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Questions asked by thanvigandhi_1
Questions
5837
questions
1
answer selected
Write the principal value of \( cos^{-1} \bigg( cos \frac{5\pi}{3} \bigg) \)
cbse
modelpaper
2012
sec-a
q2
asked
Dec 26, 2012
0
answers
Find x, if \( \begin{bmatrix} 5 & 3x \\ 2y & z \end{bmatrix} \) = \( \begin{bmatrix} 5 & 4 \\ 12 & 6 \end{bmatrix}^T \)
cbse
modelpaper
2012
sec-a
q3
ch3
easy
asked
Dec 26, 2012
1
answer
For what value of a, \( \begin{bmatrix} 2a & -1 \\ -8 & 3 \end{bmatrix} \) is a singular matrix?
cbse
modelpaper
2012
sec-a
q4
asked
Dec 26, 2012
0
answers
A square matrix A, of order 3, has | A | = 5, find | A.adj.A |.
cbse
modelpaper
2012
sec-a
q5
asked
Dec 26, 2012
1
answer
Evaluate : $\int \: 5^x dx $
cbse
modelpaper
2012
sec-a
q6
asked
Dec 26, 2012
0
answers
Write the value of $ \int_{\Large\frac{-\pi}{2}}^{\Large\frac{\pi}{2}} \sin^5 x dx $
cbse
modelpaper
2012
sec-a
q7
asked
Dec 26, 2012
0
answers
Find the position vector of the midpoint of the line segment joining the points \( A ( 5\hat i + 3\hat j )\: and \: B ( 3\hat i - \hat j ) \).
cbse
modelpaper
2012
sec-a
q8
asked
Dec 26, 2012
0
answers
If \( \overrightarrow a = 2\hat i - \hat j + 3\hat k \: and \: \overrightarrow b = (6\hat i + \lambda\hat j + 9\hat k )\) and \( \overrightarrow a | | \overrightarrow b, \) find the value of \( \lambda \).
cbse
modelpaper
2012
sec-a
q9
asked
Dec 26, 2012
0
answers
Find the distance of the point (a, b, c) from x - axis.
cbse
modelpaper
2012
sec-a
q10
asked
Dec 26, 2012
0
answers
Let N be the set of all natural numbers and R be the relation on N x N defined by (a, b) R (c, d) if ad = bc. Show that R is an equivalence relation.
cbse
modelpaper
2012
sec-b
q11
asked
Dec 26, 2012
1
answer
Prove that \( tan^{-1} \bigg(\frac{\large 1}{\large 4} \bigg) + tan^{-1} \bigg( \frac{\large 2}{\large 9} \bigg ) = \frac{\large 1}{\large 2} cos^{-1} \bigg( \frac{3}{5} \bigg). \)
cbse
modelpaper
2012
sec-b
q12
ch2
medium
asked
Dec 26, 2012
1
answer
Using properties of determinants, prove that : $ \begin{bmatrix} a^2+1 & ab & ac \\ ab & b^2+1 & bc \\ ca & cb & c^2+1 \end{bmatrix} = (1+a^2+b^2+c^2) $
cbse
modelpaper
2012
sec-b
q13
ch4
bookproblem
sec2
q14
p121
asked
Dec 26, 2012
0
answers
For what values of a and b, the function f defined as : $ f(x) = \left\{ \begin{array}{l l} 3ax+b, & \quad \text{if $x$ < 1}\\ 11, & \quad \text{ if $x$ = 1} \\ 5ax-2b, & \quad \text{if $x$ > 1} \end{array} is \: continuous\: at\: x=1. \right.$
cbse
class12
modelpaper
2012
sec-b
q14
math
asked
Dec 26, 2012
0
answers
If \( x^y + y^x = a^b,\) find $\large\frac{dy}{dx} $
cbse
class12
modelpaper
2012
sec-b
q15
math
asked
Dec 25, 2012
0
answers
Find the intervals inwhich the following function is strictly increasing or strictly decreasing \( f(x) = 20 - 9x + 6x^2 - x^3 \)
cbse
class12
modelpaper
2012
sec-b
q16
math
asked
Dec 25, 2012
0
answers
Evaluate :$\int\: \large\frac{\sin x + \cos x}{\sqrt{\sin x - \cos x }} $$dx$
cbse
class12
modelpaper
2012
sec-b
q17
math
asked
Dec 25, 2012
0
answers
Form the differeential equation of the family of circles having radii 3.
cbse
class12
modelpaper
2012
sec-b
q18
math
asked
Dec 25, 2012
0
answers
Solve the following differential equation : $ \sqrt { 1+x^2+y^2+x^2y^2} + xy \large\frac{dy}{dx} $$= 0 $
cbse
class12
modelpaper
2012
sec-b
q19
math
asked
Dec 25, 2012
0
answers
If the sum of two unit vectors is a unit vector, show that the magnitude of their difference is \( \sqrt 3\)
cbse
class12
modelpaper
2012
sec-b
q20
math
asked
Dec 25, 2012
0
answers
Find whether the lines \( \overrightarrow r = ( \hat i - \hat j - \hat k ) + \lambda (2\hat i + \hat j ) \: and \: \overrightarrow r = ( 2\hat i - \hat j ) + \mu ( \hat i + \hat j - \hat k )\) intersect or not. If intersecting find their point of intersection.
cbse
class12
modelpaper
2012
sec-b
q21
math
asked
Dec 25, 2012
0
answers
Three balls are drawn one by one without replacement from a bag containing 5 white and 4 green balls. Find the probability distribution of number of green balls drawn.
cbse
class12
modelpaper
2012
sec-b
q22
math
asked
Dec 25, 2012
0
answers
If \( A = \begin{bmatrix} 2 & 1 & 3 \\ 4 & -1 & 0 \\ -7 & 2 & 1 \end{bmatrix} \), find \( A^{-1} \) and hence solve the following system of equations : $\begin{array} 2x+y+3z=3 \\ 4x-y =3 \\ -7x+2y+z=2 \end{array} $
cbse
class12
modelpaper
2012
sec-c
q23
math
asked
Dec 25, 2012
0
answers
If the length of three sides of a trapezium, other tan the base are equal to 10 cm each, then find the area of trapezium when it is maximum.
cbse
class12
modelpaper
2012
sec-c
q24
math
asked
Dec 25, 2012
0
answers
Draw a rough sketch of the region enclosed between the circles \( x^2 + y^2 = 4 \) and \( (x-2)^2 + y^2 = 1\) . Using integration, find the area of the enclosed region.
cbse
class12
modelpaper
2012
sec-c
q25
math
asked
Dec 25, 2012
0
answers
Evaluate : \( \int_1^2 \: (x^2 + x + 2 )dx\) as a limit of sums
cbse
class12
modelpaper
2012
sec-c
q26
math
asked
Dec 25, 2012
0
answers
Find the coordinates of the foot of the perpendicular distance of the poit (1, 3, 4) from the plane \( 2x - y + z + 3 = 0 \). Find also, the image of the point in the plane.
cbse
class12
modelpaper
2012
sec-c
q27
math
asked
Dec 25, 2012
0
answers
An aerolpane can carry a maximum of 200 passengers. A profit of Rs. 1000 is made on each executive class ticket and a profit of Rs. 600 is made on each economy class ticket. The airline reserves atleast 20 seats for the executive class. However, at least 4 times as many passengers prefer to travel by ecenomy class, than by the executive class. Determine how many tickets of each type must be sold, inorder to maximise the profit for the airline. What is the maximum profit? Make an L.P.P. and solve it graphically.
cbse
class12
modelpaper
2012
sec-c
q28
math
asked
Dec 25, 2012
0
answers
Write the principal value of \( \cos^{-1} \bigg( \cos\large\frac{7\pi}{6} \bigg) \).
cbse
class12
modelpaper
2012
sec-a
q2
math
asked
Dec 25, 2012
0
answers
Solve for $x$ and $y$ $\begin{bmatrix} 3 & \quad -4 \\ 1 & \quad 2 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 3 \\ 11 \end{bmatrix} $
cbse
class12
modelpaper
2012
sec-a
q3
ch3
easy
math
asked
Dec 25, 2012
1
answer
For what value of k , the matrix \( \begin{bmatrix} k & \quad 2 \\ 3 & \quad 4 \end{bmatrix} \) has no inverse.
cbse
class12
modelpaper
2012
sec-a
q4
math
asked
Dec 25, 2012
0
answers
Evaluate : \( \begin{bmatrix} \sin10^{\circ} & \quad \cos10^{\circ} \\ \sin80^{\circ} & \quad \cos80^{\circ} \end{bmatrix} \)
cbse
class12
modelpaper
2012
sec-a
q5
math
asked
Dec 25, 2012
0
answers
Evaluate : \( \int\:\large \frac{dx}{\sqrt x + x} \)
cbse
class12
modelpaper
2012
sec-a
q6
math
asked
Dec 25, 2012
0
answers
Write the value of \( \int_{\Large\frac{-\pi}{2}}^{\Large\frac{\pi}{2}} \sin^5 xdx. \)
cbse
class12
modelpaper
2012
sec-a
q7
math
asked
Dec 25, 2012
0
answers
Find the position vector of the mid point of the vector joining the points P(2, 3, 4) and Q(4, 1, -2).
cbse
class12
modelpaper
2012
sec-a
q8
math
asked
Dec 25, 2012
0
answers
Find \( | \overrightarrow a \) x \( \overrightarrow b |\), if \( \overrightarrow a = \hat i - 7\hat j + 7\hat k\) and \( \overrightarrow b = 3\hat i - 2\hat j + 2\hat k \)
cbse
class12
modelpaper
2012
sec-a
q9
math
asked
Dec 25, 2012
0
answers
Find the cartesian equation of line which passes through the point ( -2, 4, -5 ) and parallel to the line given by \( \large\frac{x+3}{3} = \frac{y-4}{5} = \frac{z+8}{6} \)
cbse
class12
modelpaper
2012
sec-a
q10
math
asked
Dec 25, 2012
0
answers
Consider \( f : R_+ \rightarrow [ -5, \infty ] \) given by \( f(x) = 9x^2 + 6x - 5\). Show that f is invertible with \( f^{-1} (y) = \bigg[\large \frac{\sqrt {y+6} - 1}{3} \bigg] \)
cbse
class12
modelpaper
2012
sec-b
q11
math
asked
Dec 25, 2012
0
answers
Simplify\( 2\tan^{-1} \bigg(\large \frac{1}{5} \bigg) + \sec^{-1} \bigg( \large\frac{5\sqrt 2}{7} \bigg) + 2\: tan^{-1} \bigg( \frac{1}{8} \bigg) \)
cbse
class12
modelpaper
ch2
2012
sec-b
q12
medium
math
asked
Dec 25, 2012
1
answer
Two farmers Mukul and Vipul cultivates only three crops potato, tomato and wheat. The annual sale of 2010, 2011 are given below : \[ Sale 2010 = \begin{bmatrix} Potato & \quad Tomato & \quad Wheat \\ 20000 & \quad 15000 & \quad 80000 & \quad Mukul \\ 30000 & \quad 10000 & \quad 90000 & \quad Vipul \end{bmatrix} \] \[ Sale 2011 = \begin{bmatrix} Potato & \quad Tomato & \quad Wheat \\ 30000 & \quad 15000 & \quad 60000 & \quad Mukul \\ 20000 & \quad 20000 & \quad 50000 & \quad Vipul \end{bmatrix} \]
cbse
class12
modelpaper
2012
sec-b
q13
math
asked
Dec 25, 2012
0
answers
Find the value of 'a' for which the function f defined as $ f(x) = \left\{ \begin{array} {l l} a\sin \large\frac{\pi}{{2}(n+1)}, & \quad {x \: \leq \: 0} \\ \large\frac{tanx - sinx}{x^3}, & \quad {x \: > 0} \end{array} \right .$ is continuous at x=0. Differentiate \(( x \: cos \: x )^x + ( x\sin\: x )^{\frac{1}{x}}\) w.r.t. \( x \).
cbse
class12
modelpaper
2012
sec-b
q14
math
asked
Dec 25, 2012
0
answers
Verify Rolle's Theorem for the following in the given interval : \( f(x) = (x^2 - 4x + 3 ) e^{2x} \)in [ 1, 3 ]
cbse
class12
modelpaper
2012
sec-b
q15
math
asked
Dec 25, 2012
0
answers
Find the intervals in which the function f given by $ f(x) = \large\frac{4sin x - 2x - x\cos\: x}{2+ cos\: x} $ is $\text { (i) increasing (ii) decreasing } $
cbse
class12
modelpaper
2012
sec-b
q16
math
asked
Dec 25, 2012
0
answers
Evaluate :$ \int_0^{\large\frac{\pi}{2}} \log\sin\: x\:dx $
cbse
class12
modelpaper
2012
sec-b
q17
math
asked
Dec 25, 2012
0
answers
Find the particular solution of the differential equation $\large \frac{dy}{dx} - \frac{y}{x} $$+ cosec \bigg( \large\frac{y}{x} \bigg) = 0 $
cbse
class12
modelpaper
2012
sec-b
q18
math
asked
Dec 24, 2012
0
answers
Find the equation of a curve passing through the origin given that the slope of the tangent to the curve at any point ( x, y ) is equal to the sum of the coordinates of the point
cbse
class12
modelpaper
2012
sec-b
q19
math
asked
Dec 24, 2012
1
answer
If a,b,c are the lengths of the sides BC, CA and AB of a triangle ABC respectively, prove that \( \large\frac{a}{sinA} = \frac{b}{sin B} = \frac{c}{sinC} \)
cbse
class12
modelpaper
2012
sec-b
q20
math
asked
Dec 24, 2012
0
answers
Show that points ( -6, 3, 2 ) ( 3, -2, 4 ) (5, 7, 3 ) and ( -13, 17, -1 ) are coplaner.
cbse
class12
modelpaper
2012
sec-b
q21
math
asked
Dec 24, 2012
0
answers
In a hostel 50% of the student read Hindi magazine, 40% read English magazine and 20% read both Hindi and English magazine. A student is selected at random. (a) Find the probability that student read English magazine only. (b) Find the probability that student reads neither English nor Hindi magazines. (c) Explain the role of newspapers / magazines to aware a student.
cbse
class12
modelpaper
2008
sec-b
q22
math
asked
Dec 24, 2012
0
answers
Using matrices, solve the following system of linear equations : $ \begin{array} xx + 2y - 3z = -4 \\ 2x + 3y + 2z = 2 \\ 3x - 3y - 4z = 11 \end{array} $
cbse
class12
modelpaper
2008
sec-c
q23
math
asked
Dec 24, 2012
0
answers
A catering agency has two kitchens to prepare food at two places A and B. From these place " Mid-day meal' is to be supplied to three different schools situated at P, Q, R. The monthly requirements of the schools are respectively 40, 40 and 50 food packets. A packet contains lunch for 1000 students. Preparing capacity of kitchen A and B are 60 and 70 packets per month respectively. The transportation cost per packet for the kitchen to school is given below. How many packets from each kitchen should be transported to school so that the cost of transportation is minimum? Also find the minimum cost.
cbse
class12
modelpaper
2008
sec-b
q24
math
asked
Dec 24, 2012
1
answer
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