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Question : $\triangle$ XYZ is a right-angled triangle and $\angle$Y = 90° If XY = 2.5 cm and YZ = 6 cm, then the circumradius of $\triangle$XYZ is:
Option 1: 6.5 cm
Option 2: 3.25 cm
Option 3: 3 cm
Option 4: 2.5 cm
Correct Answer: 3.25 cm
Solution : Given: XYZ is a right-angled triangle and $\angle$Y = 90°, where XY = 2.5 cm and YZ = 6 cm. Let the hypotenuse of the triangle be $h$ cm. So, $h^2=6^2+(2.5)^2$ ⇒ $h=\sqrt{42.25}$ ⇒ $h=6.5$ cm We know, The circumradius of a right-angled triangle
Question : Directions: Two Statements are given followed by two conclusions numbered I and II. Assuming the statement to be true, even if it seems to be at variance with commonly known facts. decide which of the conclusions logically follow(s) from the statements. Statements: Some pupils are cutes. All boys are cutes. Conclusions: I. All cutes are boys. II. Some pupils are boys.
Option 1: Only conclusion I follows
Option 2: Neither conclusion I nor II follows
Option 3: Both conclusions I and II follow
Option 4: Only conclusion II follows
Correct Answer: Neither conclusion I nor II follows
Solution : Given: According to the given statements, the Venn diagram is given below –
Let's analyse the conclusions – Conclusion (I): All cutes are boys – From the Venn diagram, it is evident that some parts of the circle representing cutes
Question : Which among the following is a folk dance of India ?
Option 1: Mohiniattam .
Option 2: Kathakali .
Option 3: Manipuri.
Option 4: Garba .
Correct Answer: Garba .
Solution : The correct option is - Garba
The Indian folk dance known as garba is frequently performed during festivals and other special events in the state of Gujarat. A common feature of garba performances is singing, which is typically accompanied by the dhol and the
Question : Select the option that expresses the given sentence in passive voice. The mother loves the baby.
Option 1: The baby was loved by the mother.
Option 2: The baby will be loved by the mother.
Option 3: The baby has been loved by the mother.
Option 4: The baby is loved by the mother.
Correct Answer: The baby is loved by the mother.
Solution : The fourth option is the correct choice.
Passive voice is the voice in which the object experiences an action rather than the person who performs the action. Hence, the object in the active voice becomes the subject in the
Question : According to the Groundnut Crop Survey Report 2018, which of the following states is the largest producer of groundnuts?
Option 1: West Bengal
Option 2: Haryana
Option 3: Gujarat
Option 4: Bihar
Correct Answer: Gujarat
Solution : The correct answer is Gujarat.
Gujarat, Andhra Pradesh, Tamil Nadu, Karnataka, Maharashtra, and Rajasthan are key states in groundnut cultivation. Gujarat stands out as the largest producer, contributing 40% to the national output. In 2018, the All India crop coverage report indicated groundnut cultivation
Question : If $x^2+y^2=427$ and $xy=202$, then find the value of $\frac{x+y}{x-y}$.
Option 1: $\sqrt{\frac{835}{23}}$
Option 2: $\sqrt{\frac{830}{29}}$
Option 3: $\sqrt{\frac{831}{23}}$
Option 4: $\sqrt{\frac{830}{23}}$
Correct Answer: $\sqrt{\frac{831}{23}}$
Solution : Given: $x^2+y^2=427$ and $xy=202$. Now, $(x+y)^2=x^2+y^2+2xy$ ⇒ $(x+y)^2=427+2×202$ ⇒ $(x+y)=\sqrt{831}$ ---------------------------------------(1) Also, $(x-y)^2=x^2+y^2-2xy$ ⇒ $(x-y)^2=427-2×202$ ⇒ $(x-y)= \sqrt{23}$ ------------------------------------(2) So, $\frac{x+y}{x-y}$ $= \frac{\sqrt{831}}{\sqrt{23}}$ $= \sqrt{\frac{831}{23}}$. Hence, the correct answer is $\sqrt{\frac{831}{23}}$.
Question : Select the most appropriate option to fill in the blank.
He has a high-paying job, ______________ he never seems to have any money.
Option 1: yet
Option 2: by
Option 3: from
Option 4: so
Correct Answer: yet
Solution : The first option is the correct answer.
The sentence structure indicates a contrast between having a high-paying job and not having any money. Yet is a conjunction commonly used to introduce a contrast or contradiction. In this context, it is fitting to express the paradox
Question : Directions: A boy walks 15 m north, turns right, and walks 20 m. Again, he turns right and walks 15 m. Finally, he turns to his left and moves 20 m. What is the distance now from his original position?
Option 1: 40 m
Option 2: 46 m
Option 3: 50 m
Option 4: 45 m
Correct Answer: 40 m
Solution : According to the instructions given, the diagram is as follows –
Here, O is the starting point and D is the finishing point and OD is the total distance from the starting point.
OA = 15m; AB = 20m; BC = 15m; CD =
Question : Directions: What will come in the place of '?' in the following equation, if '+' and '–' are interchanged with '÷' and '×', respectively? 88 + 8 – 17 × 16 ÷ 40 = ?
Option 1: 203
Option 2: 197
Option 3: 200
Option 4: 211
Correct Answer: 211
Solution : Given: 88 + 8 – 17 × 16 ÷ 40 = ?
After interchanging the signs as per instructions, the new equation will be –
= 88 ÷ 8 × 17 – 16 + 40 = 11 × 17 – 16 + 40 = 187
Question : Directions: If A stands for ÷, B stands for ×, C stands for +, and D stands for –, what will come in place of the question mark (?) in the following equation? 3 B 26 C 15 D 36 A 3 = ?
Option 1: 82
Option 2: 80
Option 3: 81
Option 4: 83
Correct Answer: 81
Solution : Given: A stands for ÷, B stands for ×, C stands for +, and D stands for – 3 B 26 C 15 D 36 A 3 = ?
After interchanging the alphabet into the signs the equation becomes – = 3 × 26 +
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