CUET 2022 General Test inactie questions and solutions

1. CUET 2022 General Test inactie | Percentage, Profit & Loss

A shopkeeper bought toffees at a rate of 10 for Rs. 15 and sold them at a rate of 16 for Rs. 40. Find his profit percentage?

A.
65.05%
B.
33.33%
C.
50.55%
D.
66.67%

Answer: Option D

Explanation :

CP of 1 toffee = 15/10 = Rs. 1.5

SP if 1 toffee = 40/16 = Rs. 2.5

∴ Profit % = $\frac{2.5 - 1.5}{1.5}$ × 100 = 66.67%

Hence, option (d).

2. CUET 2022 General Test inactie | Geometry, Mensuration & Trigonometry

The angle of depression of the boat from the most head of 180 m high plane is 60°. How far is the boat from the plane?

A.
360 m
B.
60√3 m
C.
180√3 m
D.
180 m

Answer: Option B

Explanation :

In ∆ABC,
Tan60° = $\frac{A B}{B C}$

⇒ √3 = $\frac{A B}{B C}$ = $\frac{180}{B C}$

⇒ BC = $\frac{180}{\sqrt{3}}$ = 60√3

Hence, option (b).

3. CUET 2022 General Test inactie | Numbers

Find the value of the following expression:

$\frac{4 \frac{1}{3} + 3 \frac{1}{3} \times 1 \frac{4}{5} \div 3 \frac{3}{4} \times (6 \frac{1}{4} o f 1 \frac{1}{15})}{\frac{2}{3} \div \frac{5}{6} \times \frac{2}{3}}$

A.
$28 \frac{1}{8}$
B.

18
C.
$289 \frac{3}{8}$
D.
$12 \frac{1}{2}$

Answer: Option A

Explanation :

Given, $\frac{4 \frac{1}{3} + 3 \frac{1}{3} \times 1 \frac{4}{5} \div 3 \frac{3}{4} \times (6 \frac{1}{4} o f 1 \frac{1}{15})}{\frac{2}{3} \div \frac{5}{6} \times \frac{2}{3}}$

= $\frac{\frac{13}{3} + \frac{10}{3} \times \frac{9}{5} \times \frac{4}{15} \times (\frac{25}{4} \times \frac{16}{15})}{\frac{2}{3} \times \frac{6}{5} \times \frac{2}{3}}$

= $\frac{\frac{13}{3} + \frac{8}{5} \times (\frac{20}{3})}{\frac{8}{15}}$

= $\frac{\frac{13}{3} + \frac{32}{3}}{\frac{8}{15}}$

= $15 \times \frac{15}{8}$ = $\frac{225}{8}$

= $28 \frac{1}{8}$

Hence, option (a).

4. CUET 2022 General Test inactie | Numbers

Find the smallest number which should be added to the smallest number divisible by 6, 9 and 15 to make is a perfect square.

A.
10
B.
9
C.
19
D.
21

5. CUET 2022 General Test inactie | Geometry, Mensuration & Trigonometry

The radii of two concentric circles with center O are 26 cm and 16 cm. Chord AB of the larger circle is tangent to the smaller circle at C and AD is a diameter. What is the length of CD?

A.
42 cm
B.
36 cm
C.
35 cm
D.
38 cm

Answer: Option D

Explanation :

In right ∆AOC,
AC = $\sqrt{O A^{2} - O C^{2}}$ = $\sqrt{26^{2} - 16^{2}}$ = $\sqrt{420}$ = 2 $\sqrt{105}$ .

⇒ AB = 4√105

Now, since AD is the diameter, hence ∠ABD = 90° [Angle subtended by diameter on circle is always right angle.]

∴ In right ∆ABD
AD² = AB² + BD²
⇒ 52² = (4√105)² + BD²
⇒ BD² = 2704 – 1680 = 1024
⇒ BD = 32.

Now in ∆CBD
⇒ CD² = CB² + BD²
⇒ CD² = 420 + 1024 = 1444
⇒ CD = 38

Hence, option (d).

6. CUET 2022 General Test inactie | Numbers

Find the sum of the greatest and the smallest number which may replace k in the number 3281k6 to make the number divisible by 6.

A.
9
B.
8
C.
5
D.
4

7. CUET 2022 General Test inactie | Percentage, Profit & Loss

A household appliances company offers two successive discounts of 20% and 35% on the sale of a food processor. What is the final sale price (in Rs. to the neared rupee) of a food processor costing Rs. 4580?

A.
2519
B.
2977
C.
2382
D.
3664

8. CUET 2022 General Test inactie | Numbers

If 5x - $\frac{1}{4 x}$ = 6, x > 0, then find the value of 25x² - $\frac{1}{16 x^{2}}$ ?

A.
6√41
B.
36
C.
√246
D.
6√31

Answer: Option A

Explanation :

Given, 5x - $\frac{1}{4 x}$ = 6 ...(1)

Squaring both sides,

${(5 x - \frac{1}{4 x})}^{2}$ = 36

⇒ 25x² + $\frac{1}{16 x^{2}}$ - 2 × 5x × $\frac{1}{4 x}$ = 36

⇒ 25x² + $\frac{1}{16 x^{2}}$ + 2 × 5x × $\frac{1}{4 x}$ - 2 × 2 × 5x × $\frac{1}{4 x}$ = 36

⇒ ${(5 x + \frac{1}{4 x})}^{2}$ - 5 = 36

⇒ ${(5 x + \frac{1}{4 x})}^{2}$ = 41

⇒ 5x + $\frac{1}{4 x}$ = √41 ...(2)

From (1) × (2)

⇒ (5x)² - ${(\frac{1}{4 x})}^{2}$ = 6√41

Hence, option (a).

9. CUET 2022 General Test inactie | Geometry, Mensuration & Trigonometry

In triangle ABC, the bisector of angle BAC meets BC at point D in such a way that AB = 10 cm, AC = 15 cm and BD = 6 cm. Find the length of BC (in cm.)

A.
17
B.
11
C.
15
D.
9

10. CUET 2022 General Test inactie | Time and Work

A and B working alone can complete a work in 8 days and 12 days respectively. They started working together, but A left 2 days before completion of the work. In how many days was the work completed

A.
6
B.
5
C.
8
D.
10

11. CUET 2022 General Test inactie | Ratio, Proportion and Partnership

Person A started a business by investing Rs. 65000. After a few months, B joined him by investing Rs. 50,000. Three months after the joining of B, C joined the two with an investment of Rs. 55,000. At the end of the year, A got 50% of the profit as his share. For how many months did A alone finance the business?

A.
2
B.
3
C.
5
D.
4

12. CUET 2022 General Test inactie | Data Interpretation

The following bar graph shows receipts and expenditure by a business firm over 5 years.

Gain = Receipts – Expenditure

In which year did the company gain the minimum amount?

A.
2016
B.
2017
C.
2019
D.
2018

13. CUET 2022 General Test inactie | Ratio, Proportion and Partnership

Three positive numbers are in the ratio 2 : 3 : 4. The sum of their squares is 2349. The average of the first two numbers is:

A.
36
B.
27.5
C.
18
D.
22.5

14. CUET 2022 General Test inactie | Geometry, Mensuration & Trigonometry

The sides of a triangular field are 360 m, 480 m and 600 m. Its area is equal to the area of a square field. What is the side (in m) of the square field?

A.
120√6
B.
160√6
C.
160√3
D.
120√3

Answer: Option A

Explanation :

The ratio of sides of the triangle is 360 : 480 : 600 = 3 : 4 : 5.

Hence, it is a right triangle.

⇒ Area of the triangle = 1/2 × 360 × 480

Area of a square of side a = a² = 1/2 × 360 × 480

⇒ a² = 360 × 240

⇒ a = $\sqrt{360 \times 240}$

⇒ a = $\sqrt{3600 \times 4 \times 6}$

⇒ a = 120√6

Hence, option (a).

15. CUET 2022 General Test inactie | Percentage, Profit & Loss

A person’s salary was decreased by 50% and subsequently increased by 50%. By what percent does his salary increase or decrease?

A.
Decrease 18%
B.
Increase 15%
C.
Increase 20%
D.
Decrease 25%

Answer: Option D

Explanation :

Net change = 50 – 50 + $\frac{50 \times - 50}{100}$ = -25%

Hence, option (d).

16. CUET 2022 General Test inactie | Geometry, Mensuration & Trigonometry

In a ∆ABC, D, E and F are the mid-points of side BC, CA and AB respectively. If BC = 25.6 cm, CA = 18.8 cm and AB = 20.4 cm, what is the perimeter (in cm) of the ∆DEF?

A.
36.8
B.
30.6
C.
32.4
D.
34.4

17. CUET 2022 General Test inactie | Numbers

Find the value of the following expression: $\frac{{(7.03)}^{3} - 0.027}{{(7.03)}^{2} + 2.109 + {(0.3)}^{2}}$ ?

A.
7.06
B.
7
C.
7.33
D.
6.73

Answer: Option D

Explanation :

0.027 = (0.3)³

⇒ $\frac{{(7.03)}^{3} - 0.027}{{(7.03)}^{2} + 2.109 + {(0.3)}^{2}}$ = $\frac{{(7.03)}^{3} - {(0.3)}^{3}}{{(7.03)}^{2} + 7.03 \times 0.3 + {(0.3)}^{2}}$

We know, a³ – b³ = (a - b)(a² – ab + b²)

⇒ $\frac{{(7.03)}^{3} - 0.027}{{(7.03)}^{2} + 2.109 + {(0.3)}^{2}}$ = $\frac{(7.03 - 0.3) ({(7.03)}^{2} + 7.03 \times 0.3 + {(0.3)}^{2})}{{(7.03)}^{2} + 7.03 \times 0.3 + {(0.3)}^{2}}$ = 7.03 – 0.3 = 6.73

Hence, option (d).

18. CUET 2022 General Test inactie | Simple and Compound Interest

Anil lent a sum of Rs. 5000 on simple interest for 10 years in such a way that the rate of interest is 6% p.a. for the first 2 years, 8% p.a. for the next 2 years and 10% p.a. beyond 4 years. How much interest (in Rs.) will he earn at the end of 10 years.

A.
5000
B.
4400
C.
4200
D.
3500

Answer: Option B

Explanation :

6% for 2 years:
Interest accumulated = $\frac{5000 \times 6 \times 2}{100}$ = Rs. 600

8% for 2 years:
Interest accumulated = $\frac{5000 \times 8 \times 2}{100}$ = Rs. 800

10% for 6 years:
Interest accumulated = $\frac{5000 \times 10 \times 6}{100}$ = Rs. 3000

Total interest accumulated = 600 + 800 + 3000 = Rs. 4400

Hence, option (b).

19. CUET 2022 General Test inactie | Data Interpretation

The breakup of the total number of employees of a company working in different offices (A to E), in degree, is given in the pie-chart.

If 40% of the number of employees in office A are shifted equally to office B and E, then what will be the sum of the number of employees in B and C?

A.
648
B.
735
C.
545
D.
72

Answer: Option A

Explanation :

40% of 126° = 50.4°

Degree measure of B = 18 + 25.2 = 43.2°
Degree measure of C = 54°

Required number of employees = $\frac{43.2 + 54}{360}$ × 2400 = 648

Hence, option (a).

20. CUET 2022 General Test inactie | Geometry, Mensuration & Trigonometry

O is the center of a circle of radius 10 cm. P is a point outside the circle and PQ is a tangent to the circle. What is the length (in cm) of PQ if the OP is 26 cm?

A.
2√194
B.
20
C.
25
D.
24

21. CUET 2022 General Test inactie | Geometry, Mensuration & Trigonometry

If A = 30°, what is the value of: $\frac{8 s i n A + 11 c o s e c A - \cot^{2} A}{10 c o s 2 A}$

A.
$5 \frac{1}{4}$
B.
$4 \frac{3}{5}$
C.
$4 \frac{2}{5}$
D.
$3 \frac{4}{5}$

Answer: Option B

Explanation :

Given, $\frac{8 \sin 30 ° ° + 11 c o s e c 30 ° - \cot^{2} 30 °}{10 \cos 60 °}$

= $\frac{8 \times \frac{1}{2} + 11 \times 2 - {(\sqrt{3})}^{2}}{10 \times \frac{1}{2}}$ = $\frac{4 + 22 - 3}{5}$ = $\frac{23}{5}$ = $4 \frac{3}{5}$

Hence, option (b).

22. CUET 2022 General Test inactie | Time, Speed and Distance

The distance between two stations A and B is 200 kms. A train runs from A to B at a speed of 75 kmph, while another train runs from B to A at a speed of 85 kmph. What will be the distance between the two trains (in kms) 3 minutes before they meet?

A.
5
B.
8
C.
10
D.
6

23. CUET 2022 General Test inactie | Data Interpretation

The following histogram show the marks scored by 40 students in a test of 30 marks. A student has to score a minimum of 10 marks to pass the test. What is the percentage of students who passed the test?

A.
75%
B.
30%
C.
72%
D.
66.66%

Answer: Option A

Explanation :

% of students who passed the test = $\frac{7 + 8 + 10 + 5}{2 + 8 + 7 + 8 + 10 + 5}$ × 100 = 75%

Hence, option (a).

24. CUET 2022 General Test inactie | Data Interpretation

Performance of 1800 students in grades has been shown in the following pie-chart.

The number of students getting grade B is what percentage of the number of students getting grade A?

A.
97%
B.
90%
C.
95%
D.
85%

25. CUET 2022 General Test inactie | Geometry, Mensuration & Trigonometry

If (2cosA + 1)(2cosA – 1) = 0, 0° < A ≤ 90°, then find the value of A.

A.
90°
B.
45°
C.
30°
D.
60°

Answer: Option C

Explanation :

(2cosA + 1)(2cosA – 1) = 0

⇒ 4cos2A - 1 = 0

⇒ 4cos2A – (cos2A + sin2A) = 0

⇒ 3cos2A – sin2A = 0

⇒ 3cos2A = sin2A

⇒ $\frac{\sin^{2} A}{\cos^{2} A}$ =3

⇒ tan²A = 3

⇒ tanA = √3

∴ A = 60°

Hence, option (c).

CUET 2022 General Test inactie

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