times 4+4\times 6+6\times 8+..........$
cbse
class11
ch9
bookproblem
misc
sec-a
easy
q22
math
sequences-and-series
asked
Apr 2, 2014
by
rvidyagovindarajan_1
1
answer
Find the sum of $n$ terms of the series $\large\frac{1^3}{1}+\frac{1^3+2^3}{1+3}+\frac{1^3+2^3+3^3}{1+3+5}+.........$
cbse
class11
ch9
bookproblem
misc
sec-c
difficult
q25
math
sequences-and-series
asked
Apr 2, 2014
by
rvidyagovindarajan_1
1
answer
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