SAT (Stage-1) Mock Test

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SAT (Stage-1) Mock Test - 77

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Question 1
1 / -0

Paras rolls a die with numbers 1, 2, 3, 4, 5 and 6 on it. What is the probability that he will get 3 or a multiple of 3 on it?

A
1/6

B
1/4

C
1/3

D
1/2

Solution

Multiples of 3 on a die = 3 and 6
So, number of favourable outcomes = 2
Total number of possible outcomes = 6
Probability of getting 3 or a multiple of 3 = 2/6 = 1/3
Question 2
1 / -0

A bag contains 14 black, 10 blue and 15 red balls. A ball is picked at random from the bag and it is not of red colour. Find the probability that the colour of ball is not black (upto 2 decimal places)

A
0.42

B
0.40

C
0.52

D
0.58

Solution

Let the probability of picking a ball of color which is not red , P(A) =

Then, the probability of picking a ball of color which is not black and not red, P(B) = 10/39

Then, the probability that the colour of ball is not black if it is given that it is also not red, =
Question 3
1 / -0

Which of the following is one of the roots of the quadratic equation 12(1 - y²) = 7y?

A
4/3

B
-4/3

C
-3/4

D
-3

Solution

12(1 - y²) = 7y
12y²+ 7y - 12 = 0
12y²+ 16y - 9y - 12 = 0
4y(3y + 4) - 3(3y + 4) = 0
(3y + 4)(4y - 3) = 0

Therefore, y = -4/3 or y = 3/4
Question 4
1 / -0

Each side of a square measures 4 cm more than each side of another square. If the sum of their areas is 400 sq. cm, then what is the area of the larger square?

A
144 cm²

B
169 cm²

C
196 cm²

D
256 cm²

Solution

Let each side of the smaller square measure x cm.
Then, length of each side of the larger square = (x + 4) cm
According to problem:
(x + 4)² + x² = 400 {Area of square = Side × Side}
x² + 8x + 16 + x² = 400
Or 2x² + 8x - 384 = 0
⇒ x² + 4x - 192 = 0
Or (x + 16)(x - 12) = 0
⇒ x = 12
So, length of each side of the larger square = (12 + 4) cm = 16 cm
Area = (16)² cm²= 256 cm²
Question 5
1 / -0

If X = {2, 3, 7} and Y = {1, 2, 3, 4, 6}, what will be the value of X ∪ Y?

A
ϕ

B
{2, 3}

C
{1, 2, 3, 4, 6}

D
{1, 2, 3, 4, 6, 7}

Solution

X ∪ Y means set of elements which are present either in set X or in set Y, without repetition.

Hence, X ∪ Y = {2, 3, 7} ∪ {1, 2, 3, 4, 6} = {1, 2, 3, 4, 6, 7}
Question 6
1 / -0

If A and B are two finite sets such that A ∩ B is not a null set, then n (A ∪ B) is equal to

A
n(A) + n(B)

B
n(A) × n(B)

C
n(A) + n(B) + n(A ∩ B)

D
None of these

Solution

n(A U B) = n(A) + n(B) - n (A ∩ B)
Question 7
1 / -0

What is the relation among h, b and x in the given figure?

A
h + b = x cot α

B
x = (h + b) tan β

C
h + b = x tan β

D
x = (h + b) cos β

Solution

In ΔRQP,

x = (h + b) cot α
x = (h + b) tan(90° – α)
x = (h + b) tan β
Question 8
1 / -0

A man is standing on the top of a raised platform such that his eyes are 3 m high from the horizontal ground level and at a horizontal distance of 30 m from a tree. The angle of elevation of the top of the tree from his eyes is 30°. Estimate the height of the tree.

A
17.16 m

B
24.6 m

C
20.32 m

D
21.94 m

Solution

Let the height of the tree be 'h'.
Question 9
1 / -0

If m = 1 + tan²θ and n = 1 + cot²θ, then m/nequals

A
m + 1

B
m - 1

C
n - 1

D
n + 1

Solution

1 + tan²θ= sec²θ,

1 + cot²θ = cosec²θ

Alternate solution:

m = 1 + tan²θ = sec²θ

n = 1 + cot²θ = cosec²θ

m/n = sec² θ/cosec²θ = tan²θ = sec²θ - 1 = m - 1
Question 10
1 / -0

If secθ - tanθ = x then find the value of cosθ

A

B

C

D
None of these

Solution

secθ - tanθ = x

secθ + tanθ = 1/x

2secθ = x + 1/x
Question 11
1 / -0

When was the National Human Rights Commission (NHRC) set up?

A
1953

B
1983

C
1993

D
2003

Solution

The Rights Commission (NHRC) of India is an autonomous public body constituted on 12 October 1993 under the Protection of Human Rights Ordinance of 28 September 1993.
Question 12
1 / -0

Articles 14-18 of the Part III of the Indian Constitution enshrine:

A
Right against exploitation

B
Right to freedom

C
Right to equality

D
Right to freedom of religion

Solution

Part III of the Indian Constitution from Article 12 to Article 32 contains fundamental rights. The right to equality has been enshrined under Articles 14-18.
Right against exploitation: Articles 23-24
Right to freedom: Articles 19-22
Right to freedom of religion: Articles 25-28

Question 13

1 / -0

Here are some of the guiding values of the Constitutions and their meanings. Match them correctly.

Guiding Value	Meaning
(A) Sovereign	(I) Government will not favour any religion.
(B) Republic	(II) People have the supreme right to make decision.
(C) Fraternity	(III) The state is ruled by the elected representatives.
(D) Secular	(IV) People should live like brothers and sisters.

(II), (I), (IV), (III)

(III), (IV), (I), (II)

(IV), (III), (II), (I)

(II), (III), (IV), (I)

Solution

(A) Sovereign	(II) People have the supreme right to make decision.
(B) Republic	(III) The state is ruled by the elected representatives.
(C) Fraternity	(IV) People should live like brothers and sisters.
(D) Secular	(I) Government will not favour any religion.

The Preamble serves as an introduction to the Constitution. It was amended by the 42^nd Constitutional Amendment Act in 1976, which determined to constitute India into a sovereign, socialist, secular, and democratic republic. It secures justice, liberty and equality to all the citizens of India, and promotes fraternity among the people.

Question 14
1 / -0

According to _____________, 'Democracy is a government in which everyone has a share.'

A
Prof. Mukund

B
Prof. Thomas Harley

C
Prof. Seeley

D
Prof. Lincoln

Solution

According to Seeley, 'Democracy is a government in which every one has a share.'
Democracy is a government by the people in which the supreme power is vested in the people and exercised directly by them or by their elected agents under a free electoral system. A democratic government implies a democratic state, but a democratic state does not necessarily mean a democratic government. A democratic state means that the community as a whole possesses sovereign authority and maintains ultimate controlling and dismissing a government.
Question 15
1 / -0

The Indian Constitution is a Republican Constitution because it has

A
an elected President

B
a federal form of government

C
a parliamentary supremacy

D
an elected Prime Minister

Solution

Republic is a form of government or country in which power resides in elected individuals representing the citizen body and government leaders exercise power according to the rule of law. It provides for an elected Parliament. A Republic country follows the simple rule that the supreme head of the nation is elected, not selected. Not even by heredity one can be the President in India. Republic in the Indian Constitution means that the Head of the State, Hon'Ble President is elected directly or indirectly for a fixed period of five years.

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Re-Attempt Weekly Quiz Competition

SAT (Stage-1) Mock Test - 77

Result

SAT (Stage-1) Mock Test - 77

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SHARING IS CARING

Question 1

1/6

1/4

1/3

1/2

Solution

Question 2

0.42

0.40

0.52

0.58

Solution

Question 3

4/3

-4/3

-3/4

-3

Solution

Question 4

144 cm2

169 cm2

196 cm2

256 cm2

Solution

Question 5

ϕ

{2, 3}

{1, 2, 3, 4, 6}

{1, 2, 3, 4, 6, 7}

Solution

Question 6

n(A) + n(B)

n(A) × n(B)

n(A) + n(B) + n(A ∩ B)

None of these

Solution

Question 7

h + b = x cot α

x = (h + b) tan β

h + b = x tan β

x = (h + b) cos β

Solution

Question 8

17.16 m

24.6 m

20.32 m

21.94 m

Solution

Question 9

m + 1

m - 1

n - 1

n + 1

Solution

Question 10

None of these

Solution

Question 11

1953

1983

1993

2003

Solution

Question 12

Right against exploitation

Right to freedom

Right to equality

Right to freedom of religion

Solution

Question 13

(II), (I), (IV), (III)

(III), (IV), (I), (II)

144 cm²

169 cm²

196 cm²

256 cm²