Quiz about Extension Quiz 2

Question 1

What will be the value of k so that the quadratic equation $$kx^2\ -\ 4x\ +\ 1\ =\ 0$$ has two equal roots?

Accepted Answer

1/4

Answer

2

Answer

3

Answer

4

Answer

8

Question 2

Find the solution of the equation $$x\ -\ 8\sqrt[]{x\ }\ +\ 15\ =\ 0$$

Accepted Answer

x = 9, 25

Answer

x = 3, 5

Answer

x = -3, -5

Answer

x = -9, 25

Question 3

Find the quadratic equation whose roots are -3/4 and 4/3.

Accepted Answer

$$12m^2\ -\ 7m\ -12\ =\ 0$$

Answer

$$2m^2\ +\ 7m\ -\ 12\ =\ 0$$

Answer

$$12m^2\ -\ 9m\ -\ 12\ =\ 0$$

Answer

$$12m^2\ +\ 9m\ -\ 12\ =\ 0$$

Question 4

Find the equation whose roots are the squares of the roots of $$2a^2\ +\ 3a\ +\ 7\ =\ 0$$ .

Accepted Answer

$$4a^2+\ 19a\ +\ 49\ =\ 0$$

Answer

$$4a^2\ -\ 14a\ +\ 49\ =0$$

Answer

$$9a^2\ -\ 4a\ +\ 9\ =\ 0$$

Answer

$$9a^2\ -\ 4a\ +\ 49\ =\ 0$$

Question 5

If $$If\ \alpha\ and\ \beta\ are\ the\ roots\ of\ the\ equation\ x^2\ -\ 2x\ -\ 5\ =\ 0,\ find\ the\ equation\ whose\ roots\ are\ \alpha^2\beta\ and\ \alpha\beta^2.\ $$

Accepted Answer

$$x^2\ +\ 10x\ -\ 125\ =\ 0$$

Answer

$$x^2\ -\ 10x\ -125\ =\ 0$$

Answer

$$5x^2-\ 5x\ +\ 125\ =\ 0$$

Answer

$$5x^2+5x+125\ =\ 0$$

Question 6

$$If\ \alpha\ and\ \beta\ are\ roots\ of\ the\ equation\ 3x^2\ -\ 2x\ -\ 1\ =\ 0,\ find\ the\ eqaution\ whose\ roots\ are\ \frac{\alpha}{\beta}\ and\ \frac{\beta}{\alpha}$$

Accepted Answer

2/3

Answer

1/3

Answer

-1/3

Answer

3/2

Question 7

$$If\ \alpha\ and\ \beta\ are\ the\ roots\ of\ the\ equation\ 3x^2\ +\ 5x\ -\ 2\ =\ 0.\ Find\ the\ value\ of\ \frac{1}{\alpha}\ +\frac{1}{\beta}$$

Accepted Answer

5/2

Answer

-5/2

Answer

-2/3

Answer

1/2

Question 8

$$Find\ the\ quadratic\ equation\ whose\ roots\ 3-\sqrt[]{}3\ and\ 3\ +\ \sqrt[]{3}$$ .

Accepted Answer

$$x^2\ -\ 6x\ +\ 6\ =\ 0$$

Answer

$$x^2\ +\ 6x\ +\ 6\ =\ 0$$

Answer

$$x^2\ +\ 6x\ +\ 9\ =\ 0$$

Answer

$$6x^2\ -\ x\ +\ 6\ =\ 0$$

Question 9

Given that the vector 3i -2j and 4i + pj are parallel, find the constant P.

Accepted Answer

-8/3

Answer

-6

Answer

-3/8

Answer

1/6

Question 10

$$Given\ that\ p\ =\ \left(4i\ -3j\right)\ \ and\ q\ =\ \left(-12i\ +5j\right),\ find\ the\ vector\ U\ such\ that\ U\ is\ parallel\ to\ P+Q\ and\ is\ half\ the\ size\ of\ p+q.$$

Accepted Answer

$$\left(-4i\ +\ j\right)$$

Answer

$$\left(-8i\ -\ 2j\right)$$

Answer

- $$\left(6i\ -3j\right)$$

Answer

(i - j)

Question 11

The position vectors of points R, S and T in the X-Y plane are r= 5i +3j, s = 8i - j and t = 11i - 5j respectively. Which of the following show that R, S and T are collinear

Accepted Answer

$$\overrightarrow{RS\ }\ =\ \overrightarrow{ST}$$

Answer

$$\overrightarrow{SR\ }\ =\ \overrightarrow{TR}$$

Answer

$$\overrightarrow{TR\ }\ =\ \overrightarrow{SR}$$

Answer

$$\overrightarrow{RST\ \ \ }\ =\ \overrightarrow{TRS}$$

Question 12

What is the unit vector which is parallel to 7i - 4j?

Accepted Answer

$$\frac{7i\ -\ 4j}{\sqrt[]{65}}$$

Answer

$$\frac{7i\ +\ 5j}{\sqrt[]{56}}$$

Answer

$$\frac{5i\ -\ 7j}{\sqrt[]{65}}$$

Answer

$$\frac{5i+\ 7j}{\sqrt[]{65}}$$

Question 13

The projection of the vector a = 5i - 2j + k on the vector b = 2i + 3j is

Accepted Answer

$$\frac{4\sqrt[]{13}}{13}$$

Answer

$$4\sqrt[]{13}$$

Answer

$$\frac{5\sqrt[]{13}}{13}$$

Answer

$$\frac{\sqrt[]{30}}{15}$$

Question 14

$$Given\ that\ \left|p\right|\ =\ 3,\ \left|q\right|\ =\ 4\ and\ p\ .\ \ q\ =\ -6,\ find\ the\ angle\ between\ the\ vectors\ p\ and\ q.$$

Accepted Answer

120 degrees

Answer

30 degrees

Answer

45 degrees

Answer

135 degrees

Question 15

Find the angle between i + 5j and 5i - j.

Accepted Answer

90 degrees

Answer

30 degress

Answer

45 degrees

Answer

60 degrees

Question 16

Find the magnitude of the vector $$\overrightarrow{a\ }\ =\ 4i\ -3j\ +12k$$

Accepted Answer

13

Answer

169

Answer

26

Answer

19

Question 17

Given that a = 6i +3j and b = i -2j, evaluate $$\left|a+b\right|\ -\left|a\ -\ b\right|.$$

Accepted Answer

0

Answer

14

Answer

$$2\sqrt[]{5}$$

Answer

$$10\sqrt[]{2}$$

Question 18

$$If\ \overrightarrow{a}\ =\ 3i\ +\ 4j\ and\ \overrightarrow{b\ }\ =\ \lambda j\ +\ 2k\ are\ perpendicular,\ what\ is\ the\ vaue\ of\ \lambda?$$

Accepted Answer

0

Answer

4

Answer

-3/2

Answer

-8/3

Question 19

Find the unit vector in the direction of the resultant of p = 5i + 3j and q = 7i -8j.

Accepted Answer

$$\frac{12}{13}i\ -\ \frac{5}{13}j$$

Answer

$$\frac{1}{12}i\ -\frac{1}{5}j$$

Answer

$$\frac{2}{13}i\ +\frac{5}{13}j$$

Answer

$$\frac{5}{13}i\ +\frac{12}{13}j$$

Question 20

The position vector pf P and Q are p = i -3j and q = 4i + 5j respectively. Find the unit vector parallel to $$\overrightarrow{PQ}.$$

Accepted Answer

$$\frac{1}{\sqrt[]{72}}\left(3i\ +\ 8j\right)$$

Answer

$$1\frac{1}{\sqrt[]{73}}\left(3i\ -\ 8j\right)$$

Answer

$$-\frac{1}{73}\left(i\ -\ 3j\right)$$

Answer

$$\frac{1}{\sqrt[]{73}}\left(4i\ +\ 5j\right)$$

Question 21

PQRS is a parallelogram whose vertices are P(x,y), Q(5,7), R(-3,-8) and S(-4, -6). Find the values of x and y.

Accepted Answer

x = 4 and y = 9

Answer

x = 3 and y = 7

Answer

x = 4 and y = 8

Answer

x = 3 and y =4 4

Question 22

A particle starts from rest, its acceleration at any time t seconds is given by $$a\ =\ \left(2t\ +\ 1\right)i\ +\ 3t^2j.\ $$ Calculate its velocity at t = 3

Accepted Answer

12i + 27j

Answer

9i - 12j

Answer

12i + 9j

Answer

7i +9j

Question 23

The displacement, in metres, of a particle at any time t second is $$x\ =\ t^3i\ -\ 2t^2j.$$ Find in m/s, the magnitude of its velocity at t = 3.

Accepted Answer

$$9\sqrt[]{13}$$

Answer

$$3\sqrt[]{5}$$

Answer

$$3\sqrt[]{6}$$

Answer

$$27\sqrt[]{2}$$

Question 24

A metallic ball (A) of mass 2kg moving with velocity (6i +8j)m/s, collide with another ball (B) of the same material but of mass 1.5kg. If ball (B) is initially at rest, but moves with velocity (3i -5j) m/s after collision, find the velocity with which the ball (A) moves.

Accepted Answer

(3.25i +11.75j)

Answer

(3.25i - 11.75j)

Answer

(3.15i +11.57J)

Answer

(-3.25i -11.57j)

Question 25

Find the magnitude and the direction of resultant of a = 2i + 3j and b = 2i + j.

Accepted Answer

$$\left(4\sqrt[]{2},\ 045^o\right)$$

Answer

$$\left(4\sqrt[]{2},\ 030^o\right)$$

Answer

$$\left(2\sqrt[]{3},\ 045^o\right)$$

Answer

$$\left(2\sqrt[]{3},\ 030^o\right)$$

Question 26

Express P = (5N, 060degrees) in the form ai + bj. where a and b are scalars.

Accepted Answer

$$\frac{5}{2}\sqrt[]{3}i\ +\ \frac{5}{2}j$$

Answer

$$\frac{5}{2}i\ +\ \frac{5}{2}j$$

Answer

$$\frac{5}{2}i\ -\ \frac{5}{2}j$$

Answer

$$5\sqrt[]{3}i\ +\ 7j$$

Question 27

A binary operation * defined on R, the set of real numbers by $$x\ \cdot\ y\ =\ \sqrt[]{xy}\ for\ all\ x,y\in R.$$ If x* (2*8) = 6, find x

Accepted Answer

9

Answer

2

Answer

4

Answer

10

Question 28

A binary operation defined on the set R of real numbers is given by

m * n $$=\ m\ +\ n^2,\ m,\ n\in R.$$ If k 3 = 7 *4 , find the value of k.

Accepted Answer

14

Answer

8

Answer

$$\frac{28}{3}$$

Answer

20

Question 29

Find the identity element(e) in the binary operation on the set of real numbers defined by x y = $$\frac{3x\ +\ 3y\ -1}{3}$$

Accepted Answer

$$\frac{1}{3}$$

Answer

1

Answer

$$\frac{3}{4}$$

Answer

$$\frac{2}{3}$$

Question 30

The operation 0 is defined on the set of real numbers R by $$a\ heta\ b\ =a\ +\ b\ -\frac{1}{2}ab\ for\ all\ a,\ b\in R.$$ Find the inverse element.

Accepted Answer

$$\frac{-2a}{1-a}$$

Answer

$$\frac{2a}{1-a}$$

Answer

$$\frac{2a}{a\ -1}$$

Answer

$$\frac{1}{1-a}$$

Question 31

Find the identity element e under this operation, if the binary operation is defined by c*d = c + d + 2cd, for all c, d $$\in$$ R.

Accepted Answer

0

Answer

1 + 2c

Answer

1 + 2d

Answer

c + d

Question 32

A binary operation * is defined on the set of integers (Z) by a*b = $$\frac{a^2\ -\ b^2}{a\ -\ b},\ for\ all\ a,\ b\ \in\ Z.$$ Find the value of x if 3 *x = 23

Accepted Answer

20

Answer

26

Answer

23

Answer

17

Question 33

How many way can the letters in the word CHEMISTRY be arranged, if the vowels must always be together.

Accepted Answer

80640

Answer

89234

Answer

89012

Answer

23890

Question 34

How many words can be formed from the letters of VALEDICTORY provided the letters A,E,I, O,Y are not to be separated at all.

Accepted Answer

5040

Answer

5020

Answer

5030

Answer

5050

Question 35

How many different words can be formed from the letter of the word 'HARYANA'? If H and N are together.

Accepted Answer

240

Answer

340

Answer

940

Answer

140

Question 36

A committee of 3 men and 4 women is to be formed from 5 men and 7 women. How many different committee can be formed if: two particular women must not be on the committee.

Accepted Answer

175

Answer

350

Answer

255

Answer

675

Question 37

What is the probability of selecting a committee of 3 men and 2 women from a group of 10 men and 6 women?

Accepted Answer

$$\frac{10C_3\ x\ \ 6C_2}{10C_5}$$

Answer

$$\frac{10C_{3\ }x\ 6C_2}{10C_3}$$

Answer

$$\frac{10C_3\ +6C_2\ }{10C_5}$$

Answer

$$\frac{10C_3\ x\ 6C_2}{15C_5}$$

Question 38

Given that $$nC_{r+2\ }=\ 10C_r$$ , find the value of r.

Accepted Answer

4

Answer

2

Answer

3

Answer

5

Question 39

Simplify $$\frac{nP_3}{nC_2}\ +\ nC_0$$

Accepted Answer

2n -3

Answer

n-2

Answer

n-3

Answer

2n - 5

Question 40

Evaluate the expression $$6P_3\ -\ 6C_3$$

Accepted Answer

100

Answer

20

Answer

40

Answer

60

Question 41

Find the mean deviation of the numbers 2,5,3,6,8,6

Accepted Answer

1.67

Answer

1.30

Answer

1.40

Answer

1.75

Question 42

calculate the mean deviation of the numbers 0,-1,-3,4,5,1

Accepted Answer

7/3

Answer

0

Answer

2

Answer

$$2\ \frac{4}{5}$$

Question 43

Find the positive value of y if the standard deviation of 1,y+1 and 2y + 1 is $$\sqrt[]{6}$$ .

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 44

Calculate the standard deviation of the numbers -6,-2, 5,7, 11

Accepted Answer

6.16

Answer

2.76

Answer

3.00

Answer

5.80

Question 45

Calculate the variance of the numbers 19,21,27,37

Accepted Answer

49

Answer

0

Answer

7

Answer

14

Question 46

The mean of the numbers 1, 4, 11, x, (x + 4) is x +1. Calculate the value of x.

Accepted Answer

5

Answer

1

Answer

2

Answer

4

Question 47

The mean and the variance of the numbers 1,4,x,y,10 is 6 and 10 respectively. Find the values of x and y.

Accepted Answer

If y =7 then x = 8

Answer

If y =7 then x = 7

Answer

If y =8 then x = 8

Answer

If y =7 then x = 10

Question 48

If the mean of -1,0,9,3,k,5 is 2, where k is a constant, find the median of the set of numbers.

Accepted Answer

3/2

Answer

10

Answer

7/2

Answer

6

Question 49

In an examination, the mean score of 250 students tested was 55. Of the 250 students, 150 were boys. If the mean score of the boys was 60, what was the mean score of the girls?

Accepted Answer

47.5

Answer

49.5

Answer

46.5

Answer

43.5

Question 50

10000000x 0

Accepted Answer

0

Answer

1

Answer

100000

Answer

101

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