SAT (Stage-1) Mock Test

Result

SAT (Stage-1) Mock Test - 57

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

A cylinder, a hemisphere and a cone stand on the same base and have equal heights. The ratio of the areas of their curved surfaces is

A
2 : 2 : 1

B
√2 : √2 : 1

C
√2 : 3 : 1

D
1 : 3 : √2

Solution

Let r and h be the radius and height of the cylinder, hemisphere and cone.
The height of the hemisphere is the same as its radius.
So, r = h
The cylinder, hemisphere and cone are made on same base, so the radius is same in all. So, r = h for the cylinder as well as the cone.
Ratio of the curved surface areas of the cylinder, hemisphere and the cone standing on the same base and having equal heights =

Solving, we get the required ratio = √2 : √2 : 1
Question 2
1 / -0

Find the value of m if the given lines are coincident.

mx + 2y – 3 = 0 and 6y + 3x – 9 = 0

A
1

B
4

C
-1

D
3

Solution

Since the lines a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 are coincident,
Question 3
1 / -0

What must be added to x⁴ + 2x³ – 2x² + x – 1, so that the result is exactly divisible by x² + 2x – 3?

A
– x + 2

B
x + 2

C
x – 2

D
– x – 2

Solution

Let f(x) = x⁴ + 2x³ - 2x² + x - 1 is divided by x²+ 2x - 3.
x⁴+ 2x³ - 2x² + x -1 = {(x² + 2x -3) (x²+ 1)} - x + 2
i.e. we get remainder a= -x + 2.
Hence, x - 2 must be added to x⁴ + 2x³ - 2x² + x - 1, so that the result is exactly divisible by x² + 2x - 3.
i.e x - 2 should be added.
Question 4
1 / -0

If α,βand γ are zeroes of polynomial 6x³ - 3x² + 18x + 1, then what is the value of α²+β²+γ²?

A
23/4

B
1/4

C
-27/4

D
-23/4

Solution
Question 5
1 / -0

If , then what is the value of x?

A
7

B
6

C
8

D
9

Solution
Question 6
1 / -0

What will be the remainder when 2⁶⁰ - 1 is divided by 5?

A
3

B
2

C
1

D
0

Solution

2⁴ = 16; 2⁸ = 256; 2⁴ⁿ ends with 6
16 - 1 = 15, divisible by 5
2⁶⁰ends with the unit digit as 6.
(6 - 1) will end in 5.
So, 2⁶⁰ - 1 is divisible by 5.
Remainder = 0
Question 7
1 / -0

If 365xy is divisible by 30, then the least value of x + y =

A
9

B
5

C
0

D
1

Solution

A number is divisible by 30 only if it is divisible by 3 and 10, so for divisibility by 10, unit's place digit should be 0, so y = 0.
And for divisibility by 3, sum of numbers should be divisible by 3.
i.e. 3 + 6 + 5 + x + y = 14 + x is divisble by 3.
So, the least value of x in this case will be 1.
As 15 = 14 + 1 is divisible by 3,
So, least value of x + y = 1 + 0 = 1
Question 8
1 / -0

If a = 3√5 and b = 2√5 + 1, find the value of a/b.

A

B

C

D

Solution
Question 9
1 / -0

If 3^x = 4 and 4^y = 8, then the value of 9^{x - y} is

A
1/9

B
16/97

C
8/9

D
Cannot be determined

Solution
Question 10
1 / -0

A businessman marks his goods in such a way that even after allowing 12.5% discount on cash purchase, he gains 20%. If the cost price of the goods is Rs. 140, find the marked price.

A
Rs. 172

B
Rs. 180

C
Rs. 192

D
Rs. 198

Solution

12.5% or discount is on the marked price (MP).
∴ SP = 7/8MP …(1)
Also, CP = Rs. 140
Profit = 20%
SP = Rs. 1.2 × 140 = Rs. 168 …(2)
From (1) and (2), we get
7/8MP = Rs. 168
MP = Rs. 192
Question 11
1 / -0

At the Congress of Vienna in 1815, the great European powers divided Poland. Which of the following countries were referred to as the 'great powers'?

A
Germany, Russia and France

B
Prussia, Russia and the Netherlands

C
The Netherlands, Austria and Russia

D
Russia, Prussia and Austria

Solution

On August 5, 1772, Russia, Prussia, and Austria, the great European powers, signed a treaty that partitioned Poland. Ratified by the Polish Sejm (legislature) on September 30, 1773, the agreement deprived Poland of approximately half of its population and almost one-third [about 81,500 square miles (211,000 square km)] of its land area.
Question 12
1 / -0

Which of the following novels written by Henry Fielding was issued in six volumes priced at three shillings each, which was more than what a labourer earned in a week?

A
Sketches by 'Boz'

B
Pickwick Papers

C
Tom Jones

D
Pamela

Solution

This is the correct answer as Tom Jones was the novel written by Henry Fielding, which was sold at a price that was more than what a labourer earned in a week.
Question 13
1 / -0

Which of the following books by Charles Dickens describes Coketown, a fictitious industrial town?

A
Oliver Twist

B
A Tale of Two Cities

C
A Christmas Carol

D
Hard Times

Solution

Coketown was a fictitious industrial town described in the novel Hard Times.
Question 14
1 / -0

Which of the following is correct about Reichstag?

A
A National Assembly met at Reichstag after the defeat of Imperial Germany and the abdication of the emperor in the WW II.

B
The revolutionary uprising of the Spartacist League took place at Reichstag after the birth of the Weimar Republic.

C
Reichstag was the site of the millions of killing camps of the Nazis during the WW II.

D
Deputies were voted in the Reichstag on the basis of equal and universal votes cast by all adults including women.

Solution

Reichstag was the German Parliament of the Weimar Republic where deputies were voted on the basis of equal and universal votes cast by all adults including women.
Question 15
1 / -0

Which of the following was the symbol of Eternity in the Declaration of Rights?

A
Snake biting its tail to form a ring

B
Red Phrygian cap

C
Sceptre

D
The broken chain

Solution

Snake Biting its Tail to form a Ring, this type of ring has neither beginning nor end. It is a symbol of eternity. The ouroboros is often interpreted as a symbol for eternal cyclic renewal or a cycle of life, death, and rebirth. The skin-sloughing process of snakes symbolizes the transmigration of souls, the snake biting its own tail is a fertility symbol. The tail of the snake is a phallic symbol, the mouth is a yonic or womb-like symbol.