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Question : An isosceles triangle ABC is right-angled at B. D is a point inside the triangle ABC. P and Q are the feet of the perpendicular drawn from D on the sides AB and AC respectively of ABC. If $AP = a$ cm , $AQ = b$ cm and $\angle$BAD = 15°, $\sin$ 75°= ?

Option 1: $\frac{2b}{\sqrt 3 a }$

Option 2: $\frac{a}{2b}$

Option 3: $\frac{\sqrt 3a}{2b}$

Option 4: $\frac{2a}{\sqrt 3b}$

Team Careers360 23rd Jan, 2024

Correct Answer: $\frac{\sqrt 3a}{2b}$


Solution :

Since $\triangle$ABC is a right-angled isosceles triangle,
$\angle$A = $\frac{180 - 90}{2}$ = 45°
$\angle$DAQ = $\angle$A–$\angle$BAD = 45° – 15° = 30°
$\sin$ $\angle$ADQ = $\sin$ 60° = $\frac{AQ}{AD}$
$\frac{b}{AD}$ = $\frac{\sqrt3}{2}$
AD = $\frac{2b}{\sqrt3}$
From $\triangle$APD,
$\sin$ 75° = $\frac{AP}{AD}$ = $\frac{a}{\frac{2b}{\sqrt3}}$

154 Views

Question : A man gives 50% of his money to his son and 30% to his daughter. 80% of the rest is donated to a trust. If he is left with Rs. 16,000 now, how much money did he have in the beginning?

Option 1: Rs. 40,000

Option 2: Rs. 8,00,000

Option 3: Rs. 80,000

Option 4: Rs. 4,00,000

Team Careers360 22nd Jan, 2024

Correct Answer: Rs. 4,00,000


Solution : Let us assume the income of the man is Rs. $x$.
According to the question, he gives 50% of his money to his son and 30% to his daughter.
$\therefore$ The money he is left with = $x-\frac{x}{2}-\frac{3x}{10}$
$= \frac{10x-5x-3x}{10}$
$=\frac{2x}{10}=\frac{x}{5}$
According to the

68 Views

Question : Directions: What should come in place of the question mark (?) in the given series?
339, 340, 348, ?, 439

Option 1: 377

Option 2: 492

Option 3: 380

Option 4: 375

Team Careers360 19th Jan, 2024

Correct Answer: 375


Solution : Given:
339, 340, 348, ?, 439

Add the cubes of the consecutive numbers (starting from 1) to each term to get the next term in the series.
339 + (1)3 = 339 + 1 = 340
340 + (2)3 = 340 + 8

5 Views

Question : Directions: Which answer figure will complete the pattern in the question figure?

Option 1:

Option 2:

Option 3:

Option 4:

Team Careers360 21st Jan, 2024

Correct Answer:


Solution : On comparing the question figure and all the answer figures, the following figure will combine and make the complete pattern –

Hence, the fourth option is correct.

7 Views

Question : In the context of trans-fats, which of the following statements is not correct?

Option 1: They have a shorter shelf-life than natural fats.

Option 2: Their consumption increases LDL cholesterol and decreases HDL cholesterol.

Option 3: They are produced from the industrial process of hydrogenation.

Option 4: WHO has called for their elimination by 2023.

Team Careers360 21st Jan, 2024

Correct Answer: They have a shorter shelf-life than natural fats.


Solution : The correct answer is They have a shorter shelf life than natural fats.

The shelf life is longer than that of natural fat. Additionally, consuming trans fats can increase LDL cholesterol and decrease HDL cholesterol. These fats

30 Views

Question : If the ratio of principal and the simple interest for 5 years is 10 : 3, then the rate of interest is:

Option 1: 5%

Option 2: 6%

Option 3: 8%

Option 4: 3%

Team Careers360 19th Jan, 2024

Correct Answer: 6%


Solution : According to the question,
$\frac{\text{Principal}}{\text{Simple interest}}=\frac{10}{3}$
Let, Principal = Rs. 10
Simple Interest (SI) for 5 years = Rs. 3
So, SI for 1 year = $\frac{3}{5} =0.6$
$\therefore$ Rate = $\frac{\text{Simple interest}\times 100}{\text{Principal × Time}}=\frac{0.6\times 100}{10 \times 1}=6$%
Hence, the correct answer is 6%.

6 Views

Question : Which of the following articles of the Constitution of India declares the age of 35 years as one of the eligibility criteria for the post of the President of India?

Option 1: Article 60

Option 2: Article 62

Option 3: Article 56

Option 4: Article 58

Team Careers360 23rd Jan, 2024

Correct Answer: Article 58


Solution : The correct option is Article 58.

In the Constitution of India, Article 58 specifies the qualifications for the election of the President. According to Article 58, a person is eligible for the office of president if they:

  1. are a citizen of India,
  2. have
12 Views

Question : Directions: In the following question, some parts of the sentence may have some errors. Find out which part of the sentence has an error and select the appropriate option. If the sentence is free from error, select 'No Error'.

The severe cyclonic storm (1) / has left behind (2) / a trail of miser. (3) / No Error (4)

Option 1: (1)

Option 2: (2)

Option 3: (3)

Option 4: (4)

Team Careers360 18th Jan, 2024

Correct Answer: (3)


Solution : The error lies in the third part of the sentence.

There is an error in the use of the vocabulary in the sentence. Misery refers to great suffering or distress, which is the intended meaning, while miser refers to a person who hoards wealth and

21 Views

Question : $\triangle$ABC is similar to $\triangle$PQR and AB : PQ = 2 : 3. AD is the median to the side BC in $\triangle$ABC and PS is the median to the side QR in $\triangle$PQR. What is the value of $(\frac{BD}{QS})^2$?

Option 1: $\frac{3}{5}$

Option 2: $\frac{4}{9}$

Option 3: $\frac{2}{3}$

Option 4: $\frac{4}{7}$

Team Careers360 22nd Jan, 2024

Correct Answer: $\frac{4}{9}$


Solution :
AB : PQ = 2 : 3
As $\triangle$ABC is similar to $\triangle$PQR,
$\frac{AB}{PQ}$ = $\frac{BC}{QR}$ = $\frac{CA}{RP}$ = $\frac{AD}{PS}$ = $\frac{BD}{QS}$ = $\frac{DC}{SR}$ = $\frac{2}{3}$
$(\frac{BD}{QS})^2$ = $(\frac{2}{3})^2$ = $\frac{4}{9}$
Hence, the correct answer is $\frac{4}{9}$.

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