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Question : Directions: Select the option related to the fifth letter cluster in the same way as the second letter cluster is related to the first letter cluster and the fourth letter cluster is related to the third letter cluster.
CAM : EES :: OAT : QEZ :: TOI : ?
Option 1: USO
Option 2: VTO
Option 3: VSO
Option 4: VSP
Correct Answer: VSO
Solution : Given:
CAM : EES :: OAT : QEZ :: TOI : ?
Add the consecutive even numbers to the place value of the letters of CAM and OAT to get the related letter clusters.
CAM→C + 2 = E; A + 4 = E; M + 6 = S
So, CAM is related to EES.
OAT→O + 2 = Q; A + 4 = E; T + 6 = Z
So, OAT is related to QEZ.
Similarly, follow the same pattern for TOI –
T + 2 = V; O + 4 = S; I + 6 = O
So, TOI is related to VSO. Hence, the third option is correct.
Question : In $\triangle$PQR, the angle bisector of $\angle$P intersects QR at M. If PQ = PR, then what is the value of $\angle$PMQ?
Option 1: 75°
Option 2: 80°
Option 3: 70°
Option 4: 90°
Correct Answer: 90°
Solution :
In $\triangle$PQR, PQ = PR
⇒ $\angle$Q = $\angle$R = b
PM is the angle bisector of $\angle$P.
$\angle$QPM = $\angle$RPM = a
Apply angle sum property in $\triangle$PQR,
⇒ $\angle$P + $\angle$Q + $\angle$R = 180°
⇒ $\angle$P + b + b = 180°
⇒ $\angle$P = 180° – 2b
$\angle$QPM = $\frac{180° – 2b}{2}$ = 90° – b
In $\triangle$PQM,
Let $\angle$PMQ = $\theta$
⇒ $\angle$QPM + $\angle$Q + $\angle$M = 180°
⇒ 90° – b + b + $\theta$ = 180°
⇒ $\theta$ = 90°
Hence, the correct answer is 90°.
Question : A class is divided into two sections, with 20 students in one section and 30 students in the other. The pass percentages for these sections are 80% and 60%, respectively. What is the pass percentage for the entire class?
Option 1: 60%
Option 2: 68%
Option 3: 70%
Option 4: 78%
Correct Answer: 68%
Solution : The number of students who passed
= 80% of 20 + 60% of 30
= $\frac{80 × 20}{100}$ + $\frac{60 × 30}{100}$
= 16 + 18
= 34
Now, the pass percentage of the entire class
= $\frac{\text{Number of students passed}}{\text{Total students}}$ × 100
= $\frac{34}{(20 + 30)}$ × 100
= 68%
Hence, the correct answer is 68%.
Question : Which of the following festivals is observed by the tribal people of Jharkhand?
Option 1: Nongkrem
Option 2: Losar
Option 3: Suata
Option 4: Bhagta Parab
Correct Answer: Bhagta Parab
Solution : The correct option is Bhagta Parab.
Bhagta Parab is an important festival celebrated by the tribal communities in Jharkhand, particularly by the Oraon tribe. This festival is associated with the worship of the deity Marang Buru, who is considered to be the protector of the community. Bhagta Parab is observed to seek blessings for the well-being of the community, the fertility of the land, and the prosperity of the people.
Question : Match the columns.
Instrument | Their Function |
i. Voltmeter | a. An instrument that measures the magnitude of the current |
ii. Ammeter | b. An instrument that measures voltage |
iii.Galvanometer | c. An instrument that measures resistance |
iv. Ohmmeter | d. An instrument that measures the direction and the magnitude of the current |
Option 1: i-a, ii-c, iii-b, iv-d
Option 2: i-b, ii-a, iii-d, iv-c
Option 3: i-b, ii-a, iii-c, iv-d
Option 4: i-a, ii-b, iii-c, iv-d
Correct Answer: i-b, ii-a, iii-d, iv-c
Solution : The correct answer is i-b, ii-a, iii-d, iv-c.
- Voltmeter: An instrument that measures voltage.
- Ammeter: an instrument that measures the magnitude of the current.
- Galvanometer: an instrument that measures the direction and magnitude of the current.
- Ohmmeter: An instrument that measures resistance.
Question : If $\sqrt{11-3 \sqrt{8}}=a+b \sqrt{2}$, then what is the value of (2a + 3b) ?
Option 1: 7
Option 2: 9
Option 3: 3
Option 4: 5
Correct Answer: 3
Solution : Given: $\sqrt{11-3 \sqrt{8}}=a+b \sqrt{2}$
⇒ $\sqrt{11-3 \sqrt{2\times2\times2}}=a+b \sqrt{2}$
⇒ $\sqrt{9+2-2×3\sqrt{2}}=a+b \sqrt{2}$
⇒ $\sqrt{(3)^2+(\sqrt2)^2-2\times3\sqrt{2}}=a+b \sqrt{2}$
⇒ $\sqrt{(3-\sqrt{2})^2}=a+b \sqrt{2}$
⇒ $3-\sqrt{2}=a+b \sqrt{2}$
Comparing both sides, we get, $a=3,b=-1$
Now, $(2a+3b)$
= $(2\times3+3\times(-1))$
= $3$
Hence, the correct answer is 3.
Question : Select the most appropriate option that can substitute the underlined segment in the given sentence.
He was looking into his book for the last two hours but couldn't find it.
Option 1: looking down on his book
Option 2: looking above his book
Option 3: looking for his book
Option 4: looking after his book
Correct Answer: looking for his book
Solution : The correct choice is the third option.
In this context, looking for is the correct phrase to convey the idea of searching for his book. The preposition for is used with the verb looking to indicate the purpose or direction of the action whereas "looking into" means to investigate.
Therefore, the correct sentence is: He was looking for his book for the last two hours but couldn't find it.
Question : Directions: In a certain code RAIN is written as TCKP. How is CLOUD written in that code?
Option 1: ENQWF
Option 2: EMQWF
Option 3: FNQWE
Option 4: ENRWF
Correct Answer: ENQWF
Solution : Given:
RAIN is written as TCKP.
Add 2 to the place value of each letter of RAIN to obtain the required code –
R + 2 = T; A + 2 = C; I + 2 = K; N + 2 = P
Thus, RAIN is coded as TCKP.
Similarly, follow the same pattern for CLOUD –
C + 2 = E; L + 2 = N; O + 2 = Q; U + 2 = W; D + 2 = F
So, CLOUD is coded as ENQWF. Hence, the first option is correct.
Question : A person covers the first 25 km in 60 minutes and the next 38 km in 30 minutes. What is his average speed for the whole journey?
Option 1: 46 km /hr
Option 2: 49 km/hr
Option 3: 42 km/hr
Option 4: 36 km /hr
Correct Answer: 42 km/hr
Solution : Given: A person covers the first 25 km in 60 minutes and the next 38 km in 30 minutes.
Total distance = 25 + 38 = 63 km
Total time = (60 + 30) = 90 minutes = $\frac{90}{60}$ = $\frac{3}{2}$ hours
So, the average speed = $\frac{63}{\frac{3}{2}}$ = $63×\frac{2}{3}$ = 42 km/hr
Hence, the correct answer is 42 km/hr.
Question : A shopkeeper sold an item at 10% loss after giving a discount equal to half the marked price. Then the cost price is:
Option 1: $\frac{1}{9}$th of the marked price
Option 2: $\frac{4}{9}$th of the marked price
Option 3: $\frac{5}{9}$th of the marked price
Option 4: $\frac{7}{9}$th of the marked price
Correct Answer: $\frac{5}{9}$th of the marked price
Solution : Let the marked price = $p$ and the cost price = $q$
According to the question,
∴ 50% of $p$ = 90% of $q$
⇒ $\frac{p×50}{100}=\frac{q×90}{100}$
∴ $q=\frac{5}{9}p$
So, the cost price is $\frac{5}{9}$th of the marked price.
Hence, the correct answer is $\frac{5}{9}$th of the marked price.