Q1.
If x = 10³x 0.0099 and y = 10^-2x 110 , find the value of (y/x)^1/2

1
2
3
1/3

Solution:

1/3

Q2.
Find the value of x,

2log_x 5 - log_x 5 + 3log_x (1/5) = 2

1/5
1
5
1/4

Solution:

1/5

Q3.
Find the value of p, if the quadratic equation has real and equal roots,

px(x - 2) = -6

5
6
7
8

Solution:

6

Q4.
If one root of a quadratic equation is 2 + \( { \sqrt{3}}\)

find the product of roots

2
4
1
3

Solution:

1

Q5.
On solving the inequalities x + 4y \(\le\) 12; 6x + y \(\le\) 18; 2x + y \(\le\) 10; x \(\ge\) 0; y \(\ge\) 0 we get which of the following solutions ?

(18, 0), (0, 12), (4,2), (0, 0), (7, 6)
(0, 18), (8, 0), (4,2), (0, 0), (7, 6)
(0, 18), (12, 0), (4,2), \(({84 \over 23},{54 \over 23})\), (7, 6)
None of these

Solution:

NA

Q6.
An automobile company manufactures two cars A and B . Model A requires 15 man-hours for assembly; 5 man-hours for painting and finishing and 1 man-hours for checking and testing . Model B requires 6 man-hours for assembly; 4 man-hours for painting and finishing and 2 man-hours for checking and testing. There are 400 man-hours for assembly shop; 150 man-hours for painting and finishing shop and 40 man-hours are available in checking and testing division . Express this using linear inequalities.

\(\begin{cases} 15x + 6y \le 400\\5x + 4y \le 150\\ x + 2y \le 40\\ x \ge0; y\ge0 \end{cases}\)
\(\begin{cases} 15x + 6y \ge 400\\5x + 4y \ge 150\\ x + 2y \ge 40\\ x \ge0; y\ge0 \end{cases}\)
\(\begin{cases} 15x + 6y \le 400\\5x + 4y \le 150\\ x + 2y \ge 40\\ x \ge0; y\ge0 \end{cases}\)
None of these

Solution:

NA

Q7.
The present value of an annuity of Rs. 3,000 for 15 years at 4.5%p.a. C.I. is :

[Given that (1.045)¹⁵ = 1.935282]

Rs. 23,809.67
Rs. 32,218.67
Rs. 32,908.67
None of these

Solution:

NA

Q8.
A company establishes a sinking fund to provide for the payment of Rs. 2,00,000 debt maturing in 20 years . Contributions to the fund are to be made are to be made at the end of every year. Find the amount of each annual deposit if interest is 5% per annum :

Rs. 6,142
Rs. 6,049
Rs. 6,052
Rs. 6,159

Solution:

NA

Q9.
A person deposited Rs 5,000 in a bank. The deposit was left to accumulate at 6% compounded quarterly for the first five years and at 8% compounded semi-annually for the next eight years . The compound amount at the end of 13 years is :

Rs 12621.50
Rs 12613.10
Rs 13613.10
None

Solution:

NA

Q10.
On what sum difference between compound interest and simple interest for two years at 7% p.a. interest is Rs. 29.4

Rs 5000
Rs 5500
Rs 6000
Rs 6500

Solution:

NA

Q11.
How many numbers can be formed from the digits 1, 2, 3, 9 if the repetition of digits is not allowed ?

60
62
55
64

Solution:

NA

Q12.
Find the total of natural numbers that can be formed by using the digits 0, 1, 2, 3, 4 and 5, repetition of digits is not allowed .

1630
1603
1450
1600

Solution:

NA

Q13.
Find n if :

^{2n + 1}P_{n - 1}: ^{2n - 1}P_n = 3 : 5

2
5
4
0

Solution:

NA

Q14.
Out of 6 boys and 4 girls , a committee of 5 is to be formed . In how many ways can this be done if atleast 2 girls are included ?

186
180
170
168

Solution:

NA

Q15.
If the sum of 'n' terms of an Arithmetic Progression (A.P) is 3x² + 5x and its m^th term is 164, then the value of m is :

27
28
24
26

Solution:

NA

Q16.
A G.P. (Geometric Progression) consists of 2n terms . If the sum of the terms occupying the odd places is S₁ and that of terms in the even places is S₂, the common ratio of the progression is :

n
2S₁
S₂/S₁
S₁/S₂

Solution:

NA

Q17.
If \( {1 \over b + c}, {1 \over c + a}, {1 \over a + b}\) are in arithmetic progression then a², b², c², are in

Arithmetic Progression
Geometric Progression
Both in arithmetic and geometric progression
None of these

Solution:

NA

Q18.
The sum of first 7 terms of an A.P. is 10 and that of next 7 terms is 27 . The common difference in the A.P. is

7
1/7
-7
-1/7

Solution:

NA

Q19.
If n^thterms of a G.P. is 2ⁿ; the sum of 6 terms is

128
126
130
120

Solution:

NA

Q20.
If n(A) = 8, n( A x B ) = 56, n (B) = ?

7
8
9
10

Solution:

7

Q21.
The number of subsets of { p, q, {p, q}} are----------

4
8
2
9

Solution:

8

Q22.
There are 40 students, 30 of them passed on english, 25 of them passed in maths and 15 of them passed in both. Assuming that every student has passed at least in one subject. How many students passed in english only but not in maths.

15
12
22
9

Solution:

15

Q23.
Which statement is wrong.

(1). Telephonic Interview method is the quickest methos to collect the primary data.

(2). A table has five parts.

(3). The column headings of a table are known as caption.

(4). Ogive curve gives us mode.

1
2
3
4

Solution:

4

Q24.
Which statement is wrong ?

(1). Data collected on education from the census reports are secondary data.

(2). Ratio chart uses logarithms of variable.

(3). There are three types of classification of data.

(4). Pie-chart is a two dimensional diagram.

1
2
3
4

Solution:

3

Q25.
If x and y are related as 3x - 4y = 30, and the mean deviation of x is 16, then find the M.D. of y.

11
14
12
13

Solution:

12

Q26.
Quartiles can be determined graphically using

cumulative frequency curve
histogram
pie-chart
frequency curve

Solution:

cumulative frequency curve

Q27.
In the particular bivariate data the following results were obtained for two variables x and y.

Mean of x = 53.2, mean of y = 27.9, b_yx= - 1.5, b_xy= - 0.2, find y if x = 60.

17.8
16.4
32
12

Solution:

17.8

Q28.
If r_xy= 0.8, and U = (x - 5)/6, and V = ( y + 5)/(-3), then find the value of r_uv

0.8
-0.8
0.6
-0.3

Solution:

-0.8

Q29.
The two regression equations are :

2x + 3y + 18 = 0 and x + 2y - 25 = 0, find the value of y if x = 15.

2
3
5
4

Solution:

5

Q30.
An unbiased die is thrown for three times, find the probability that digit 2 appears exactly two times.

5/72
1/35
1/18
0.56

Solution:

5/72

Q31.
If P(A) = 1/3, P(B) = 3/4 and P(AUB) = 11/12, find the probability of P(A'/B')

1/2
1/4
2/5
1/3

Solution:

1/3

Q32.
A dice is thrown once. Find the expected value of the number on the dice?

3
4
3.5
4.5

Solution:

3.5

Q33.
If X ~ B ( 9, 1/3), where X is a random variable. Find the value of E(X) and V(X)

3, 2
2, 3
4, 3
9, 1/3

Solution:

3, 2

Q34.
If x is a random varable in a poisson distribution whose variance is 2. Find the probability of P( x = atleast 2).( where e^-2 = 0.13534)

0.42
0.87
0.59
0.45

Solution:

0.59

Q35.
In normal distribution if lower quartile is 13.25 and mean deviation about mode is 8. Find the value of mode?

10
20
30
40

Solution:

20

Q36.
If TODAY is coded as UQECZ, then what will be the code for BEFORE ?

CCBHIG
HIJQSG
CGGQSG
CPSSF

Solution:

NA

Q37.
LJHF : USQO :: QOMK : ?

QPSR
PNMK
VTRP
YXWU

Solution:

NA

Q38.
9, 15, 23, 33, _ , ?

44
36
38
45

Solution:

NA

Q39.
4, 7, 14, 24, 41, _ ?

71
68
72
51

Solution:

NA

Q40.
Deepa moved a distance of 75 m toward the north. She then turned to the left and walking for about 25 m, turned left again and walked 80 m . Lastly , she turned to the right at an angle of 45^o . In which direction was she moving lastly ?

North - east
South - West
East
South

Solution:

NA

Q1. If x = 103 x 0.0099 and y = 10-2 x 110 , find the value of (y/x)1/2

Q2. Find the value of x, 2logx 5 - logx 5 + 3logx (1/5) = 2

Q3. Find the value of p, if the quadratic equation has real and equal roots, px(x - 2) = -6

Q4. If one root of a quadratic equation is 2 + \( { \sqrt{3}}\) find the product of roots

Q5. On solving the inequalities x + 4y \(\le\) 12; 6x + y \(\le\) 18; 2x + y \(\le\) 10; x \(\ge\) 0; y \(\ge\) 0 we get which of the following solutions ?

Q7. The present value of an annuity of Rs. 3,000 for 15 years at 4.5%p.a. C.I. is : [Given that (1.045)15 = 1.935282]

Q8. A company establishes a sinking fund to provide for the payment of Rs. 2,00,000 debt maturing in 20 years . Contributions to the fund are to be made are to be made at the end of every year. Find the amount of each annual deposit if interest is 5% per annum :

Q9. A person deposited Rs 5,000 in a bank. The deposit was left to accumulate at 6% compounded quarterly for the first five years and at 8% compounded semi-annually for the next eight years . The compound amount at the end of 13 years is :

Q10. On what sum difference between compound interest and simple interest for two years at 7% p.a. interest is Rs. 29.4

Q11. How many numbers can be formed from the digits 1, 2, 3, 9 if the repetition of digits is not allowed ?

Q12. Find the total of natural numbers that can be formed by using the digits 0, 1, 2, 3, 4 and 5, repetition of digits is not allowed .

Q13. Find n if : 2n + 1Pn - 1 : 2n - 1Pn = 3 : 5

Q14. Out of 6 boys and 4 girls , a committee of 5 is to be formed . In how many ways can this be done if atleast 2 girls are included ?

Q15. If the sum of 'n' terms of an Arithmetic Progression (A.P) is 3x2 + 5x and its mth term is 164, then the value of m is :

Q16. A G.P. (Geometric Progression) consists of 2n terms . If the sum of the terms occupying the odd places is S1 and that of terms in the even places is S2, the common ratio of the progression is :

Q17. If \( {1 \over b + c}, {1 \over c + a}, {1 \over a + b}\) are in arithmetic progression then a2, b2, c2, are in

Q18. The sum of first 7 terms of an A.P. is 10 and that of next 7 terms is 27 . The common difference in the A.P. is

Q19. If nth terms of a G.P. is 2n; the sum of 6 terms is

Q20. If n(A) = 8, n( A x B ) = 56, n (B) = ?

Q21. The number of subsets of { p, q, {p, q}} are----------

Q22. There are 40 students, 30 of them passed on english, 25 of them passed in maths and 15 of them passed in both. Assuming that every student has passed at least in one subject. How many students passed in english only but not in maths.

Q23. Which statement is wrong. (1). Telephonic Interview method is the quickest methos to collect the primary data. (2). A table has five parts. (3). The column headings of a table are known as caption. (4). Ogive curve gives us mode.

Q24. Which statement is wrong ? (1). Data collected on education from the census reports are secondary data. (2). Ratio chart uses logarithms of variable. (3). There are three types of classification of data. (4). Pie-chart is a two dimensional diagram.

Q25. If x and y are related as 3x - 4y = 30, and the mean deviation of x is 16, then find the M.D. of y.

Q26. Quartiles can be determined graphically using

Q27. In the particular bivariate data the following results were obtained for two variables x and y. Mean of x = 53.2, mean of y = 27.9, byx = - 1.5, bxy = - 0.2, find y if x = 60.

Q28. If rxy = 0.8, and U = (x - 5)/6, and V = ( y + 5)/(-3), then find the value of ruv

Q29. The two regression equations are : 2x + 3y + 18 = 0 and x + 2y - 25 = 0, find the value of y if x = 15.

Q30. An unbiased die is thrown for three times, find the probability that digit 2 appears exactly two times.

Q31. If P(A) = 1/3, P(B) = 3/4 and P(AUB) = 11/12, find the probability of P(A'/B')

Q32. A dice is thrown once. Find the expected value of the number on the dice?

Q33. If X ~ B ( 9, 1/3), where X is a random variable. Find the value of E(X) and V(X)

Q34. If x is a random varable in a poisson distribution whose variance is 2. Find the probability of P( x = atleast 2).( where e-2 = 0.13534)

Q35. In normal distribution if lower quartile is 13.25 and mean deviation about mode is 8. Find the value of mode?

Q36. If TODAY is coded as UQECZ, then what will be the code for BEFORE ?

Q37. LJHF : USQO :: QOMK : ?

Q38. 9, 15, 23, 33, _ , ?

Q39. 4, 7, 14, 24, 41, _ ?

Q40. Deepa moved a distance of 75 m toward the north. She then turned to the left and walking for about 25 m, turned left again and walked 80 m . Lastly , she turned to the right at an angle of 45o . In which direction was she moving lastly ?

Q1.
If x = 10³x 0.0099 and y = 10^-2x 110 , find the value of (y/x)^1/2

Q2.
Find the value of x,

2log_x 5 - log_x 5 + 3log_x (1/5) = 2

Q3.
Find the value of p, if the quadratic equation has real and equal roots,

px(x - 2) = -6

Q4.
If one root of a quadratic equation is 2 + \( { \sqrt{3}}\)

find the product of roots

Q5.
On solving the inequalities x + 4y \(\le\) 12; 6x + y \(\le\) 18; 2x + y \(\le\) 10; x \(\ge\) 0; y \(\ge\) 0 we get which of the following solutions ?

Q7.
The present value of an annuity of Rs. 3,000 for 15 years at 4.5%p.a. C.I. is :

[Given that (1.045)¹⁵ = 1.935282]

Q8.
A company establishes a sinking fund to provide for the payment of Rs. 2,00,000 debt maturing in 20 years . Contributions to the fund are to be made are to be made at the end of every year. Find the amount of each annual deposit if interest is 5% per annum :

Q9.
A person deposited Rs 5,000 in a bank. The deposit was left to accumulate at 6% compounded quarterly for the first five years and at 8% compounded semi-annually for the next eight years . The compound amount at the end of 13 years is :

Q10.
On what sum difference between compound interest and simple interest for two years at 7% p.a. interest is Rs. 29.4

Q11.
How many numbers can be formed from the digits 1, 2, 3, 9 if the repetition of digits is not allowed ?

Q12.
Find the total of natural numbers that can be formed by using the digits 0, 1, 2, 3, 4 and 5, repetition of digits is not allowed .

Q13.
Find n if :

^{2n + 1}P_{n - 1}: ^{2n - 1}P_n = 3 : 5

Q14.
Out of 6 boys and 4 girls , a committee of 5 is to be formed . In how many ways can this be done if atleast 2 girls are included ?

Q15.
If the sum of 'n' terms of an Arithmetic Progression (A.P) is 3x² + 5x and its m^th term is 164, then the value of m is :

Q16.
A G.P. (Geometric Progression) consists of 2n terms . If the sum of the terms occupying the odd places is S₁ and that of terms in the even places is S₂, the common ratio of the progression is :

Q17.
If \( {1 \over b + c}, {1 \over c + a}, {1 \over a + b}\) are in arithmetic progression then a², b², c², are in

Q18.
The sum of first 7 terms of an A.P. is 10 and that of next 7 terms is 27 . The common difference in the A.P. is

Q19.
If n^thterms of a G.P. is 2ⁿ; the sum of 6 terms is

Q20.
If n(A) = 8, n( A x B ) = 56, n (B) = ?

Q21.
The number of subsets of { p, q, {p, q}} are----------

Q22.
There are 40 students, 30 of them passed on english, 25 of them passed in maths and 15 of them passed in both. Assuming that every student has passed at least in one subject. How many students passed in english only but not in maths.

Q23.
Which statement is wrong.

(1). Telephonic Interview method is the quickest methos to collect the primary data.

(2). A table has five parts.

(3). The column headings of a table are known as caption.

(4). Ogive curve gives us mode.

Q24.
Which statement is wrong ?

(1). Data collected on education from the census reports are secondary data.

(2). Ratio chart uses logarithms of variable.

(3). There are three types of classification of data.

(4). Pie-chart is a two dimensional diagram.

Q25.
If x and y are related as 3x - 4y = 30, and the mean deviation of x is 16, then find the M.D. of y.

Q26.
Quartiles can be determined graphically using

Q27.
In the particular bivariate data the following results were obtained for two variables x and y.

Mean of x = 53.2, mean of y = 27.9, b_yx= - 1.5, b_xy= - 0.2, find y if x = 60.

Q28.
If r_xy= 0.8, and U = (x - 5)/6, and V = ( y + 5)/(-3), then find the value of r_uv

Q29.
The two regression equations are :

2x + 3y + 18 = 0 and x + 2y - 25 = 0, find the value of y if x = 15.

Q30.
An unbiased die is thrown for three times, find the probability that digit 2 appears exactly two times.

Q31.
If P(A) = 1/3, P(B) = 3/4 and P(AUB) = 11/12, find the probability of P(A'/B')

Q32.
A dice is thrown once. Find the expected value of the number on the dice?

Q33.
If X ~ B ( 9, 1/3), where X is a random variable. Find the value of E(X) and V(X)

Q34.
If x is a random varable in a poisson distribution whose variance is 2. Find the probability of P( x = atleast 2).( where e^-2 = 0.13534)

Q35.
In normal distribution if lower quartile is 13.25 and mean deviation about mode is 8. Find the value of mode?

Q36.
If TODAY is coded as UQECZ, then what will be the code for BEFORE ?

Q37.
LJHF : USQO :: QOMK : ?

Q38.
9, 15, 23, 33, _ , ?

Q39.
4, 7, 14, 24, 41, _ ?

Q40.
Deepa moved a distance of 75 m toward the north. She then turned to the left and walking for about 25 m, turned left again and walked 80 m . Lastly , she turned to the right at an angle of 45^o . In which direction was she moving lastly ?