Problem 1 :
For every real number x, does x2 - 1
(A) > 0 (B) < 0 (C) = 0
Solution :
x2 - 12
(x - 1)(x + 1)
Since x is real value, we can take all positive and negative values of x.
So, the answer is < 0.
Problem 2 :
If two sides of a triangle are equal, then the angles opposite to them are
(A) Not Equal (B) Equal (C) Supplementary
Solution :
By isosceles triangle theorem,
If two sides of a triangle are equal, then the angles opposite to these sides are equal.
So, the answer is Equal.
Problem 3 :
The sum of the digits of the two digit number is 8. If the digits are reversed the number is increasing by 18. Find the number.
(A) 33 (B) 20 (C) 35
Solution :
Let the two digit number be xy
Sum of two digit numbers,
x + y = 8 ----(1)
Expand form,
xy = 10x + y
yx = 10y + x
Digits are reversed the number is increasing by 18,
10y + x = 10x + y + 18
10y = 10x + y + 18
9y - 9x = 18
y - x = 2 ----(2)
Add (1) and (2), we get
x + y + y - x = 8 + 2
2y = 10
y = 5
By applying y = 5 in equation (1), we get
x + 5 = 8
x = 3
So, the number xy is 35
Problem 4 :
If the slope of the line is not defined, then the line is
(A) Falling line (B) Parallel to x-axis (C) Parallel to y-axis
Solution :
If the Slope of a line is not defined, then the line is parallel to y-axis.
So, the answer is parallel to y-axis.
Problem 5 :
The slope of the line passing through (5, 6) and (15, 9) is
(A) -3/8 (B) 4/9 (C) 3/10
Solution :
Given points, (5, 6) and (15, 9)
Using Two Point form :
Slope = (y2 - y1)/(x2 - x1)
(5, 6) -----> (x1, y1)
(15, 9) -----> (x2, y2)
Slope = (9 - 6)/(15 - 5)
Slope = 3/10
So, the answer is 3/10
Problem 6 :
What is the x-intercept and y-intercept of the line 3x + 4y = 12 ?
(A) (2, 1) (B) (4, 3) (C) (6, 8)
Solution :
Given, 3x + 4y = 12
Finding x-intercept :
When y = 0
3x + 4(0) = 12
3x = 12
x = 4
Finding y-intercept :
When x = 0
3(0) + 4y = 12
4y = 12
x = 3
So, the answer is (4, 3)
Problem 7 :
Find the equation of the line having slope 21 and y-intercept -3.
(A) 2x + y = 0 (B) x + 2y = 0 (C) 21x - y - 3 = 0
Solution :
Using Slope-intercept form :
y = mx + b
Here m = 21 and b = -3
y = 21x - 3
21x - y - 3 = 0
Problem 8 :
If sin θ = 7/25, then the value cot θ is
(A) 10/27 (B) 21/35 (C) 24/7
Solution :
We know that,
sin2θ + cos2θ = 1
We have, sin θ = 7/25
(7/25)2 + cos2θ = 1
49/625 + cos2θ = 1
cos2θ = 1 - 49/625
cos2θ = 576/625
cos θ = 24/25
Now,
cot θ = cos θ/sin θ
= 24/25 × 25/7
= 24/7
So, the answer is 24/7.
Problem 9 :
Find the median of the numbers 23, 25, 29, 30, 39
(A) 29 (B) 20 (C) 31
Solution :
Given data 23, 25, 29, 30, 39 in ascending order.
So, Median = Middle value
= 29
So, the answer is 29
Problem 10 :
Find the compound interest on $64,000 for 1 year at the rate of 10% per year compounded quarterly.
(A) $6644.03 (B) $4921 (C) $421
Solution :
Given,
Principal (p) = $64000
Rate (r) = 10% = 10/4% (for Quarterly)
Time = 1 year = 1 × 4 = 4(for Quarterly)
By using this formula,
Amount = P(1 + R/100)n
= 64000[1 + (10/4 × 1/100)]4
= 64000[1 + 10/400]4
= 64000[410/400]4
= 64000[1.025]4
= 64000[1.1038]
Amount = $70644.03
Compound interest = Amount - Principal
= 70644.03 - 64000
= $6644.03
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