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Question : PX is a tangent drawn from point X, that touches the circle at P. O is the centre of the circle. The radius of this circle is 10 cm and OX = 26 cm. What is the length of PX?
Option 1: 24.5 cm
Option 2: 24 cm
Option 3: 23.5 cm
Option 4: 25 cm
Correct Answer: 24 cm
Solution : In a circle, the radius is perpendicular to the tangent at the point of tangency. Therefore, in this case, OP is perpendicular to PX. This forms a right-angled triangle OPX. $OX^2 = OP^2 + PX^2$ Substituting the given values, $⇒26^2 = 10^2 + PX^2$
Question : ________ is the father of the modern periodic table.
Option 1: J. J. Thomson
Option 2: Ernest Rutherford
Option 3: John Newland
Option 4: Dmitri Mendeleev
Correct Answer: Dmitri Mendeleev
Solution : The correct option is Dmitri Mendeleev.
Dmitri Mendeleev is considered the father of the modern periodic table. Mendeleev, a Russian chemist, published his version of the periodic table in 1869, arranging elements based on their atomic mass and properties. His table predicted the
Question : Directions: Select the related letter cluster from the given alternatives in the given question. HJLN : PRTV :: BDFH : ?
Option 1: JMOR
Option 2: JLNP
Option 3: KLOR
Option 4: JKOR
Correct Answer: JLNP
Solution : Given: HJLN : PRTV :: BDFH : ?
Add 8 to the place value of each letter of HJLN to get the related letter cluster. H + 8 = P; J + 8 = R; L + 8 = T; N + 8 = V
Question : Study the given pie chart and answer the question that follows. Percentage-wise distribution of teachers in six different subjects in a school is given in the pie chart. The total number of teachers is 600. The ratio of male and female teachers is 3 : 1. Find the total number of teachers in Mathematics, Biology, and Social Studies.
Option 1: 320
Option 2: 420
Option 3: 360
Option 4: 400
Correct Answer: 360
Solution : From the Pie chart, ⇒ Total number of Mathematics teachers = 20% of the total number of teachers $=\frac{20}{100} \times 600=120$ ⇒ Total number of Biology teachers = 20% of the total number of teachers $=\frac{20}{100} \times 600=120$ ⇒ Total number of Social Studies teachers
Question : Directions: Which two signs and two numbers should be interchanged in the following equation to make it correct: 24 ÷ 12 × 21 – 273 + 14 = 179
Option 1: 14 and 21, × and +
Option 2: 14 and 21, + and ÷
Option 3: 21 and 12, + and ÷
Option 4: 14 and 24, × and +
Correct Answer: 14 and 21, + and ÷
Solution : Given: 24 ÷ 12 × 21 – 273 + 14 = 179
Replace the signs and numbers according to the given options, to balance the equation. Let's check the options – First option: 14 and 21, × and + ⇒24
Question : Name a single letter, which can be deleted from the body of the following words to form entirely new words?
HOST POST COST LOST STOP
Option 1: O
Option 2: P
Option 3: T
Option 4: S
Correct Answer: S
Solution : Given: HOST POST COST LOST STOP
Here,
If we remove the letter S from each of the words, we get:
HOST becomes HOT POST becomes POT COST becomes COT LOST becomes LOT STOP becomes TOP
These are entirely new words.
Certainly, here are the meanings
Question : Select the option that expresses the given sentence in active voice. My request should be considered.
Option 1: Please have consider my request.
Option 2: Please do consider mine request.
Option 3: Consider my request.
Option 4: Please consider my request.
Correct Answer: Please consider my request.
Solution : The correct choice is the fourth option.
Explanation: Active voice in a sentence occurs when the subject of the sentence performs the action expressed by the verb. In the case of imperative sentences, the subject is usually implied.
The structure of the
Question : If $\frac{\sin\theta+\cos\theta}{\sin\theta-\cos\theta}=3$, then the value of $\sin^{4}\theta$ is:
Option 1: $\frac{2}{5}$
Option 2: $\frac{1}{5}$
Option 3: $\frac{16}{25}$
Option 4: $\frac{3}{5}$
Correct Answer: $\frac{16}{25}$
Solution : Given that $\frac{\sin\theta+\cos\theta}{\sin\theta-\cos\theta}=3$ $\frac{\sin\theta+\cos\theta}{\sin\theta-\cos\theta}=\frac{3}{1}$ Applying Componendo and Dividendo, $⇒\frac{2\sin\theta}{2\cos\theta} = \frac{4}{2}$ $⇒\frac{\sin\theta}{\cos\theta} = 2$ $⇒\tan\theta = \frac{2}{1}$ We know that, $\tan\theta =\frac{\text{Perpendicular}}{\text{Base}}$ Let be perpendicular = $2k$, and base = $k$. Using Pythagoras theorem, hypotenuse = $\sqrt{(2k)^2+k^2}=\sqrt5k$ $\sin\theta =\frac{2}{\sqrt5}$ ⇒ $\sin^{4}\theta=(\frac{2}{\sqrt5})^4=\frac{16}{25}$ Hence, the correct answer
Question : The most important safeguard of liberty is :
Option 1: Bold and impartial judiciary
Option 2: Well-knit party system
Option 3: Decentralisation of power
Option 4: Decentralisation of rights
Correct Answer: Bold and impartial judiciary
Solution : The correct answer is Bold and impartial judiciary.
The ability to choose one's actions is a quality referred to as liberty. For the defence and preservation of individual liberty, there must be an impartial, independent judiciary. The judiciary needs to be free
Question : Directions: In the following question, some parts of the sentence have errors, and some are correct. Find out which part of the sentence has an error. The number of that part is the answer. If a sentence is error-free, your answer is "No Error".
I enjoyed during (1) / my tenure (2) / in Shimla. (3) / No Error (4)
Option 1: 1
Option 2: 2
Option 3: 3
Option 4: 4
Correct Answer: 1
Solution : The first option is the correct answer.
A reflexive pronoun is used when the object of a sentence is the same as the subject.
Therefore, the correct sentence should be: "I enjoyed myself during my tenure in Shimla."
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