Extramarks-background-image
Q:

A:
100.
Q:

Show that the sequence < an> defined by
an =4n+5 is an A.P. also its common difference is

A:
4.
Q:

A:
Q:

The equation of line passing through (-4, -3) and parallel to x-axis is

A:
y + 3 = 0
Q:

A:
55.
Q:

In the expansion of (1 + x)2n (x N), the coefficients of (p+1)th and (p + 3)th terms are equal, then

A:
p = n - 1.
Q:

If A+B=/2 and cos A + cos B =1, then cos (A - B) is equal to

A:
0.
Q:

In the Venn diagram shown below, (A B C)' =

A:

{}.

Q:

For the following relation

R = {(0, 0), (0, 1), (1, 1), (2, 1), (2, 2), (2, 0), (1, 0), (0, 2), (0, 1)}

A:
range = {0, 1, 2}
Q:

A:

1/2a.

Q:

The value of 0! × 2! × 3! is ____.

A:

0! × 2! × 3! = 1× (2 × 1) × (3 × 2× 1)
= 12

The value of 0! × 2! × 3! is 12.

Q:

If n C 10 =   n C 3 , then value of n is___. MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2Daebbfv3ySLgzGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaabMeacaqGMbGaaeiiamaaCaaaleqabaGaaeOBaaaakiaaboeadaWgaaWcbaGaaeymaiaabcdaaeqaaOGaeyypa0JaaGPaVpaaCaaaleqabaGaaeOBaaaakiaaboeadaWgaaWcbaGaae4maaqabaGccaGGSaGaaeiiaiaabshacaqGObGaaeyzaiaab6gacaqGGaGaaeODaiaabggacaqGSbGaaeyDaiaabwgacaqGGaGaae4BaiaabAgacaqGGaGaaeOBaiaabccacaqGPbGaae4Caiaab+facaqGFbGaae4xaiaab6caaaa@59B7@

A:
  n C 10 =   n C 3 [ Given ]  =   n C n−3 [ ∵   n C r = n C n−r ] ⇒10=n−3 ⇒     n=10+3     =13 If n C 10 =   n C 3 , then value of n is 13 ¯ . MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2Daebbfv3ySLgzGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=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@A524@
Q:

There are 4 elements in a set A and 5 elements in the set B, then there will be ___ elements in A × B.

A:

It is given that n(A) = 4
and n(B) = 5
Therefore, n(A × B) = 4 × 5
= 20

There are 4 elements in a set A and 5 elements in the set B, then there will be 20 elements in A × B.

Q:

The imaginary part in (3 + 2i)(1 – 4i) is _____.

A:

(3 + 2i)(1 – 4i) = 3 – 12i + 2i – 8i2

= 3 – 10i – 8(–1)

= 3 – 10i + 8
= 11 – 10i
The imaginary part in (3 + 2i)(1 – 4i) is –10.

Q:

The value of i9 – i19 is _____.

A:

i9 – i19 = i4.i3 – (i4)4i3
= 1(–i) – (1)4(–i) [Since i4 = 1 and i3 = - i]
= 0

The value of i9 – i19 is 0.

Q:

The derivative of x3(x – 3)2 is ______.

A:
The given function is x 3 ( x−3 ) 2 . Let y= x 3 ( x−3 ) 2 Differentiating w.r.t. x, we get    dy dx = d dx { x 3 ( x−3 ) 2 } = x 3 d dx ( x−3 ) 2 + ( x−3 ) 2 d dx x 3 = x 3 ×2( x−3 )+ ( x−3 ) 2 ×3 x 2 =2 x 3 ( x−3 )+3 x 2 ( x−3 ) 2 = x 2 ( x−3 ){ 2x+3( x−3 ) } = x 2 ( x−3 )( 2x+3x−9 ) = x 2 ( x−3 )( 5x−9 ) The derivative of x 3 ( x−3 ) 2 is x 2 ( x−3 )( 5x−9 ) ¯ . MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2Daebbfv3ySLgzGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=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@2056@
Q:

The value of lim x→a x m − a m x−a is_____. MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2Daebbfv3ySLgzGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaabsfacaqGObGaaeyzaiaabccacaqG2bGaaeyyaiaabYgacaqG1bGaaeyzaiaabccacaqGVbGaaeOzaiaabccadaWfqaqaaiGacYgacaGGPbGaaiyBaaWcbaGaamiEaiabgkziUkaadggaaeqaaOWaaSaaaeaacGaMagiEamacycihaaWcbKaMagacycOaiGjGb2gaaaGccWaMaAOeI0IaiGjGbggadGaMaYbaaSqajGjGbGaMakacycyGTbaaaaGcbaGaaeiEaiabgkHiTiaabggaaaGaaeiiaiaabMgacaqGZbGaae4xaiaab+facaqGFbGaae4xaiaab+facaqGUaaaaa@6810@

A:
x m – a m =( x – a )( x m–1 + x m–2 a+ x m–3 a 2 + x m–3 a 3 +…+ xa m–2 + a m–1 ) lim x→a x m – a m x−a = lim x→a ( x m–1 + x m–2 a+ x m–3 a 2 + x m–3 a 3 +…+ xa m–2 + a m–1 )    = x m–1 + x m–2 a+ x m–3 a 2 +...+x a m–2 + a m–1    = x m–1 + x m–1 + x m–1 + x m–1 +...+ x m–1 + x m–1    =m x m–1 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2Daebbfv3ySLgzGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=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@FA2F@
Q:

Which type of set is the set of odd natural numbers divisible by 2?

A:
Null set, as there is no odd natural number which is divisible by 2.
Q:

Find solution of cos x = (1/2).

A:

Here,

where n is any integer.

Q:

Find solution of sin x = (3/2).

A:

Here,

where n is any integer.

Q:

In how many ways 7 pictures can be hung from 5 nails on a wall?

A:
Q:

Find the equation of the angle bisectors of the angle between
the coordinate axes.

A:
Let l1 and l2 be the lines bisecting the angles between coordinate axes.
For l1, m = tan 45° = 1 and c = 0.
The equation of l1 is y = 1.x + 0 i.e. x – y = 0.
For l2, m = tan 135° = - 1 and c = 0.
The equation of l2 is y = -1.x + 0 i.e. x + y = 0.
Q:

Find the distance between the parallel lines 2x - 5y + 7 = 0 and
2x - 5y + 5 = 0.

A:
Here, the equation of the line is of the form Ax + By + C = 0.

Given that A = 2, B = -5, C1 = 7 and C2 = 5.

Q:

A:
Q:

Find the term independent of x in the expansion of .

A:
Q:

A:

Q:

Find the component statements of the following compound statements:
(i) The roof is white and the wall is red.
(ii) 0 is a positive number or a negative number.

A:
(i) The component statements are:
p: The roof is white.
q: The wall is red.
(ii) The component statements are:
p: 0 is a positive number.
q: 0 is a negative number.
Q:

A:

Q:

A:

Q:

Find the ratio in which the line segment joining the points (4, 8, 10) and (6, 10, -8) is divided by the XZ-plane.

A:

Q:

Find the distance between (2, -1, 3) and (-2, 1, 3).

A:

Q:

Find the distance of the point (5,-2) from the line 7x - 2y + 3 = 0.

A:

The perpendicular distance (d) of a line Ax + By + C = 0 from a point
(x1 , y1) is given by :

Q:

Taking U = {x : x is natural number} write the complements of the following sets:
1. A = {x : x is an even natural number}
2. B = {x : 2x + 5 = 9}
3. C = {x : x 7}
4. D = {x : x is a prime number}

A:

1. A' = {x : x is an odd natural number}

2. B' = {x : x N, x 2}

3. C' = {x : x N and x < 7}

4. D' = {x : x is a composite number}

Q:

Prove that: by using principle of mathematical induction.

A:

Q:

If , then find the least positive integral value of m.

A:

Q:

From a class of 15 students, 10 are to be chosen for an excursion party. There are 3 students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen?

A:
There are two cases.

(a) If the 3 students join the excursion party then the number of combinations will be C1= C(12, 7)

(b) If the 3 students do not join the excursion party. Then the number of combinations C2= C(12, 10)

If C is the combination of choosing the excursion party, then

Q:

In an examination a question paper consists of 12 questions divided into two parts, i.e., Part 1 and Part II, containing 5 and 7 questions respectively. A student is required to attempt 8 question in all, selecting at least 3 form each part. In how many ways can a student select the questions?

A:
Student may select 8 question according to following-scheme

I (5 questions) II (7 question)

(a) 3 5

(b) 4 4

(c) 5 3

If P is the required number of ways, then

Q:

A coin is tossed. If it shows a tail, we draw a ball from a box which contains 4 black and 3 white balls. If it shows a head, we throw a die. Find the sample space of this experiment.

A:
Let the black and white balls contained in the box be denoted by

B1, B2, B3, B4, W1, W2 and W3 respectively.

Case 1: When the coin shows a tail, a ball is drawn from a box containing 4 black and 3 white balls

Sample space, S1 = { TB1, TB2, TB3, TB4, TW1, TW2, TW3}

Case 2: When the coin shows a head, a die is thrown which can have any outcome between 1 and 6.

Sample space, S2 = { H1, H2, H3, H4, H5, H6 }

Total Sample Space, S = { TB1, TB2, TB3, TB4, TW1, TW2, TW3, H1, H2, H3, H4, H5, H6}.

Q:

Find the coordinates of the focus, axis of the parabola, equation of the directrix and the length of the latus rectum for the parabola y2= 16x.

A:
The given parabola contains y2, so the axis of the parabola is the x-axis.
The given parabola is of the form y2 = 4ax. Therefore,

a = 4.

Focus is at (4, 0).

Equation of the directrix is : x = - 4.

Length of latus rectum = 4a
= 4(4)
= 16.

Q:

Find the equation of the ellipse, with minor axis is along the x-axis and passing through the points (2, 1) and (1, -3).

A:
The standard form of the ellipse is

x2/a2 + y2/b2 =1

Since the points (2, 1) and (1, -3) lie on the ellipse, we have



Q:

A:

Q:

Prove that

A:

Q:

Prove that

A:

Q:

Find the sum of the series:

A:

Q:

The sum and sum of squares corresponding to height x (in cm) and weight y (in gram) of 50 plant products are given below:



Which is more varying, the height or weight?

A:

Q:

Find the mean deviation about the median for the following data:

Class

0-10

10-20

20-30

30-40

40-50

50-60

Frequency

7

15

6

16

2

4

A:
We construct the following table:

Class

Frequency, f

Cumulative Frequency(c.f)

Mid-point,x

0-10

7

7

5

-20

20

140

10-20

15

22

15

-10

10

150

20-30

6

28

25

0

0

0

30-40

16

44

35

10

10

160

40-50

2

46

45

20

20

40

50-60

4

50

55

30

30

120

50

=610



















The class-interval containing (N/2)th or 25th item is 20-30. Therefore, it is the

median class.

Here, l = 20, N = 50, C = 22, f= 6 and h = 10

= 20+{(50/2 - 22)}/6 10=25

M.D.( ) = = 610/50= 12.2

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