SAT (Stage-2) Mock Test

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SAT (Stage-2) Mock Test - 63

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Weekly Quiz Competition

Question 1
1 / -0

A pebble is thrown vertically upwards from a bridge with an initial velocity of 4.9 m/s. It strikes the water after 2 s. The height of the bridge is

A
19.6 m

B
14.7 m

C
9.8 m

D
4.9 m

Solution
Question 2
1 / -0

A bomb is released by a horizontally flying aeroplane. The trajectory of the bomb is a

A
straight line

B
parabola

C
hyperbola

D
circle

Solution

It would be a parabola.

The bomb will have some inital velocity when it will be droped from the plane. also, it will be acted by gravity. As a result the final trajectory will be that of a parabola.
Question 3
1 / -0

A river is flowing at the rate of 50 km/h. A person, who can row the boat at 10 km/h, wants to reach a point just opposite on the other bank of the river. He should row

A
upstream

B
straight

C
inclined to the bank upstream

D
inclined to the bank downstream

Solution

To reach B from A, a person will have to swim inclined upstream because he has to reach the exact opposite point. The current will cause him to reach the point.
Question 4
1 / -0

Two identical strings are stretched at tensions T_A and T_B. A tuning fork is used to set them in vibration. If A vibrates in its fundamental mode and B in its second harmonic mode, which of the following relations holds true?

A
T_A = 2T_B

B
T_A= 4T_B

C
2T_A = T_B

D
4T_A = T_B

Solution

Let n be the frequency of the tuning fork, lbe the length of each string and m be the mass per unit length of each string.
Question 5
1 / -0

A parachutist steps from an aircraft, falls freely for two seconds, and then opens his parachute. Which of the following acceleration-time (a - t) graphs best represents his downward acceleration during the first 5 seconds?

A

B

C

D

Solution

Initially the object is falling down with constant acceleration. As the parachute opens its surface area is increases as a result upthrust on the parachute increases.

For a moment, upthrust will increase the weight of the person and direction of the acceleration will change. Slowly, it will be balanced by the weight and acceleration becomes zero.
Question 6
1 / -0

How many 3 digit numbers have their last digit as 9?

A
100

B
99

C
92

D
90

Solution

109, 119, 129, ----------- 999
999 = 109 + (n - 1) × 10
n = 90
Question 7
1 / -0

Which of the following identities should be used to factorise 9x² + 6xy + y²?

A
(a - b)² = a² + b² - 2ab

B
(a + b)² = a² + b² + 2ab

C
a² - b² = (a - b) (a + b)

D
None of these

Solution

Let p(x) = 9x²+ 6xy + y²
= (3x)² + 2(3x)(y) + y²
= (3x + y)²
The identity used above is (a + b)² = a² + b² + 2ab
Question 8
1 / -0

If the polynomial x³ + 2x² - 3x - 4 is divided by (x + 3), what will be the remainder?

A
- 4

B
3

C
- 2

D
5

Solution

g(x) = x + 3
Now, put x + 3 = 0, x = - 3.
The remainder can be found by using p(- 3).
Now, p(-3) = (- 3)³ + 2 (- 3)² - 3(- 3) - 4
= - 27 + 18 + 9 - 4
= - 31 + 27
= - 4
So, remainder is - 4.
Question 9
1 / -0

Given that one of the zeroes of the cubic polynomial ax³ + bx² + cx + d is zero, what will be the product of the other two zeroes?

A

B
c/a

C
0

D

Solution

Let the zeroes of the polynomial be α, β and γ

Then according to the condition of cubic polynomial formula:

Since one of the zeroes is zero

Let γ = 0

Then from equation (1)

Product of the other two zeroes = α, β = c/a
Question 10
1 / -0

The pair of equations x = a and y = b graphically represents the lines which are

A
parallel

B
intersecting at (b, a)

C
coincident

D
intersecting at (a, b)

Solution

The pair of equations x = a and y = b graphically represents the lines which are intersecting at (a, b).
Question 11
1 / -0

The graph of the linear equation 2x + 3y = 6 cuts the y-axis at the point

A
(2, 0)

B
(0, 3)

C
(3, 0)

D
(0, 2)

Solution

The point at which a line meets y-axis, the value of x is 0.
Substituting 0 for x in the equation 2x + 3y = 6, we get y = 2. So, the coordinates of that point is (0, 2).
Question 12
1 / -0

The sum of the roots of which of the following equations is 3?

A
2x² - 3x + 6 = 0

B
- x² + 3x - 3 = 0

C
x² + 4x + 3 = 0

D
3x² - 3x + 3 = 0

Solution
Question 13
1 / -0

Which of the following is a quadratic equation?

A
x² + 2x + 1 = (4 - x)² + 3

B
- 2x² = (5 - x) (2x - 2/5)

C
(k + 1)x² + 3/2 x = 7, where k = - 1

D
x³ - x² = (x - 1)³

Solution

Solving x³ - x² = (x - 1)³, we get the quadratic equation 2x²- 3x + 1 = 0
Question 14
1 / -0

If 1/2 is a root of the equation x² + kx - 5/4 = 0, then the value of k is

A
2

B
-2

C
1/4

D
1/2

Solution

Given, 1/2 is a solution of the equation
So, (1/2)² + k/2 - 5/4 = 0
or, 1/4 - 5/4 = -k/2
or, -k/2 = -1
or k = 2
Question 15
1 / -0

Which term of the AP : 21, 42, 63, 84, ... is 210?

A
9^th

B
10^th

C
11^th

D
12^th

Solution

a = 21
d = 21
Applying the formula for the n^th term of an AP, we get
210 = 21 + (n - 1) x 21
On solving for n, we get n = 10.
Hence, 210 is the 10^th term of the given AP.