SAT (Stage-2) Mock Test

Result

SAT (Stage-2) 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

Find the square root of √50 + √48.

A
2 [√3 + √2]

B
2^1/4 [√3 + √2]

C
(98)²

D
2[√3 - √2]

Solution
Question 2
1 / -0

By which rational number should 9 be divided so that the result is not a rational number?

A
-1

B
0

C
2

D
3

Solution

For numbers to be closed under division,
a ÷ b = c (where, a, b and c are rational numbers)
a = 9, b = 0
9 ÷ 0 = 9/0 = not defined
So, 9 ÷ 0 proves that rational numbers are not closed under division.
Question 3
1 / -0

Which of the following options is a polynomial?

A

B

C

D

Solution

Exponent of 'x' in (i) is 2 and -2.
Exponent of 'x' in (ii) is 1/2.
Exponent of 'x' in (iii) is 1 and 2.
Exponent of 'x' in (iv) is 1 and -1.
Question 4
1 / -0

Which of the following quadratic polynomials has its zeros as -3 and 4?

A
x² - x + 12

B
x² + x + 12

C

D
2x² + 2x - 24

Solution

Sum of the roots will be (-3 + 4) = 1 and
Product of the roots = (-3)(4) = -12
For option 3, we have
Sum of the roots = 1
Product of the roots = -12
Question 5
1 / -0

If one of the zeros of the quadratic polynomial (k - 1)x² + kx + 1 is -3, then the value of k is

A
4/3

B
-4/3

C
2/3

D
-2/3

Solution

If 3 is the zero of the quadratic polynomial (k - 1) x² + kx + 1, then
9(k - 1) - 3k + 1 = 0
9k - 9 - 3k + 1 = 0
6k - 8 = 0
Question 6
1 / -0

What is the common difference of an arithmetic progression in which a₁₈ - a₁₄ = 32?

A
8

B
-8

C
-4

D
4

Solution

a₁₈ - a₁₄ = 32
Thus,
a + 17d - (a + 13d) = 32 (a = first term, d = common difference)
4d = 32
d = 8
Hence, common difference of the arithmetic progression is 8.
Question 7
1 / -0

If 3 sinθ+ 2 cosθ= 2, what is value of 2 sinθ- 3 cosθ?

A
0

B
± 1

C
± 2

D
± 3

Solution

3 sinθ+ 2 cosθ= 2 ... (i)
Let 2 sinθ- 3 cosθ= x ... (ii)

Squaring both sides,
9 sin²θ + 4 cos²θ + 12 sinθ cosθ = 4
4 sin²θ + 9cos²θ - 12 sinθ cosθ = x²

Adding both the equations,
13 sin²θ + 13 cos²θ = 4 + x²
x² = 9
x = ±3

Hence, value of 2 sinθ- 3 cosθ= ±3
Question 8
1 / -0

The number of planks of dimensions 4 m × 50 cm × 20 cm that can be stored in a pit which is 16 m long, 12 m wide and 4 m deep is

A
1900

B
1920

C
1800

D
1840

Solution

The number of planks of dimensions 4 m × 50 cm × 20 cm that can be stored in a pit which is 16 m long, 12 m wide and 4 m deep is:
Question 9
1 / -0

In the given figure, if PA and PB are tangents to the circle with centre O such that ∠APB = 50°, then ∠OAB is equal to

A
25°

B
30°

C
40°

D
50°

Solution

From the quadrilateral angle sum property,
50° + 90° + 90° + ∠AOB = 360°
∠AOB = 130°
Now, in ΔAOB,
∠AOB + ∠OBA + ∠OAB = 180°
2∠OAB + 130° = 180°(As OA = OB = radius)
∠OAB = 25°
Question 10
1 / -0

In the figure given below, if OP || RS, ∠OPQ = 110° and ∠QRS = 130°, then find the measure of ∠PQR.

A
40°

B
50°

C
60°

D
70°

Solution

Now, ∠RQT = 180° - 130°= 50°
∠PQT = 110° (alternate interior angles)
∠PQR = ∠PQT - ∠RQT = 110°- 50°= 60°
Question 11
1 / -0

If the bisectors of ∠A and ∠B of a quadrilateral ABCD intersect each other at P, that of ∠B and ∠C at Q, that of ∠C and ∠D at R and that of ∠D and ∠A at S, then PQRS is a

A
rectangle

B
rhombus

C
parallelogram

D
quadrilateral whose opposite angles are supplementary

Solution

Hence we can say that the quadrilateral PQRS is a cyclic quadrilteral.
Hence in general, angle bisectors in a quadrilateral form another quadrilateral which is cyclic.
Question 12
1 / -0

In the figure given below, ABCD is a trapezium with parallel sides AB = a cm and DC = b cm. E and F are the mid-points of the non-parallel sides. The ratio of ar(ABFE) and ar(EFCD) is

A
a : b

B
(3a + b) : (a + 3b)

C
(a + 3b) : (3a + b)

D
(2a + b) : (3a + b)

Solution

Suppose AB is the base and h is the perpendicular distance between AB and CD.

EF || AB and EF lies half way between AB and CD.
Therefore, the perpendicular distances between AB and EF and between DF and CD are (1/2)h each.
The length of EF lies half way between that of AB and CD.

Therefore, the ratio of areas of ABFE and EFCD is (3a + b) : (a + 3b).
Question 13
1 / -0

In the figure given below, ∠AOB = 90° and ∠ABC = 30°. What is the measure of ∠CAO?

A
30°

B
45°

C
90°

D
60°

Solution
Question 14
1 / -0

A line passes through the point of intersection of the lines 3x + y + 1 = 0 and 2x - y + 3 = 0 and makes equal positive intercepts with axes. Then, equation of the line is

A
5x + 5y - 3 = 0

B
x + 5y - 3 = 0

C
5x - y - 3 = 0

D
5x + 5y + 3 = 0

Solution

Lines make equal intercepts with axes.
Then, suppose equation of the line is:
x + y + a = 0 ... (1)
Question 15
1 / -0

Tickets numbered from 1 to 20 are mixed and then a ticket is drawn at random. What is the probability that the drawn ticket has a number which is a multiple of 3 or 7?

A
2/5

B
13/20

C
7/20

D
3/5

Solution

Favourable cases = 3, 6, 9, 12, 15, 18, 7, 14
Probability = 8/20 = 2/5