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Recent questions and answers in Math
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CBSE XI
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Math
Math
Sets
Relations and Functions
Trigonometric Functions
Principle of Mathematical Induction
Complex Numbers and Quadratic Equations
Linear Inequalities
Permutations and Combinations
Binomial Theorem
Sequences and Series
Straight Lines
Conic Sections
Introduction to Three Dimensional Geometry
Limits and Derivatives
Mathematical Reasoning
Statistics
Probability
Prove the following statement by the principle of mathematical induction : \[\] $1+5+9+...+(4n-3)=n(2n-1)$ for all natural numbers $n$.
cbse
class11
ch4
mathematical-induction
exemplar
q16
answered
Feb 3
by
abdulrahimshafiuyusuf
1
answer
Choose the correct answer for all $n \in N, 3.5^{2n+1}+2^{3n+1}$ is divisible by
cbse
class11
ch4
mathematical-induction
exemplar
q27
answered
Sep 25, 2020
by
apoorva14544
1
answer
If $P(n) : 2n < n!, n \in N$, then $P(n)$ is true for all $n \geq $______ .
cbse
class11
ch4
mathematical-induction
exemplar
q29
answered
Aug 14, 2019
by
s9466813326
1
answer
The equation of the ellipse whose focus is $(1,-1)$,the directrix the line $x-y-3=0$ and eccentricity $\large\frac{1}{2}$ is
cbse
class11
math
conic-sections
ellipse
exemplar
sec-a
medium
q54
answered
Mar 6, 2019
by
meiopde4
2
answers
True-or-False:There will be only at 24 selections containing atleast one red ball out of a bag containing 4 red and 5 black balls.It is being given that balls of the same colour are identical.
cbse
math
class11
ch7
permutations-and-combinations
exercise7-3
true-or-false
exemplar
q56
sec-a
easy
answered
Feb 6, 2019
by
yesgayathri
1
answer
If for real values of $x\cos\theta=x+\large\frac{1}{x}$,then
cbse
math
class11
ch3
trigonometric-functions
exemplar
q59
sec-b
medium
answered
Dec 21, 2018
by
ravishankhwar88
2
answers
$2\sin ^2\large\frac{3\pi}{4}$$+2\cos^2\large\frac{\pi}{4}$$+2\sec^2\large\frac{\pi}{3}$ =
cl38429
sat
trigonometry
cbse
math
class11
ch3
trigonometric-functions
bookproblem
exercise3-3
q4
sec-b
medium
answered
Jul 3, 2018
by
pady_1
1
answer
Find the sixth term of the expansion $(y^{\Large\frac{1}{2}}+x^{\Large\frac{1}{3}})^n$.If the binomial coefficient of the third term from the end is 45.
cbse
math
class11
ch8
binomial-theorem
exemplar
q8
sec-b
medium
answered
Feb 8, 2018
by
rohit0112004
1
answer
The number of different words that can be formed from the letters of the word INTERMEDIATE.Such that two vowels never come together is ________
cbse
math
class11
ch7
permutations-and-combinations
exercise7-3
exemplar
q44
sec-b
medium
answered
Jan 28, 2018
by
nikitadalwale95
2
answers
The wheel of a railway carriage is 40cm in diameter and makes 6 revolutions in a second. How fast is the train going?
sat
math
trigonometry
cbse
class11
ch3
trigonometric-functions
additionalproblem
sec-b
medium
answered
Jan 3, 2018
by
mahawarravi036
2
answers
State whether each of the following statement is True or False.Justify your answer. ${2,6,10}$ and ${3,7,11}$ are disjoint sets.
cbse
math
class11
ch1
sets
bookproblem
exercise1-4
q12-iv
sec-a
easy
answered
Jul 2, 2017
by
yaswanthrreddy4231
2
answers
Find all pairs of consecutive even possitive integers both of which are lar
math
answered
Jun 15, 2017
by
pady_1
1
answer
If $\cos\theta=\large\frac{\cos\alpha-\cos\beta}{1-\cos\alpha\cos\beta}$ then prove that one of the values of $\tan\large\frac{\theta}{2}$ is $\tan \large\frac{\alpha}{2}$$\cot \large\frac{\beta}{2}$
cbse
math
class11
ch3
trigonometric-functions
additionalproblem
sec-c
difficult
answered
Feb 23, 2017
by
nehanagwani
2
answers
Write the following sets in roster form : The set of all letters in word TRIGONOMETRY
cbse
math
class11
ch1
sets
bookproblem
exercise1-1
q3-v
sec-a
easy
answered
Jul 30, 2016
by
sweetypiesneha18
2
answers
3x2−11xy+10y2−7x+13y+k=0 denotes a pair of straight lines find the value of k
answered
Jul 1, 2015
by
meena.p
1
answer
if the pair of straight lines x^2-2pxy-y^2=0 and x^2-2qxy-y^2=0 be such that each pair bisects the angles between the other pair prove that pq= -1
pair
of
straight
line
answered
Feb 21, 2015
by
sharmaaparna1
1
answer
Let $(x_1,y_1)$ be the point of intersection of the tangent to the parabola $y^2=4ax$ at the points $t_1$ and $t_2$ . Then $x_1=a{t_1}{t_2}$ and $y_1=a(t_1+t_2)$
parabola
answered
Feb 20, 2015
by
meena.p
1
answer
how to remember equation of tangent . can you show how did you find out Equation of tangent at $(a{t_1}^2,2a{t_1})$ is
parabola
answered
Feb 20, 2015
by
vijayalakshmi.r
1
answer
locus of the point of intersection of tangent to $y^2=4ax$ which intercept a constant length d on the directrix
answered
Jan 19, 2015
by
meena.p
1
answer
Find equation the circum circle of triangle ABC with A(1,0),B(-1,0)C(0,0)
straight
lines
answered
Oct 21, 2014
by
pady_1
1
answer
Show that the point $(x,y)$ given by $x=\large\frac{2at}{1+t^2}$ and $y=\large\frac{a(1-t^2)}{1+t^2}$ lies on a circle for all real values of $t$ such that $-1\leq t \leq 1$ where $a$ is any given real numbers.
cbse
class11
math
conic-sections
circle
exemplar
sec-b
medium
q2
answered
Oct 17, 2014
by
sreemathi.v
1
answer
Equation of the hyperbola with eccentricity $\large\frac{3}{2}$ and foci at $(\pm 2,0)$ is
cbse
class11
math
conic-sections
hyperbola
exemplar
sec-a
easy
q59
answered
Oct 17, 2014
by
sreemathi.v
1
answer
The distance between the foci of a hyperbola is $16$ and its eccentricity is $\sqrt 2$.Its equation is
cbse
class11
math
conic-sections
hyperbola
exemplar
sec-a
easy
q58
answered
Oct 17, 2014
by
sreemathi.v
1
answer
The eccentricity of the hyperbola whose latus rectum is $8$ and conjugate axis is equal to half of the distance between the foci is
cbse
class11
math
conic-sections
hyperbola
exemplar
sec-a
easy
q57
answered
Oct 17, 2014
by
sreemathi.v
1
answer
If $e$ is the eccentricity of the ellipse $\large\frac{x^2}{a^2}+\frac{y^2}{b^2}\normalsize =1\;(a < b)$,then
cbse
class11
math
conic-sections
ellipse
exemplar
sec-a
easy
q56
answered
Oct 17, 2014
by
sreemathi.v
1
answer
The length of the latus rectum of the ellipse $3x^2+y^2=12$ is
cbse
class11
math
conic-sections
ellipse
exemplar
sec-a
easy
q55
answered
Oct 16, 2014
by
sreemathi.v
1
answer
If the vertex of the parabola is the point $(-3,0)$ and the directrix is the line $x+5=0$,then its equation is
cbse
class11
math
conic-sections
parabola
exemplar
sec-a
easy
q53
answered
Oct 16, 2014
by
sreemathi.v
1
answer
If the parabola $y^2=4ax$ passes through the point $(3,2)$,then the length of its latus rectum is
cbse
class11
math
conic-sections
parabola
exemplar
sec-a
easy
q52
answered
Oct 16, 2014
by
sreemathi.v
1
answer
If the focus of a parabola is $(0,-3)$ and its directrix is $y=3$,then its equation is
cbse
class11
math
conic-sections
parabola
exemplar
sec-a
easy
q51
answered
Oct 16, 2014
by
sreemathi.v
1
answer
The equation of a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length $3a$ is
cbse
class11
math
conic-sections
circle
exemplar
sec-a
easy
q50
answered
Oct 16, 2014
by
sreemathi.v
1
answer
Equation of the circle with centre on the $y$-axis and passing through the origin and the point $(2,3)$ is
cbse
class11
math
conic-sections
circle
exemplar
sec-a
medium
q49
answered
Oct 16, 2014
by
sreemathi.v
1
answer
Equation of a circle which passes through $(3,6)$ and touches the axes is
cbse
class11
math
conic-sections
circle
exemplar
sec-a
medium
q48
answered
Oct 16, 2014
by
sreemathi.v
1
answer
The area of the circle centred at $(1,2)$ and passing through $(4,6)$ is
cbse
class11
math
conic-sections
circle
exemplar
sec-a
easy
q47
answered
Oct 16, 2014
by
sreemathi.v
1
answer
The equation of the hyperbola with vertices at $(0,\pm 6)$ and eccentricity $\large\frac{5}{3}$ is _________ and its foci are ___________
cbse
class11
math
conic-sections
hyperbola
exemplar
sec-a
medium
q46
answered
Oct 16, 2014
by
sreemathi.v
1
answer
The equation of the parabola having focus at $(-1,-2)$ and the directrix $x-2y+3=0$ is _________
cbse
class11
math
conic-sections
parabola
exemplar
sec-a
medium
q45
answered
Oct 16, 2014
by
sreemathi.v
1
answer
The equation of the ellipse having foci $(0,1),(0,-1)$ and minor axis of length $\sqrt 5$ is ____________
cbse
class11
math
conic-sections
ellipse
exemplar
sec-a
medium
q44
answered
Oct 16, 2014
by
sreemathi.v
1
answer
An ellipse is described by using an endless string which is passed over two pins.If the axes are 6 cm and 4 cm,the length of the string and distance between the pins are ____________
cbse
class11
math
conic-sections
ellipse
exemplar
sec-a
medium
q43
answered
Oct 16, 2014
by
sreemathi.v
1
answer
The equation of the circle circumscribing the triangle whose sides are the lines $y=x+2,3y=4x,2y=3x$ is _____________
cbse
class11
math
conic-sections
circle
exemplar
sec-c
medium
q42
answered
Oct 15, 2014
by
sreemathi.v
1
answer
The equation of the circle having centre at $(3,-4)$ and touching the line $5x+12y-12=0$ is __________
cbse
class11
math
conic-sections
circle
exemplar
sec-a
medium
q41
answered
Oct 15, 2014
by
sreemathi.v
1
answer
State whether the following statement is True or False : The locus of the point of intersection of lines $\sqrt 3x-y-4\sqrt 3k=0$ and $\sqrt 3kx+ky-4\sqrt 3=0$ for different value of $k$ is a hyperbola whose eccentricity is 2.
cbse
class11
math
conic-sections
hyperbola
exemplar
sec-a
medium
q40
answered
Oct 15, 2014
by
sreemathi.v
1
answer
State whether the following statement is True or False : The line $2x+3y=12$ touches the ellipse $\large\frac{x^2}{9}+\frac{y^2}{4}$$=2$ at the point $(3,2)$
cbse
class11
math
conic-sections
ellipse
exemplar
sec-a
medium
q39
answered
Oct 15, 2014
by
sreemathi.v
1
answer
State whether the following statement is True or False : If $P$ is a point the ellipse $\large\frac{x^2}{16}+\frac{y^2}{25}$$=1$ whose foci are $S$ and $S'$,then $PS+PS'=8$.
cbse
class11
math
conic-sections
ellipse
exemplar
sec-a
easy
q38
answered
Oct 15, 2014
by
sreemathi.v
1
answer
State whether the following statement is True or False : The line $lx+my+n=0$ will touch the parabola $y^2=4ax$ if $ln=am^2$
cbse
class11
math
conic-sections
parabola
exemplar
sec-a
medium
q37
answered
Oct 15, 2014
by
sreemathi.v
1
answer
State whether the following statement is True or False : The point $(1,2)$ lies inside the circle $x^2+y^2-2x+6y+1=0$.
cbse
class11
math
conic-sections
circle
exemplar
sec-a
easy
q36
answered
Oct 15, 2014
by
sreemathi.v
1
answer
State whether the following statement is True or False: If the line $lx+my=1$ is a tangent to the circle $x^2+y^2=a^2$,then the point $(l,m)$ lies on a circle.
cbse
class11
math
conic-sections
circle
exemplar
sec-a
medium
q35
answered
Oct 15, 2014
by
sreemathi.v
1
answer
State whether the following statement is True or False:The shortest distance from the point $(2,-7)$ to the circle $x^2+y^2-14x-10y-151=0$ is equal to $5$.
cbse
class11
math
conic-sections
circle
exemplar
sec-a
medium
q34
answered
Oct 15, 2014
by
sreemathi.v
1
answer
State whether the following statement is True or False: The line $x+3y=0$ is a diameter of the circle $x^2+y^2+6x+2y=0$.
cbse
class11
math
conic-sections
circle
exemplar
sec-a
easy
q33
answered
Oct 15, 2014
by
sreemathi.v
1
answer
Find the equation of the hyperbola with foci $(0,\pm\sqrt{10})$,passing through $(2,3)$.
cbse
class11
math
conic-sections
hyperbola
exemplar
sec-b
medium
q32-c
answered
Oct 15, 2014
by
sreemathi.v
1
answer
Find the equation of the hyperbola with vertices $(0,\pm 7),e=\large\frac{4}{3}$.
cbse
class11
math
conic-sections
hyperbola
exemplar
sec-b
easy
q32-b
answered
Oct 15, 2014
by
sreemathi.v
1
answer
Find the equation of the hyperbola with vertices $(\pm 5,0)$,foci $(\pm 7,0)$.
cbse
class11
math
conic-sections
hyperbola
exemplar
sec-b
easy
q32-a
asked
Oct 15, 2014
by
sreemathi.v
1
answer
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