Q. The parabola y^2 = 12x opens in which direction?
A.
Upwards
B.
Downwards
C.
Left
D.
Right
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Solution
The equation y^2 = 12x indicates that the parabola opens to the right since it is in the form y^2 = 4px.
Correct Answer:
D
— Right
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Q. The Parliament consists of two houses. If the Lok Sabha has 545 members and the Rajya Sabha has 245 members, what is the ratio of Lok Sabha members to Rajya Sabha members?
A.
5:2
B.
11:5
C.
9:4
D.
7:3
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Solution
Ratio = 545:245 = 11:5.
Correct Answer:
B
— 11:5
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Q. The Parliament of India consists of two houses. If the Lok Sabha has 545 members and the Rajya Sabha has 245 members, what is the total number of members in both houses? (2021)
A.
790
B.
800
C.
750
D.
780
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Solution
Total members = Members in Lok Sabha + Members in Rajya Sabha = 545 + 245 = 790.
Correct Answer:
A
— 790
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Q. The perimeter of a square is 40 cm. What is the length of one side? (2021)
A.
5 cm
B.
10 cm
C.
15 cm
D.
20 cm
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Solution
Perimeter = 4 × side. Therefore, side = Perimeter / 4 = 40 cm / 4 = 10 cm.
Correct Answer:
B
— 10 cm
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Q. The perimeter of a square is 64 cm. What is the length of one side? (2021)
A.
12 cm
B.
14 cm
C.
16 cm
D.
18 cm
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Solution
Perimeter of a square = 4 × side. Therefore, side = 64 cm / 4 = 16 cm.
Correct Answer:
C
— 16 cm
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Q. The perimeter of an equilateral triangle is 36 cm. What is the length of each side? (2021)
A.
9 cm
B.
12 cm
C.
10 cm
D.
8 cm
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Solution
In an equilateral triangle, all sides are equal. Therefore, each side = Perimeter / 3 = 36 / 3 = 12 cm.
Correct Answer:
B
— 12 cm
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Q. The Pradhan Mantri Fasal Bima Yojana was launched to provide insurance coverage for which sector?
A.
Agriculture
B.
Education
C.
Health
D.
Housing
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Solution
The Pradhan Mantri Fasal Bima Yojana provides insurance coverage and financial support to farmers in the agriculture sector.
Correct Answer:
A
— Agriculture
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Q. The Pradhan Mantri Gram Sadak Yojana (PMGSY) primarily aims to: (2000)
A.
Provide electricity to rural areas
B.
Construct all-weather roads in rural areas
C.
Ensure housing for all
D.
Promote digital connectivity
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Solution
The Pradhan Mantri Gram Sadak Yojana aims to construct all-weather roads to improve connectivity in rural areas.
Correct Answer:
B
— Construct all-weather roads in rural areas
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Q. The Pradhan Mantri Gram Sadak Yojana (PMGSY) was launched to improve connectivity in which areas?
A.
Urban areas
B.
Rural areas
C.
Coastal areas
D.
Hilly areas
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Solution
The Pradhan Mantri Gram Sadak Yojana (PMGSY) was launched to improve road connectivity in rural areas.
Correct Answer:
B
— Rural areas
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Q. The Pradhan Mantri Jan Dhan Yojana (PMJDY) primarily aims to promote which of the following? (2014)
A.
Financial inclusion
B.
Digital literacy
C.
Agricultural productivity
D.
Health insurance
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Solution
The Pradhan Mantri Jan Dhan Yojana (PMJDY) aims to promote financial inclusion by providing banking facilities to the unbanked population.
Correct Answer:
A
— Financial inclusion
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Q. The Pradhan Mantri Jan Dhan Yojana aims to achieve which of the following?
A.
Universal access to banking facilities
B.
Free health insurance for all
C.
Skill development for youth
D.
Housing for all
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Solution
The Pradhan Mantri Jan Dhan Yojana aims to ensure universal access to banking facilities for all citizens.
Correct Answer:
A
— Universal access to banking facilities
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Q. The Pradhan Mantri Ujjwala Yojana aims to provide which of the following? (2016)
A.
Free education to girls
B.
Clean cooking fuel to women from below poverty line
C.
Financial assistance for housing
D.
Employment opportunities for rural youth
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Solution
The Pradhan Mantri Ujjwala Yojana aims to provide clean cooking fuel (LPG) to women from below the poverty line.
Correct Answer:
B
— Clean cooking fuel to women from below poverty line
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Q. The Pradhan Mantri Ujjwala Yojana is primarily aimed at providing which of the following? (2016)
A.
Free education to girls
B.
Clean cooking fuel to rural households
C.
Financial assistance for farmers
D.
Employment to urban youth
Show solution
Solution
The Pradhan Mantri Ujjwala Yojana aims to provide clean cooking fuel (LPG) to women from Below Poverty Line (BPL) households.
Correct Answer:
B
— Clean cooking fuel to rural households
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Q. The Pradhan Mantri Ujjwala Yojana primarily aims to provide which of the following?
A.
Electricity to rural households
B.
Clean cooking fuel to women from Below Poverty Line households
C.
Financial assistance for education
D.
Health insurance for the poor
Show solution
Solution
The Pradhan Mantri Ujjwala Yojana aims to provide clean cooking fuel (LPG) to women from Below Poverty Line households.
Correct Answer:
B
— Clean cooking fuel to women from Below Poverty Line households
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Q. The Preamble of the Indian Constitution declares India to be a:
A.
Sovereign State
B.
Federal State
C.
Monarchy
D.
Theocratic State
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Solution
The Preamble of the Indian Constitution declares India to be a Sovereign State.
Correct Answer:
A
— Sovereign State
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Q. The President of India is elected by an electoral college consisting of the elected members of which bodies? (2022)
A.
Lok Sabha and Rajya Sabha
B.
State Legislative Assemblies and Rajya Sabha
C.
Lok Sabha, Rajya Sabha, and State Legislative Assemblies
D.
Only Lok Sabha
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Solution
The President of India is elected by an electoral college comprising the elected members of both Houses of Parliament and the elected members of the Legislative Assemblies of States and Union territories.
Correct Answer:
C
— Lok Sabha, Rajya Sabha, and State Legislative Assemblies
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Q. The product of the roots of the equation 2x^2 - 3x + 1 = 0 is equal to?
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Solution
The product of the roots is given by c/a. Here, c = 1 and a = 2, so the product is 1/2.
Correct Answer:
A
— 1/2
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Q. The product of the roots of the equation 2x^2 - 4x + 2 = 0 is equal to what?
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Solution
The product of the roots of the equation ax^2 + bx + c = 0 is given by c/a. Here, c = 2 and a = 2, so the product is 2/2 = 1.
Correct Answer:
A
— 1
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Q. The product of the roots of the equation 2x^2 - 8x + 6 = 0 is equal to?
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Solution
The product of the roots of the equation ax^2 + bx + c = 0 is given by c/a. Here, c = 6 and a = 2, so the product is 6/2 = 3.
Correct Answer:
A
— 3
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Q. The product of the roots of the quadratic equation 3x^2 - 12x + 9 = 0 is: (2021)
Show solution
Solution
The product of the roots is given by c/a, which is 9/3 = 3.
Correct Answer:
B
— 3
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Q. The product of the roots of the quadratic equation x^2 + 5x + 6 = 0 is: (2021)
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Solution
The product of the roots is given by c/a = 6/1 = 6.
Correct Answer:
A
— 6
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Q. The product of two consecutive integers is 240. What are the integers? (2022)
A.
14 and 15
B.
15 and 16
C.
16 and 17
D.
12 and 13
Show solution
Solution
Let the integers be n and n+1. Then n(n+1) = 240. Solving the quadratic equation n^2 + n - 240 = 0 gives n = 14, so the integers are 14 and 15.
Correct Answer:
A
— 14 and 15
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Q. The quadratic equation 2x^2 - 4x + k = 0 has no real roots. What is the condition on k? (2022)
A.
k < 0
B.
k > 0
C.
k > 8
D.
k < 8
Show solution
Solution
The discriminant must be less than zero: (-4)^2 - 4*2*k < 0 leads to k > 8.
Correct Answer:
C
— k > 8
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Q. The quadratic equation 2x^2 - 4x + k = 0 has no real roots. What is the condition for k? (2022)
A.
k < 0
B.
k > 0
C.
k > 8
D.
k < 8
Show solution
Solution
The discriminant must be less than zero: (-4)^2 - 4*2*k < 0 leads to k > 8.
Correct Answer:
C
— k > 8
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Q. The quadratic equation 3x^2 + 12x + 12 = 0 can be simplified to what form? (2022)
A.
x^2 + 4x + 4 = 0
B.
x^2 + 3x + 4 = 0
C.
x^2 + 2x + 1 = 0
D.
x^2 + 6x + 4 = 0
Show solution
Solution
Dividing the entire equation by 3 gives x^2 + 4x + 4 = 0.
Correct Answer:
A
— x^2 + 4x + 4 = 0
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Q. The quadratic equation 4x^2 - 12x + 9 = 0 can be factored as: (2023)
A.
(2x - 3)(2x - 3)
B.
(4x - 3)(x - 3)
C.
(2x + 3)(2x + 3)
D.
(4x + 3)(x + 3)
Show solution
Solution
The equation can be factored as (2x - 3)(2x - 3) = 0, indicating a perfect square.
Correct Answer:
A
— (2x - 3)(2x - 3)
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Q. The quadratic equation 5x^2 + 3x - 2 = 0 has roots that can be expressed in which form? (2023)
A.
Rational
B.
Irrational
C.
Complex
D.
Imaginary
Show solution
Solution
The discriminant is 3^2 - 4*5*(-2) = 9 + 40 = 49, which is a perfect square, hence the roots are rational.
Correct Answer:
A
— Rational
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Q. The quadratic equation x^2 + 6x + 9 = 0 can be expressed in the form of (x + a)^2. What is the value of a? (2022)
Show solution
Solution
The equation can be factored as (x + 3)^2 = 0, hence a = 3.
Correct Answer:
A
— 3
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Q. The quadratic equation x^2 + 6x + 9 = 0 can be expressed in which of the following forms? (2020)
A.
(x + 3)^2
B.
(x - 3)^2
C.
(x + 6)^2
D.
(x - 6)^2
Show solution
Solution
This is a perfect square trinomial: (x + 3)(x + 3) = 0.
Correct Answer:
A
— (x + 3)^2
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Q. The quadratic equation x^2 + 6x + k = 0 has equal roots. What is the value of k? (2020)
Show solution
Solution
For equal roots, b^2 - 4ac = 0. Here, 6^2 - 4(1)(k) = 0, so k = 9.
Correct Answer:
A
— 9
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