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Recent questions tagged difficult
Questions
Find the middle term in the expansion of $\big(\large\frac{3}{3}$$+9y\big)^{10}$
cbse
math
class11
ch8
binomial-theorem
exercise8.2
q8
sec-c
difficult
asked
Jun 23, 2014
by
sreemathi.v
1
answer
Find the middle term in the expansion of $(3-\large\frac{x^3}{6})^7$
cbse
math
class11
ch8
binomial-theorem
exercise8.2
q7
sec-c
difficult
asked
Jun 23, 2014
by
sreemathi.v
1
answer
Find the coefficient of $a^5b^7$ in $(a-2b)^{12}$
cbse
math
class11
ch8
binomial-theorem
exercise8.2
q2
sec-c
difficult
asked
Jun 23, 2014
by
sreemathi.v
1
answer
Show that $9^{n+1}-8n-9$ is divisible by 64 whenever n is a positive integer.
cbse
math
class11
ch8
binomial-theorem
exercise8.1
q13
sec-c
difficult
asked
Jun 23, 2014
by
sreemathi.v
1
answer
The number of ways in which one can select three distinct integers between 1 and 30 both inclusive ,whose sum is even is
cbse
math
class11
ch7
permutations-and-combinations
additionalproblem
q47
sec-c
difficult
asked
Jun 20, 2014
by
sreemathi.v
1
answer
9 balls are to be placed in 9 boxes and 5 of the balls cannot fit into 3 small boxes.The number of ways of arranging one ball in each of the boxes is
cbse
math
class11
ch7
permutations-and-combinations
additionalproblem
q40
sec-c
difficult
asked
Jun 20, 2014
by
sreemathi.v
1
answer
The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order as in an English dictionary.The number of words that appear before the word COCHIN is
cbse
math
class11
ch7
permutations-and-combinations
additionalproblem
q32
sec-c
difficult
asked
Jun 20, 2014
by
sreemathi.v
1
answer
The number of triangles whose vertices are at the vertices of an octagon but none of whose sides happen to come from the octagon is
cbse
math
class11
ch7
permutations-and-combinations
additionalproblem
q26
sec-c
difficult
asked
Jun 20, 2014
by
sreemathi.v
1
answer
Two numbers are chosen from 1,3,5,7.....147,149 and 151 and multiplied together in all possible ways.The number of ways which will give us the product a multiple of 5 is
cbse
math
class11
ch7
permutations-and-combinations
additionalproblem
q25
sec-c
difficult
asked
Jun 20, 2014
by
sreemathi.v
1
answer
ABCD is a convex quadrilateral 3,4,5 and 6 points are marked on the sides AB,BC,CD and DA respectively.The number of triangles with vertices on different sides is
cbse
math
class11
ch7
permutations-and-combinations
additionalproblem
q23
sec-c
difficult
asked
Jun 20, 2014
by
sreemathi.v
1
answer
A person standing at the junction (crossing) of two straight paths represented by the equations $2x – 3y + 4 = 0$ and $3x + 4y – 5 = 0 $ wants to reach the path whose equation is $6x – 7y + 8 = 0$ in the least time. Find equation of the path that he should follow.
cbse
class11
ch10
straight-lines
bookproblem
misc
sec-c
q24
difficult
asked
May 23, 2014
by
thanvigandhi_1
1
answer
Prove that the product of the lengths of the perpendiculars drawn from the points $ ( \sqrt{a^2-b^2}, 0)$ and $ ( -\sqrt{a^2-b^2}, 0)$ to the line $ \large\frac{x}{a}$$ \cos \theta + \large\frac{y}{b}$$ \sin \theta = 1$ is $b^2$
cbse
class11
ch10
straight-lines
bookproblem
misc
sec-c
q23
difficult
asked
May 23, 2014
by
thanvigandhi_1
1
answer
A ray of light passing through the point (1, 2) reflects on the $x$ - axis at point $A$ and the reflected ray passes through the point (5, 3). Find the coordinates of $A$
cbse
class11
ch10
straight-lines
bookproblem
misc
sec-c
q22
difficult
asked
May 23, 2014
by
thanvigandhi_1
1
answer
Find equation of the line which is equidistant from parallel lines $9x + 6y – 7 = 0$ and $3x + 2y + 6 = 0.$
cbse
class11
ch10
straight-lines
bookproblem
misc
sec-c
q21
difficult
asked
May 23, 2014
by
thanvigandhi_1
1
answer
If sum of the perpendicular distances of a variable point $P (x, y)$ from the lines $ x + y – 5 = 0$ and $3x – 2y +7 = 0$ is always 10. Show that $ P$ must move on a line
cbse
class11
ch10
straight-lines
bookproblem
misc
sec-c
q20
difficult
asked
May 22, 2014
by
thanvigandhi_1
1
answer
Solve the equation $\sec^22x=1-\tan 2x$
cbse
math
class11
ch3
trigonometric-functions
additionalproblem
sec-c
difficult
asked
May 22, 2014
by
sreemathi.v
1
answer
Solve the equation $\sin 9\theta=\sin \theta$
cbse
math
class11
ch3
trigonometric-functions
additionalproblem
sec-c
difficult
asked
May 22, 2014
by
sreemathi.v
1
answer
If $\tan(\cot x)=\cot(\tan x)$,prove that $\sin 2x=\large\frac{4}{(2n+1)\pi}$
cbse
math
class11
ch3
trigonometric-functions
additionalproblem
sec-c
difficult
asked
May 22, 2014
by
sreemathi.v
1
answer
Solve $3\tan(\theta-15^{\large\circ})=\tan(\theta+15^{\large\circ})$
cbse
math
class11
ch3
trigonometric-functions
additionalproblem
sec-c
difficult
asked
May 22, 2014
by
sreemathi.v
1
answer
If $\cos\theta=\large\frac{\cos\alpha-\cos\beta}{1-\cos\alpha\cos\beta}$ then prove that one of the values of $\tan\large\frac{\theta}{2}$ is $\tan \large\frac{\alpha}{2}$$\cot \large\frac{\beta}{2}$
cbse
math
class11
ch3
trigonometric-functions
additionalproblem
sec-c
difficult
asked
May 22, 2014
by
sreemathi.v
2
answers
If $\cos \theta=\cos \alpha.\cos\beta$ prove that $\tan\large\frac{\theta+\alpha}{2}$$\tan\large\frac{\theta-\alpha}{2}=$$\tan^2\large\frac{\beta}{2}$
cbse
math
class11
ch3
trigonometric-functions
additionalproblem
sec-c
difficult
asked
May 22, 2014
by
sreemathi.v
1
answer
If $\sin x+\sin y=a$ and $\cos x+\cos y=b$,show that $\sin(x+y)=\large\frac{2ab}{a^2+b^2}$
cbse
math
class11
ch3
trigonometric-functions
additionalproblem
sec-c
difficult
asked
May 22, 2014
by
sreemathi.v
1
answer
Prove that $\tan\alpha\tan(60^{\large\circ}-\alpha)\tan (60^{\large\circ}+\alpha)=\tan 3\alpha$
cbse
math
class11
ch3
trigonometric-functions
additionalproblem
sec-c
difficult
asked
May 21, 2014
by
sreemathi.v
1
answer
Find the direction in which a straight line must be drawn through the point (–1, 2) so that its point of intersection with the line $ x + y = 4$ may be at a distance of 3 units from this point
cbse
class11
ch10
straight-lines
bookproblem
misc
sec-c
q16
difficult
asked
May 21, 2014
by
thanvigandhi_1
1
answer
Prove that $\cos^3A\cos 3A+\sin^3A\sin 3A=\cos^32A$
cbse
math
class11
ch3
trigonometric-functions
additionalproblem
sec-c
difficult
asked
May 21, 2014
by
sreemathi.v
1
answer
Prove that $\tan\alpha+2\tan 2\alpha+4\tan 4\alpha+8\cot 8\alpha=\cot\alpha$
cbse
math
class11
ch3
trigonometric-functions
additionalproblem
sec-c
difficult
asked
May 21, 2014
by
sreemathi.v
1
answer
Prove that $\tan(60^{\large\circ}+A)\tan(60^{\large\circ}-A)=\large\frac{2\cos 2A+1}{2\cos 2A-1}$
cbse
math
class11
ch3
trigonometric-functions
additionalproblem
sec-c
difficult
asked
May 21, 2014
by
sreemathi.v
1
answer
Show that the equation of the line passing through the origin and making an angle $ \theta $ with the line $y=mx+c$ is $ \large\frac{y}{x}$$ = \large\frac{m \pm \tan \theta}{1 \mp m \tan \theta}$
cbse
class11
ch10
straight-lines
bookproblem
misc
sec-c
q13
difficult
asked
May 21, 2014
by
thanvigandhi_1
1
answer
Prove that the value of $5\cos \theta+3\cos (\theta+\large\frac{\pi}{3})+$$3$ lies between -4 and 10
cbse
math
class11
ch3
trigonometric-functions
additionalproblem
sec-c
difficult
asked
May 21, 2014
by
sreemathi.v
1
answer
If $\alpha$ and $\beta$ are the solution of the equation $a\sec\theta+b\tan\theta=c$,then show that $\tan(\alpha+\beta)=\large\frac{2bc}{b^2-c^2}$
cbse
math
class11
ch3
trigonometric-functions
additionalproblem
sec-c
difficult
asked
May 21, 2014
by
sreemathi.v
1
answer
Prove that $\cos^2A+\cos ^2B-2\cos A\cos B.\cos(A+B)=\sin^2(A+B)$
cbse
math
class11
ch3
trigonometric-functions
additionalproblem
sec-c
difficult
asked
May 21, 2014
by
sreemathi.v
1
answer
Find the equation of the line passing through the point of intersection of the lines $4x + 7y – 3 = 0$ and $2x – 3y + 1 = 0$ that has equal intercepts on the axes.
cbse
class11
ch10
straight-lines
bookproblem
misc
sec-b
q12
difficult
asked
May 21, 2014
by
thanvigandhi_1
1
answer
Prove that $\tan 70^{\large\circ}=2\tan 50^{\large\circ}+\tan 20^{\large\circ}$
cbse
math
class11
ch3
trigonometric-functions
additionalproblem
sec-c
difficult
asked
May 21, 2014
by
sreemathi.v
1
answer
Evaluate :$\sin(n\pi+(-1)^n\large\frac{\pi}{4})$ where $n$ is an integer,
cbse
math
class11
ch3
trigonometric-functions
additionalproblem
sec-c
difficult
asked
May 21, 2014
by
sreemathi.v
1
answer
In right-angled triangle, the difference between the two acute angles is $(\large\frac{\pi}{15})^c$.Find the angles in degrees
sat
trigonometry
cbse
math
class11
ch3
trigonometric-functions
additionalproblem
sec-c
difficult
asked
May 20, 2014
by
sreemathi.v
1
answer
Find the equation of the lines through the point (3, 2) which make an angle of $45^{\circ}$ with the line $x-2y=3.$
cbse
class11
ch10
straight-lines
bookproblem
misc
sec-c
q11
difficult
asked
May 20, 2014
by
thanvigandhi_1
1
answer
If three lines whose equations are $y = m_1, x+ c_1, y = m_2, x+c_2$ and $y = m_3, x+c_3$ are concurrent, then show that $m_1(c_2-c_3)+m_2(c_3-c_1)+m_3(c_1-c_2)=0$
cbse
class11
ch10
straight-lines
bookproblem
misc
sec-c
q10
difficult
asked
May 20, 2014
by
thanvigandhi_1
1
answer
In a circle of diameter 50cm,the length of a chord is 25cm.Find the length of the minor arc of the chord
cbse
math
class11
ch3
trigonometric-functions
additionalproblem
sec-c
difficult
asked
May 20, 2014
by
sreemathi.v
1
answer
True-or-False :If $\tan(\pi \cos \theta)=\cot (\pi \sin \theta)$,then $\cos(\theta-\large\frac{\pi}{4})$$=\pm \large\frac{1}{2\sqrt 2}$
cbse
math
class11
ch3
trigonometric-functions
exemplar
true-or-false
q75
sec-c
difficult
asked
May 20, 2014
by
sreemathi.v
1
answer
$3(\sin x-\cos x)^4+6(\sin x+\cos x)^2+4(\sin ^6x+\cos ^6x)$=_______
cbse
math
class11
ch3
trigonometric-functions
exemplar
q65
sec-c
difficult
asked
May 20, 2014
by
sreemathi.v
1
answer
In a triangle ABC with $\angle C=90^{\large\circ}$ the equation whose roots are $\tan A$ and $\tan B$ is ___________
cbse
math
class11
ch3
trigonometric-functions
exemplar
q64
sec-c
difficult
asked
May 20, 2014
by
sreemathi.v
1
answer
Find perpendicular distance from the origin to the line joining the points $ (\cos \theta, \sin \theta) $ and $(\cos \phi, \sin \phi)$
cbse
class11
ch10
straight-lines
bookproblem
misc
sec-c
q5
difficult
asked
May 20, 2014
by
thanvigandhi_1
1
answer
Find the general solution of the equation $(\sqrt 3+1)\cos \theta+(\sqrt 3-1)\sin \theta=2$
cbse
math
class11
ch3
trigonometric-functions
exemplar
q29
sec-c
difficult
asked
May 20, 2014
by
sreemathi.v
1
answer
Prove that $\cos \theta \cos\large\frac{\theta}{2}-$$\cos 3\theta\cos \large\frac{9\theta}{2}=$$\sin 7\theta\sin 8\theta$
cbse
math
class11
ch3
trigonometric-functions
exemplar
q6
sec-c
difficult
asked
May 20, 2014
by
sreemathi.v
1
answer
In a polygon no three diagonals are concurrent.If the total number of points of intersection of diagonals interior to the polygon be 70,then the number of diagonals of the polygon is
cbse
math
class11
ch7
permutations-and-combinations
additionalproblem
q20
sec-c
difficult
asked
May 20, 2014
by
sreemathi.v
1
answer
The number of words of four letters containing equal number of vowels and consonants ,repetition allowed is
cbse
math
class11
ch7
permutations-and-combinations
additionalproblem
q14
sec-c
difficult
asked
May 19, 2014
by
sreemathi.v
1
answer
A team of four students is to be selected from a total of 12 students.Total number of ways in which team can be selected such that two particular students refuse to be together and other two particular students wish to be together only is equal to
cbse
math
class11
ch7
permutations-and-combinations
additionalproblem
q12
sec-c
difficult
asked
May 19, 2014
by
sreemathi.v
1
answer
Find the equations of the lines, which cut-off intercepts on the axes whose sum and product are 1 and – 6, respectively
cbse
class11
ch10
straight-lines
bookproblem
misc
sec-b
q3
difficult
asked
May 18, 2014
by
thanvigandhi_1
1
answer
If $p$ is the length of perpendicular from the origin to the line whose intercepts on the axes are $a$ and $b$, then show that $ \large\frac{1}{p^2}$$= \large\frac{1}{a^2}$$ +\large\frac{1}{b^2}$
cbse
class11
ch10
straight-lines
bookproblem
exercise10-3
sec-c
q18
difficult
asked
May 18, 2014
by
thanvigandhi_1
1
answer
A committee of 6 is to be chosen from 10 men and 7 women so as to contain atleast 3 men and 2 women . In how many different ways can this be done if two particular women refuse to serve on the same committee.
cbse
math
class11
ch7
permutations-and-combinations
exercise7-3
exemplar
q49
sec-c
difficult
asked
May 16, 2014
by
sreemathi.v
1
answer
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