a) 1
b) -1
c) ±1
d) 0
Given: sin θ + cos θ = 1
Squaring both sides, we get:
⇒ sin^2 θ + cos^2 θ + 2 sin θ cos θ = 1
⇒ 1 + sin 2θ = 1
⇒ sin 2θ = 0
Using sin^2 θ + cos^2 θ = 1, we can say:
sin^2 2θ + cos^2 2θ = 1
⇒ 0 + cos^2 2θ = 1
⇒ cos 2θ = ±1.
2. If a product is sold at a 10% discount, the selling price is Rs.
72.
a) Rs. 50
b) Rs. 64
c) Rs. 60
d) Rs. 54
Suppose marked price = Rs. x
S.P = x × (100 – 10)/100
⇒ 0.9x = 72
⇒ x = Rs. 80
On discount of 25%:
S.P = 80 × (100 – 25)/100
⇒ 80 × 0.75
⇒ Rs. 60
∴ If the discount rate is 25% then the selling price of the product is Rs.
60
3. A can complete a work in 50 days, B can complete the same work in half time of A, C can complete the same work in double the time of A, then find out the number of days taken B and C to complete the work.
a) 10
b) 15
c) 20
d) 25
B's one day work = 1/25
C's one day work = 1/100
Total work of B and C for one day = (1/25) + (1/100)
⇒ = 1/20
Total number of days for B and C = 20
4. A man goes with the average speed of 18 km/hr from Indore to Bhopal and return back to Indore with the speed of 22 km/hr.
Find the average speed of man?
a) 20.8 km/hr
b) 17.8 km/hr
c) 18.8 km/hr
d) 19.8 km/hr
Average speed of man when he go from Indore to Bhopal is 18 km/hr and average speed of man when he go from Bhopal to Indore is 22 km/hr
∴ Average speed = (2 × 18 × 22/(40)) = 19.8 km/hr
∴ The average speed of man is 19.8 km/hr
5. The ratio of two numbers is 12 : 5.
If each number is increased by 6 then their ratio becomes 12 : 6, then find the sum of the numbers is?
a) 34
b) 51
c) 68
d) 85
Let number is 12x and 5x
According to question,
(12x + 6) ÷ (5x + 6) = 12 ÷ 6
⇒ 72x + 36 = 60x + 72
⇒ 12x = 36
So, x = 3
Then numbers 12 × 3 = 36 and 5 × 3 = 15
Sum of the number = 36 + 15 = 51
6. The salary of A is 50% more than the salary of B.
If A got a 50% rise in his salary and B got a 25% rise in his salary, then the percentage increase in their combined salaries will be:
a) 50%
b) 20%
c) 30%
d) 40%
Let the B's salary is Rs. x.
Then, A's salary = x × {(100 + 50 )/100}
⇒ x × (150/100)
⇒ 1.5x
A's new salary = 1.5x × {(100 + 50)/100}
⇒ 1.5x × {150/100}
⇒ 2.25x
B's new salary = x × {(100 + 25)/100}
⇒ x × {125/100}
⇒ 1.25x
Sum of A's old salary and B's old salary = x + 1.5x
⇒ 2.5x
Sum of A's new salary and B's new salary = 2.25x + 1.25x
⇒
3.5xPercentage increase in combined salary of A and B = {(3.5x - 2.5x)/2.5x} × 100
⇒ {1/2.5} × 100
⇒ 40%
7. The floor of a room is to be decorated with tiles of length 60 cm and width 40 cm.
If dimension of floor of room is 72 m × 48 m then find the number of required tiles.
a) 16400
b) 14000
c) 14400
d) 14800
Dimension of floor = 72 m × 48 m = 7200 cm × 4800 cm
Let the number of tiles be n.
Now,
Area of total tiles = Area of floor
⇒ n × 60 × 40 = 7200 × 4800
⇒ n = (7200 × 4800)/(60 × 40)
⇒ n = 14400
8. A sum of money amounts to Rs.
4500 in 3 years and Rs.
10000 in 8 years at the same rate of simple interest.
What is the principal?
a) Rs.
1600
b) Rs.
1000
c) Rs.
1200
d) Rs.
1400
S.I. for 5 years = 10000 – 4500 = Rs. 5500
⇒ SI for 1 years = 5500/5 = Rs. 1100
S I for 3 years = 3 × 1100 = Rs. 3300
Principal = 4500 – 3300 = Rs.
1200
9. Evaluate the following:
5 - [96 ÷ 4 of 3 - (16 - 55 ÷ 5)] = ?
a) 2
b) 0
c) 4
d) 1
5 - [96 ÷ 4 of 3 - (16 - 55 ÷ 5)] = ?
⇒ 5 – [96 ÷ 4 of 3 – (16 – 55/5)] = ?
⇒ 5 – [96 ÷ 4 of 3 – (16 – 11)] = ?
⇒ 5 – [96 ÷ 4 of 3 – 5] = ?
⇒ 5 – [96 ÷ 12 – 5] = ?
⇒ 5 – [96/12 – 5] = ?
⇒ 5 – [8 – 5] = ?
⇒ 5 – 3 = ?
⇒ 2 = ?
10. The ratio of the monthly income of X and Y is 5 ∶ 4 and that of their monthly expenditures is 9 ∶ 7.
If the income of Y is equal to the expenditure of X, then what is the ratio of the savings of X and Y?
a) 9 : 8
b) 8 : 9
c) 4 : 3
d) 3 : 4
Let, the income ratio of X and Y is 5a and 4a.
The expenditure ratio of X and Y is 9b and 7b.
⇒ 4a = 9b
⇒ a/b = 9/4
⇒ Saving of X = 5a - 9b
⇒ Saving of Y = 4a - 7b
⇒ Ratio = (5a - 9b)/(4a - 7b)
By dividing b
⇒ Ratio = (45 - 36)/(36 - 28)
⇒ Ratio = 9/8
