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11 Views

Question : If $(a+b+c)=17$ and $\left(a^2+b^2+c^2\right)=101$, then find the value of $(a-b)^2+(b-c)^2+(c-a)^2$.

Option 1: 12

Option 2: 14

Option 3: 10

Option 4: 16

Team Careers360 25th Jan, 2024

Correct Answer: 14


Solution : Given: $(a+b+c)=17$ and $\left(a^2+b^2+c^2\right)=101$
We know that $(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ac$
Squaring both sides, we get
⇒ $a^2+b^2+c^2+2ab+2bc+2ac=289$
⇒ $101+2ab+2bc+2ac=289$
⇒ $2ab+2bc+2ac=188$
Now, $(a-b)^2+(b-c)^2+(c-a)^2$
= $2a^2+2b^2+2c^2-2ab-2bc-2ac$
= $2\times101-188$
= $202-188=14$
Hence, the correct answer is 14.

9 Views

Question : The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. The height of the tower is:

Option 1: 4 metres

Option 2: 7 metres

Option 3: 9 metres

Option 4: 6 metres

Team Careers360 23rd Jan, 2024

Correct Answer: 6 metres


Solution : Given: The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower.
$ \angle C$ and $ \angle D$ are complementary.
We know that $\tan\theta=\frac{\text{Perpendicular}}{\text{Base}}$ and $\tan

18 Views

Question : Osteocytes are found in:

Option 1: bone

Option 2: blood

Option 3: cartilage

Option 4: lymph

Team Careers360 24th Jan, 2024

Correct Answer: bone


Solution : The correct answer is bone.

Osteocytes are found in the bone tissue. The bone tissue consists of various cell types, including osteoblasts, osteoclasts, and osteocytes. Osteoblasts are responsible for bone formation.

16 Views

Question : Which among the following birds impersonates the calls of other birds to steal food?

Option 1: Drongo

Option 2: Eagle

Option 3: Owl

Option 4: Mynah

Team Careers360 21st Jan, 2024

Correct Answer: Drongo


Solution : The correct option is drongo.

The drongo, a clever bird found in Asia and Africa, is known for its exceptional mimicry skills. Using its imitative talents, the drongo mimics the calls of other birds to create false alarms, causing them to flee and

39 Views

Question : Directions: Four letter clusters have been given, out of which three are alike in some manner and one is different. Select the odd letter cluster.

Option 1: WYRS

Option 2: PSJK

Option 3: PRKL

Option 4: FHAB

Team Careers360 23rd Jan, 2024

Correct Answer: PSJK


Solution : Let's check each option –
First option: WYRS; W + 2 = Y; Y – 7 = R; R + 1 = S
Second option: PSJK; P + 3 = S; S – 9 = J; J + 1 = K
Third option: PRKL; P

15 Views

Question :

Which is the anti-coagulant substance in blood ?
 

Option 1:

Fibrinogen

Option 2:

Heparin

Option 3:

Thrombin

 

Option 4: Globin

Team Careers360 23rd Jan, 2024

Correct Answer:

Heparin


Solution : The correct option is Heparin.

Heparin is an anticoagulant that occurs naturally in the body. It inhibits the action of thrombin, an enzyme that transforms fibrinogen into fibrin, a protein that produces blood clots, by binding to antithrombin III. Antithrombin is a protein that prevents

5 Views

Question : An item is sold at two successive gains of 30% and 20%. If the final selling price is Rs. 31,200, of the item what is the cost price (in Rs.) of the item?

Option 1: 15000

Option 2: 20000

Option 3: 22250

Option 4: 24000

Team Careers360 22nd Jan, 2024

Correct Answer: 20000


Solution : Let $x$ be the cost price.
When profit = 30%, Selling price = $x$ + 30% of $x$ = 130% of $x$
When profit = 20%,
Final selling price = 130% of $x$ + 20% of 130% of $x$ = 130% of $x$ + 26%

26 Views

Question : Directions: Select the correct combination of mathematical signs to replace the * signs and balance the given equation.
5 * 15 * 320 * 2 * 45 = 190

Option 1: +, ÷, ×, − 

Option 2: ×, +, ÷, −

Option 3: +, ×, ÷, −

Option 4: ×, ÷, −, +

Team Careers360 21st Jan, 2024

Correct Answer: ×, +, ÷, −


Solution : Given:
5 * 15 * 320 * 2 * 45 = 190

Let's check the options –
First option: +, ÷, ×, −
⇒ 5 + 15 ÷ 320 × 2 − 45 = 190
Solving the L.H.S. of the given equation

21 Views

Question :

The coralloid root of cycas helps in

Option 1:

absorption of water

Option 2:

absorption of water and fixation of nitrogen

Option 3: anchorage

Option 4: transport of food

Team Careers360 23rd Jan, 2024

Correct Answer:

absorption of water and fixation of nitrogen


Solution : The correct answer is the absorption of water and the fixation of nitrogen.

The coralloid roots of cycads are specialised structures that have a knobby appearance, resembling coral. The cyanobacteria live within specialised cells in the coralloid roots

76 Views

Question : The following sentence has been split into four segments. Identify the segment that contains a grammatical error.
My mother said / that Ben will done / the assignment / today.

Option 1: today

Option 2: My mother said

Option 3: that Ben will done

Option 4: the assignment

Team Careers360 25th Jan, 2024

Correct Answer: that Ben will done


Solution : The correct choice is the third option.

The part of the sentence "that Ben will done" contains a grammatical error because it uses the past participle "done" instead of the base form "do" to form the future tense.

So, the correct sentence

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