Straight Lines Test 35

Result

Straight Lines Test 35

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

Find the area of the triangle formed by the mid points of sides of the triangle whose vertices are $$(2, 1)$$, $$(-2, 3)$$, $$(4, -3)$$.

A
$$1.5$$ sq. units

B
$$3$$ sq. units

C
$$6$$ sq. units

D
$$20$$ sq. units
Question 2
1 / -0

A box contains 5 pairs of shoes. If 4 shoes are selected, then the number of ways in which exactly one pair of shoes obtained is :

A
120

B
140

C
160

D
180

Solution

We have,

A box contains pair of shoes $$=5$$

Selected pair of shoes $$=4$$

Then,

Exactly one pair of shoes obtained is

$$ {{=}^{5}}{{P}_{4}} $$

$$ =\dfrac{5!}{\left( 5-4 \right)!} $$

$$ =\dfrac{5!}{1!}=5! $$

$$ =5\times 4\times 3\times 2\times 1 $$

$$ =120 $$
Hence, this is the answer.
Question 3
1 / -0

Find: $$6,25,62,123,(?),341$$

A
$$216$$

B
$$214$$

C
$$215$$

D
$$218$$

Solution

$$6=2^{3}-2=6$$
$$25=3^{3}-2=25$$
$$62=4^{3}-2=62$$
$$123=5^{3}-2=123$$
$$214=6^{3}-2=214$$
$$341=7^3-2=341$$

Missing term is $$214$$
Question 4
1 / -0

Let $$5 < n_1 < n_2 < n_3 < n_4$$ be integers such that $$n_1+n_2+n_3+n_4=35$$. The number of such distinct arrangements $$(n_1, n_2, n_3, n_4)$$.

A
$$^{38}C_3$$

B
$$^8C_3$$

C
$$5$$

D
$$6$$

Solution

$${ n }_{ 1 }+{ n }_{ 2 }+{ n }_{ 3 }+.....+{ n }_{ k }=R$$
for this arrangement,
No. of arrangement or distinct arrangements are $${ R+K-1 }_{ { C }_{ K-1 } }$$
So, for $${ n }_{ 1 }+{ n }_{ 2 }+{ n }_{ 3 }+{ n }_{ 4 }=35$$
No. of arrangements $$={ 35+4-1 }_{ { C }_{ 4-1 } }={ 38 }_{ { C }_{ 3 } }$$
Question 5
1 / -0

Select the missing number from the given responses ?

A
$$15$$

B
$$10$$

C
$$12$$

D
$$17$$

Solution
Question 6
1 / -0

Number of five-digit numbers divisible by 5 that can be formed from the digits $$0,1, 2, 3, 4, 5$$ without repetition of digits are

A
$$240$$

B
$$360$$

C
$$148$$

D
$$216$$

Solution
Question 7
1 / -0

Find the missing factor among the given figure ?

A
$$4$$

B
$$6$$

C
$$8$$

D
$$12$$

Solution
Question 8
1 / -0

There are n locks and n matching keys. If all the locks and keys are to be perfectly matched, find the maximum number of trails required to open a lock.

A
$$^{n}C_{2}$$

B
$$\sum _{ k=2 }^{ n }{ \left( k+2 \right) } $$

C
$$\dfrac{n(n+1)}{2}$$

D
$$^{n+1}C_{2}$$

Solution
Question 9
1 / -0

Let $$p=\dfrac{1}{1\times2}+\dfrac{1}{3\times4}+\dfrac{5}{1\times6}+.......+\dfrac{1}{2013\times2014}$$ and $$Q=\dfrac{1}{1008\times2014}+\dfrac{1}{1009\times2013}+.........+\dfrac{1}{2014\times1008}$$
then $$\dfrac{P}{Q}=$$

A
$$2013$$

B
$$2014$$

C
$$1511$$

D
$$2$$
Question 10
1 / -0

The number of intersection points of diagonals of $$2009$$ sides polygon, which lie inside the polygon.

A
$$^{2009}C_4$$

B
$$^{2009}C_2$$

C
$$^{2008}C_4$$

D
$$^{2008}C_2$$

Solution

Choosing any $$4$$ vertices make $$1$$ intersection

$$\therefore \ $$ No. of intersection points of diagonals $$=^nC_4$$

Here $$n=2009$$, No. of points $$=^{2009}C_4$$

$$\therefore \ $$ Option $$A$$ is correct.