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Recent questions tagged misc
Questions
An equilateral triangle is inscribed in the parabola $y^2 = 4 ax$, where one vertex isat the vertex of the parabola. Find the length of the side of the triangle.
cbse
class11
math
conic-sections
hyperbola
exercise11-misc
misc
q8
sec-b
medium
asked
Apr 8, 2014
by
balaji.thirumalai
1
answer
A man running a racecourse notes that the sum of the distances from the two flag posts from him is always 10 m and the distance between the flag posts is 8 m. Find the equation of the posts traced by the man.
cbse
class11
math
conic-sections
hyperbola
exercise11-misc
misc
q7
sec-a
easy
asked
Apr 8, 2014
by
balaji.thirumalai
1
answer
Find the area of a triangle formed by the lines joining the vertex of the parabola $x^2 = 12y$ to the ends of its latus rectum.
cbse
class11
math
conic-sections
hyperbola
exercise11-misc
misc
q6
sec-b
easy
asked
Apr 8, 2014
by
balaji.thirumalai
1
answer
A rod of length 12cm moves with its ends always touching the coordinate axes. Determine the equation of the locus of a point P on the rod, which is 3cm from the end in contact with the x-axis.
cbse
class11
math
conic-sections
hyperbola
exercise11-misc
misc
sec-b
easy
q5
asked
Apr 8, 2014
by
balaji.thirumalai
1
answer
An arch is in the form of a semi ellipse. It is 8m wide and 2 m high at the centre. Find the height of the arch at a point 1.5 m from one end.
cbse
class11
math
conic-sections
hyperbola
exercise11-misc
misc
sec-b
q4
medium
asked
Apr 8, 2014
by
balaji.thirumalai
1
answer
The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway which is horizontal and 100 m long is supported by vertical wires attached to the cable, the longest wire being 30 m and the shortest being 6 m. Find the length of a supporting wire attached to the roadway 18 m from the middle.
cbse
class11
math
conic-sections
hyperbola
exercise11-misc
misc
sec-b
medium
q3
asked
Apr 8, 2014
by
balaji.thirumalai
1
answer
An arch is in the form of a parabola with its axis vertical. The arch is 10 m high and 5 m wide at the base. How wide is it 2 m from the vertex of the parabola?
cbse
class11
math
conic-sections
hyperbola
exercise11-misc
misc
sec-a
medium
q2
asked
Apr 8, 2014
by
balaji.thirumalai
1
answer
If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.
cbse
class11
math
conic-sections
hyperbola
exercise11-misc
misc
q1
easy
sec-a
asked
Apr 8, 2014
by
balaji.thirumalai
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
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 $20^{th}$ 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
If $S_1,S_2,S_3$ are the sum of $n$ natural numbers,sum of their squares and sum of their cubes respectively then Show that $9S_2^2=S_3(1+8S_1)$
cbse
class11
ch9
bookproblem
misc
sec-a
medium
q24
math
sequences-and-series
asked
Apr 2, 2014
by
rvidyagovindarajan_1
1
answer
Find the sum of $n$ terms of the series $0.6+0.66+0.666+......$
cbse
class11
ch9
bookproblem
misc
medium
sec-b
q21-2
math
sequences-and-series
asked
Apr 2, 2014
by
rvidyagovindarajan_1
1
answer
Find the sum of the series $5+55+555+..........$ upto $n$ terms.
cbse
class11
ch9
bookproblem
misc
medium
sec-b
q21-1
math
sequences-and-series
asked
Apr 2, 2014
by
rvidyagovindarajan_1
1
answer
If $a,b,c$ are in A.P., $b,c,d$ are in G.P. and $\large\frac{1}{c},\frac{1}{d},\frac{1}{e}$ are in A.P., then prove that $a,c,e$ are in G.P.$
cbse
class11
ch9
bookproblem
misc
sec-b
medium
q20
math
sequences-and-series
asked
Apr 2, 2014
by
rvidyagovindarajan_1
1
answer
The ratio of A.M. and G.M. of two positive numbers $a$ and $b$ is $m:n$. Show that $a:b=(m+\sqrt {m^2-n^2}):(m-\sqrt {m^2-n^2})$
cbse
class11
ch9
bookproblem
misc
difficult
sec-c
q19
math
sequences-and-series
asked
Mar 31, 2014
by
rvidyagovindarajan_1
1
answer
If $a$ and $b$ are roots of $x^2-3x+p=0$ and $c$ and $d$ are roots of $x^2-12x+q=0$, where $a,b,c,d$ form a G.P. then prove that $(q+p):(q-p)=17:15$
cbse
class11
ch9
bookproblem
misc
difficult
sec-c
q18
math
sequences-and-series
asked
Mar 31, 2014
by
rvidyagovindarajan_1
1
answer
If $a,b,c,d$ are in G.P. then show that $(a^n+b^n),(b^n+c^n),(c^n+d^n)$ are in G.P.
cbse
class11
ch9
bookproblem
sec-b
difficult
misc
q17
math
sequences-and-series
asked
Mar 31, 2014
by
rvidyagovindarajan_1
1
answer
If $a\bigg(\large\frac{1}{b}+\frac{1}{c}\bigg)$$,\:b\bigg(\large\frac{1}{c}+\frac{1}{a}\bigg)$$,\:c\bigg(\large\frac{1}{a}+\frac{1}{b}\bigg)$ are in A.P., then prove that $a,b,c$ are in A.P.
cbse
class11
ch9
bookproblem
misc
difficult
sec-b
q16
math
sequences-and-series
asked
Mar 31, 2014
by
rvidyagovindarajan_1
1
answer
If $p^{th},\:q^{th}\:\:and\:\:r^{th}$ terms oa an A.P. are $a,\:b\:and\:c$ respectively, then show that $(q-r)a+(r-p)b+(p-q)c=0$
cbse
class11
ch9
misc
bookproblem
medium
sec-b
q15
math
sequences-and-series
asked
Mar 31, 2014
by
rvidyagovindarajan_1
1
answer
Let $S$ be the sum, $P$ the product and $R$ the sum of reciprocals of $n$ terms of a G.P. Prove that $P^2R^n=S^n$
cbse
class11
ch9
bookproblem
misc
difficult
sec-c
q14
math
sequences-and-series
asked
Mar 31, 2014
by
rvidyagovindarajan_1
1
answer
If $\large\frac{a+bx}{a-bx}=\frac{b+cx}{b-cx}=\frac{c+dx}{c-dx}$$\:(x\neq0)$, then show that $a,b,c\:and\:d$ are in G.P.
cbse
class11
ch9
bookproblem
misc
difficult
sec-b
q13
math
sequences-and-series
asked
Mar 30, 2014
by
rvidyagovindarajan_1
1
answer
The sum of first four terms of an A.P. is $56$. The sum of last four terms is $112$. If its first term is $11$ then find the number of terms.
cbse
class11
ch9
bookproblem
misc
sec-b
medium
q12
math
sequences-and-series
asked
Mar 30, 2014
by
rvidyagovindarajan_1
1
answer
A G.P. consists of even number of terms. If the sum of all the numbers is $5$ times the sum of terms occupying the odd places, then find the common ratio.
cbse
class11
ch9
bookproblem
misc
sec-b
difficult
q11
math
sequences-and-series
asked
Mar 30, 2014
by
rvidyagovindarajan_1
1
answer
The sum of three numbers in G.P. is $56$. If we subtract $1,7,21$ from the numbers in that order, we obtain an A.P. Find the numbers.
cbse
class11
ch9
bookproblem
sec-b
medium
misc
q10
math
sequences-and-series
asked
Mar 30, 2014
by
rvidyagovindarajan_1
1
answer
The first term of a G.P. is $1$. The sum of third term and fifth term is $90$. Find the common ratio of the G.P.
cbse
class11
ch9
bookproblem
misc
sec-b
easy
q9
math
sequences-and-series
asked
Mar 30, 2014
by
rvidyagovindarajan_1
1
answer
The sum of some terms of a G.P. is $315$ whose first term and the common ratio are $5$ and $2$ respectively. Find the last term and number of terms of the series.
cbse
class11
ch9
bookproblem
misc
sec-b
easy
q8
math
sequences-and-series
asked
Mar 30, 2014
by
rvidyagovindarajan_1
1
answer
If $f$ is a function satisfying $f(x+y)=f(x).f(y)\:\:\forall x,y\in N$ such that $f(1)=3\:\:and\:\:\displaystyle\sum ^{n}_{x=1} f(x)=120$, then find the value of $n$.
cbse
class11
ch9
bookproblem
misc
sec-b
medium
q7
math
sequences-and-series
asked
Mar 29, 2014
by
rvidyagovindarajan_1
1
answer
Find the sum of all two digit numbers which when divided by $4$ yields $1$ as remainder.
cbse
class11
ch9
bookproblem
misc
sec-b
easy
q6
math
sequences-and-series
asked
Mar 29, 2014
by
rvidyagovindarajan_1
1
answer
Find the sum of all the integers from $1$ and $100$ that are divisible by $2$ or $5$.
cbse
class11
ch9
bookproblem
misc
medium
sec-b
q5
math
sequences-and-series
asked
Mar 29, 2014
by
rvidyagovindarajan_1
1
answer
Find the sum of all the numbers between $200$ and $400$ which are divisible by $7$.
cbse
class11
ch9
bookproblem
misc
medium
sec-b
q4
math
sequences-and-series
asked
Mar 28, 2014
by
rvidyagovindarajan_1
1
answer
If the sum of $n,2n\:and\:3n$ terms of an A.P. are $S_1,S_2\:and\:S_3$ respectively, then show that $S_3=3(S_2-S_1)$
cbse
class11
ch9
bookproblem
misc
medium
sec-b
q3
math
sequences-and-series
asked
Mar 28, 2014
by
rvidyagovindarajan_1
1
answer
If the sum of three numbers in A.P. is $24$ and their product is $440$, then find the numbers.
cbse
class11
ch9
bookproblem
misc
easy
sec-b
q2
math
sequences-and-series
asked
Mar 28, 2014
by
rvidyagovindarajan_1
1
answer
Show that the sum of $(m+n)^{th}$ and $(m-n)^{th}$ terms of an A.P is twice its $m^{th}$ term.
cbse
class11
ch9
misc
bookproblem
sec-a
easy
q1
math
sequences-and-series
asked
Mar 27, 2014
by
rvidyagovindarajan_1
1
answer
Evaluate: $\large \int \limits_{-1}^1 $$x$ $ \left | x \right |$ $ dx$.
cl1124
cbse
class12
bookproblem
ch8
misc
q17
p376
sec-a
medium
math
asked
Feb 10, 2014
by
rvidyagovindarajan_1
1
answer
If O be the origin and the coordinates of P be (1, 2, – 3), then find the equation of the plane passing through P and perpendicular to OP.
cbse
class12
bookproblem
ch11
misc
p499
q16
sec-b
medium
math
asked
Feb 3, 2014
by
rvidyagovindarajan_1
1
answer
Suppose that 5% of men and 0.25% of women have grey hair. A grey haired person is selected at random. What is the probability of this person being male? Assume that there are equal number of males and females.
cbse
class12
bookproblem
ch13
misc
p582
q3
sec-b
medium
math
asked
Jan 30, 2014
by
balaji
1
answer
Let $(f:R \to R)$ be defined as $(f(x)=2x+3.)$Find the function $(g(x):R \to R)$ such that $(g\;o\;f = f\;o\;g = I_R.)$
cbse
class12
additionalproblem
ch1
misc
sec-b
easy
math
jeemain
sets-relations-and-functions
relations-and-functions
asked
Jan 29, 2014
by
balaji
1
answer
Find the area under the given curves and given lines: $ (ii)\:y = x^4, x = 1, x = 5 \: and\: x - axis$
cbse
class12
bookproblem
ch8
misc
q1
q1-2
p375
sec-a
math
asked
Aug 16, 2013
by
sreemathi.v
1
answer
For each of the exercises given below, verify that the given function (implicit or explicit) is a solution of the corresponding differential equation $( iv)\quad x^2=2y^2 \log y : \qquad (x^2+y^2)\large\frac{dy}{dx}$$-xy=0$
cbse
class12
bookproblem
ch9
misc
q2
q2-4
p420
medium
sec-a
math
asked
Jul 30, 2013
by
sreemathi.v
1
answer
Verify that the given function (implicit or explicit) is a solution of the corresponding differential equation
cbse
class12
bookproblem
ch9
misc
q2
q2-3
p420
medium
sec-a
math
asked
Jul 30, 2013
by
sreemathi.v
1
answer
Verify that the given function (implicit or explicit) is a solution of the corresponding differential equation
cbse
class12
bookproblem
ch9
misc
q2
q2-2
p420
medium
sec-a
math
asked
Jul 30, 2013
by
sreemathi.v
1
answer
For each of the differential equations given below,indicate its order and degree(if defined) $(iii)\;\large\frac{d^4y}{dx^4}-\sin\big(\large\frac{d^3y}{dx^3}\big)$$=0$
cbse
class12
bookproblem
misc
q1
q1-3
p419
easy
sec-a
math
asked
Jul 29, 2013
by
sreemathi.v
1
answer
For each of the differential equations given below,indicate its order and degree(if defined) $(ii)\;\big(\large\frac{dy}{dx}\big)^3-4\big(\large\frac{dy}{dx}\big)^2+7y=\sin x$
cbse
class12
bookproblem
misc
q1
q1-2
p419
easy
sec-a
math
asked
Jul 29, 2013
by
sreemathi.v
1
answer
Prove the following function: 7.$ tan^{-1}\frac{63}{16} = sin^{-1} \frac{5}{13}+cos^{-1} \frac {3}{5}$
cbse
class12
bookproblem
ch2
misc
q7
p51
medium
sec-b
math
asked
Mar 14, 2013
by
balaji.thirumalai
1
answer
Let $S=\{a,b,c\}\;$ and$ \;T = \{1,2,3\}$. Find $F^{-1}$ of the following functions \(F\) from \(S\) to \(T\), if it exists - - $(ii)\;\; F=\{(a,2), (b,1), (c,1)\}$
cbse
class12
bookproblem
ch1
misc
q11
q11-2
p30
sec-a
math
asked
Mar 13, 2013
by
sreemathi.v
1
answer
A manufacturer produces three products $( x, y, z )$ which he sells in two markets. Annual sales are indicated below: \[ \begin{array} { c c } \textbf{Market} & \textbf{Products} \\ I & 10,000 \quad 2,000 \quad 18,000 \\ II & 6,000 \quad 20,000 \quad 8,000 \end{array} \] If the unit costs of the above three commodities are Rs 2.00, Rs 1.00 and 50 paise respectively. Find the gross profit.
cbse
class12
bookproblem
ch3
misc
q10
p101
easy
10-2
sec-b
math
asked
Mar 5, 2013
by
balaji.thirumalai
1
answer
Let A = $\begin{bmatrix} 1 & -2 & 1\\ -2 & 3 & 1\\ 1 & 1 & 5 \end{bmatrix}$. Verify that \[\] $(ii)\big(A^{-1}\big)^{-1}$
cbse
class12
bookproblem
ch4
misc
q8
q8-2
p142
easy
sec-b
math
asked
Mar 1, 2013
by
sreemathi.v
1
answer
If $A=\begin{bmatrix}\alpha & \beta\\\gamma & -\alpha\end{bmatrix}$ is such that $A^2=I,$ then which of the following is true:
cbse
class12
bookproblem
ch3
misc
q13
p101
easy
shortanswer
sec-a
math
asked
Feb 19, 2013
by
sreemathi.v
1
answer
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