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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
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.
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
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
Question : Osteocytes are found in:
Option 1: bone
Option 2: blood
Option 3: cartilage
Option 4: lymph
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.
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
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
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
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
Question :
Which is the anti-coagulant substance in blood ?
Option 1:
Fibrinogen
Option 2:
Heparin
Option 3:
Thrombin
Option 4: Globin
Correct Answer:
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
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
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%
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: ×, ÷, −, +
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
The coralloid root of cycas helps in
absorption of water
absorption of water and fixation of nitrogen
Option 3: anchorage
Option 4: transport of food
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
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
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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