Differentiation Test 25

Result

Differentiation Test 25

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

Area of triangle whose vertices are $$(0, 0), (2, 3), (5, 8)$$ is ____ square units.

A
$$\dfrac 12$$

B
$$1$$

C
$$2$$

D
$$\dfrac 32$$

Solution

Area of the triangle with three vertices $$(x_1,y_1)$$, $$(x_2,y_2)$$ and $$(x_3,y_3)$$ is
$$A=\dfrac { 1 }{ 2 } \left| { y }_{ 1 }({ x }_{ 2 }-{ x }_{ 3 })+{ y }_{ 2 }({ x }_{ 3 }-{ x }_{ 1 })+{ y }_{ 3 }({ x }_{ 1 }-{ x }_{ 2 }) \right|$$
Therefore, the area of triangle with vertices $$(1,2)$$, $$(3,4)$$ and $$(5,6)$$ is:
$$A=\dfrac { 1 }{ 2 } \left| 0(2-5)+3(5-0)+8(0-2) \right| =\dfrac { 1 }{ 2 } \left| 0+15-16 \right| =\dfrac { 1 }{ 2 } \left| -1 \right| =\dfrac { 1 }{ 2 }$$
Hence, the area of the triangle is $$\dfrac { 1 }{ 2 }$$ square units.
Question 2
1 / -0

In how many ways can 3 diamond cards be drawn simultaneously from a pack of cards?

A
$$78$$

B
$$1716$$

C
$$286$$

D
$$13$$

Solution

Pack of cards $$52$$
Diamond cards are $$13$$
To select $$3$$ cards
Total number of choices =$$^{ 13 }C_{ 3 }$$
$$= \dfrac { 13\times 12\times 11 }{ 3\times 2\times 1 } \\ = 143\times 2\\ = 286$$
Hence $$286$$ ways are possible and is a correct answer.
Question 3
1 / -0

Find the area of $$\Delta ABC$$, in which $$A = (2, 1), B = (3, 4)$$ and $$C = (-3, -2).$$

A
$$3$$ square units

B
$$4$$ square units

C
$$6$$ square units

D
$$12$$ square units

Solution

Area of triangle with vertices $$(x_1,y_1)$$, $$(x_2,y_2)$$ and $$(x_3,y_3)$$ is:
$$A=\dfrac { 1 }{ 2 } \left| x_{ 1 }(y_{ 2 }-y_{ 3 })+x_{ 2 }(y_{ 3 }-y_{ 1 })+x_{ 3 }(y_{ 1 }-y_{ 2 }) \right|$$
Therefore, the area of triangle with vertices $$(2,1)$$, $$(3,4)$$ and $$(-3,-2)$$ is:
$$A=\displaystyle \frac { 1 }{ 2 } \left| 2(4-(-2))+3(-2-1)-3(1-4) \right| $$
$$=\dfrac { 1 }{ 2 } \left| 2(6)+3(-3)-3(-3) \right| $$
$$=\dfrac { 1 }{ 2 } \left| 12-9+9 \right|$$
$$ =\dfrac { 1 }{ 2 } \left| 12 \right| =6$$ square units.
Question 4
1 / -0

The area of triangle with vertices $$A(5,\,0),\,B(8,\,0)$$ and $$C(9,\,5)$$ is

A
$$7\dfrac{1}{4}$$

B
$$7\dfrac{1}{2}$$

C
$$\dfrac{15}{4}$$

D
None of the above

Solution

Area of triangle $$=\dfrac{1}{2}\begin{bmatrix}x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\end{bmatrix}$$
$$A=\dfrac{1}{2}\begin{bmatrix}5(0-5)+8(5-0)+9(0-0)\end{bmatrix}$$
$$A=\dfrac{1}{2}\begin{bmatrix}-25+40\end{bmatrix}=\dfrac{15}{2}$$ square units.
So, option B is correct.
Question 5
1 / -0

Directions For Questions

In a certain code, ' il be pee ' means 'roses are blue', silk hee means ' red flowers' and ' pee mit hee' means ' flowers are vegctables'

...view full instructions

How is 'red written in that code ?

A
hee

B
silk

C
be

D
cannot be determined

Solution

Type Direct coding (Jumbled fashion)
S.no. code sentence
1. il be pee roses are blue
2. silk hee red flowers
3. pee mit hee Flowers are Vegetables
common word in sentences 1 & 3 $$ \displaystyle \rightarrow $$ 'are' and code $$ \displaystyle \rightarrow $$ 'pee'
common word in sentences 2 & 3 $$ \displaystyle \rightarrow $$ flowers and code $$ \displaystyle \rightarrow $$ 'hee'
Therefore
Codes words
pee are
hee flowers
silk red
niit vegetables
il roses/ blue
be blue./ rose
Question 6
1 / -0

How is 'vegetables are red flowers' written in this code ?

A
Pec silk mit hee

B
silk peehee be

C
il silk mit hee

D
none

Solution

Type Direct coding (Jumbled fashion)
S.no. code sentence
1. il be pee roses are blue
2. silk hee red flowers
3. pee mit hee Flowers are Vegetables
common word in sentences 1 & 3 $$ \displaystyle \rightarrow $$ 'are' and code $$ \displaystyle \rightarrow $$ 'pee'
common word in sentences 2 & 3 $$ \displaystyle \rightarrow $$ flowers and code $$ \displaystyle \rightarrow $$ 'hee'
Therefore
Codes words
pee are
hee flowers
silk red
niit vegetables
il roses/ blue
be blue./ rose
nit silk hee pee
Question 7
1 / -0

Find the missing number in the pattern: $$2, 5, 8, 11,$$ __$$, 17, 20, 23, 26$$

A
11

B
12

C
13

D
14

Solution

The series adds $$3$$ to each number to get the next number.
So, the next number is $$11 + 3 = 14$$
Question 8
1 / -0

The area of triangle with vertices $$A(0,\,9),\,B(0,\,4)$$ and $$C(-5,\,-9)$$ is

A
$$\dfrac{25}{2}$$ sq. units

B
$$\dfrac{23}{2}$$ sq. units

C
$$\dfrac{19}{2}$$ sq. units

D
None of the above

Solution

Area of triangle $$=\dfrac{1}{2}\begin{bmatrix}x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\end{bmatrix}$$
$$=\dfrac{1}{2}\begin{bmatrix}0(4+9)+0(-9-9)+(-5)(9-4)\end{bmatrix}$$
$$=\dfrac{1}{2}\begin{bmatrix}-5\times5\end{bmatrix}$$
$$=-\dfrac{25}{2}$$
The area cannot be negative.
$$\therefore$$ It must be $$\dfrac{25}{2}$$ sq. units
So, option A is correct.
Question 9
1 / -0

Complete the pattern: $$3, 5, 8, 13,$$ ___

A
21

B
22

C
23

D
24

Solution

The next number is $$21$$.
We get the next number by adding the previous two numbers.
Question 10
1 / -0

Which pair of numbers comes next?
$$25, 23, 5, 20, 16, 5,....$$

A
$$11, 5$$

B
$$5, 6$$

C
$$10, 5$$

D
$$9, 5$$

Solution

This is an alternating subtraction series with the interpolation of a random number, $$5$$, as every third number.
In the subtraction series, $$2$$ is subtracted, then $$3$$ then $$4$$, and so on.
The next pair of numbers are $$11$$ and $$5$$.

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

Differentiation Test 25

Result

Differentiation Test 25

Score

-

Rank

-

SHARING IS CARING

Question 1

$$\dfrac 12$$

$$1$$

$$2$$

$$\dfrac 32$$

Solution

Question 2

$$78$$

$$1716$$

$$286$$

$$13$$

Solution

Question 3

$$3$$ square units

$$4$$ square units

$$6$$ square units

$$12$$ square units

Solution

Question 4

$$7\dfrac{1}{4}$$

$$7\dfrac{1}{2}$$

$$\dfrac{15}{4}$$

None of the above

Solution

Question 5

hee

silk

be

cannot be determined

Solution

Question 6

Pec silk mit hee

silk peehee be

il silk mit hee

none

Solution

Question 7

11

12

13

14

Solution

Question 8

$$\dfrac{25}{2}$$ sq. units

$$\dfrac{23}{2}$$ sq. units

$$\dfrac{19}{2}$$ sq. units

None of the above

Solution

Question 9

21

22

23

24

Solution

Question 10

$$11, 5$$

$$5, 6$$

$$10, 5$$

$$9, 5$$

Solution

User

Question Analysis

My Perfomance

Score

-

Rank

-

Results Announcement on: coming Monday

Stay Tuned: We’ll update you on your result via email or SMS.