Free Printable Exam_Focus_Math

1.

If a, b, c are in AP then

a)

(a) b = a + c

b)

(b) 2b = a + c

c)

(c) b² = a + c

d)

(d) 2b² = a + c

2.

Three numbers form an increasing GP. If the middle term is doubled, then the new numbers are in Ap. The common ratio of GP is

a)

(a) 2 + √3

b)

(b) 2 – √3

c)

(c) 2 ± √3

d)

(d) None of these

3.

The sum of n terms of the series (1/1.2) + (1/2.3) + (1/3.4) + …… is

a)

(a) n/(n+1)

b)

(b) 1/(n+1)

c)

(c) 1/n

d)

(d) None of these

4.

If 1/(b + c), 1/(c + a), 1/(a + b) are in AP then

a)

(a) a, b, c are in AP

b)

(b) a², b², c² are in AP

c)

(c) 1/1, 1/b, 1/c are in AP

d)

(d) None of these

5.

The sum of series 1/2! + 1/4! + 1/6! + ….. is

a)

(a) e² – 1 / 2

b)

(b) (e – 1)² /2 e

c)

(c) e² – 1 / 2 e

d)

(d) e² – 2 / e

6.

The third term of a geometric progression is 4. The product of the first five terms is

a)

(a) 4³

b)

(b) 4⁵

c)

(c) 4⁴

d)

(d) none of these

7.

Let Tr be the r th term of an A.P., for r = 1, 2, 3, … If for some positive integers m, n, we have Tm = 1/n and Tn = 1/m, then Tm n equals

a)

(a) 1/m n

b)

(b) 1/m + 1/n

c)

(c) 1

d)

(d) 0

8.

The sum of two numbers is 13/6 An even number of arithmetic means are being inserted between them and their sum exceeds their number by 1. Then the number of means inserted is

a)

(a) 2

b)

(b) 4

c)

(c) 6

d)

(d) 8

9.

If the sum of the roots of the quadratic equation ax² + bx + c = 0 is equal to the sum of the squares of their reciprocals, then a/c, b/a, c/b are in

a)

(a) A.P.

b)

(b) G.P.

c)

(c) H.P.

d)

(d) A.G.P.

10.

If 1/(b + c), 1/(c + a), 1/(a + b) are in AP then

a)

(a) a, b, c are in AP

b)

(b) a², b², c² are in AP

c)

(c) 1/1, 1/b, 1/c are in AP

d)

(d) None of these

11.

The 35th partial sum of the arithmetic sequence with terms a_n = n/2 + 1

a)

(a) 240

b)

(b) 280

c)

(c) 330

d)

(d) 350

12.

The sum of two numbers is 13/6 An even number of arithmetic means are being inserted between them and their sum exceeds their number by 1. Then the number of means inserted is

a)

(a) 2

b)

(b) 4

c)

(c) 6

d)

(d) 8

13.

The first term of a GP is 1. The sum of the third term and fifth term is 90. The common ratio of GP is

a)

(a) 1

b)

(b) 2

c)

(c) 3

d)

(d) 4

14.

The sum of AP 2, 5, 8, …..up to 50 terms is

a)

(a) 3557

b)

(b) 3775

c)

(c) 3757

d)

(d) 3575

15.

If 2/3, k, 5/8 are in AP then the value of k is

a)

(a) 31/24

b)

(b) 31/48

c)

(c) 24/31

d)

(d) 48/31

16.

The sum of n terms of the series (1/1.2) + (1/2.3) + (1/3.4) + …… is

a)

(a) n/(n+1)

b)

(b) 1/(n+1)

c)

(c) 1/n

d)

(d) None of these

17.

If the third term of an A.P. is 7 and its 7 th term is 2 more than three times of its third term, then the sum of its first 20 terms is

a)

(a) 228

b)

(b) 74

c)

(c) 740

d)

(d) 1090

18.

If the sum of the first 2n terms of the A.P. 2, 5, 8, ….., is equal to the sum of the first n terms of the A.P. 57, 59, 61, ….., then n equals

a)

(a) 10

b)

(b) 12

c)

(c) 11

d)

(d) 13

19.

If a is the A.M. of b and c and G₁ and G₂ are two GM between them then the sum of their cubes is

a)

(a) abc

b)

(b) 2abc

c)

(c) 3abc

d)

(d) 4abc

20.

Two cards from a pack of 52 cards are lost. One card is drawn from the remaining cards. If drawn card is diamond then the probability that the lost cards were both hearts is

a)

(a) 143/1176

b)

(b) 143/11760

c)

(c) 143/11706

d)

(d) 134/11760

21.

If four whole numbers taken at random are multiplied together, then the chance that the last digit in the product is 1, 3, 5, 7 is

a)

(a) 16/25

b)

(b) 16/125

c)

(c) 16/625

d)

(d) none of these

22.

Three identical dice are rolled. The probability that the same number will appear on each of them is

a)

(a) 1/6

b)

(b) 1/36

c)

(c) 1/18

d)

(d) 3/28

23.

There are four machines and it is known that exactly two of them are faulty. They are tested, one by one, in a random order till both the faulty machines are identified. Then the probability that only two tests are needed is

a)

(a) 1/3

b)

(b) 1/6

c)

(c) 1/2

d)

(d) 1/4

24.

Two unbiased dice are thrown. The probability that neither a doublet nor a total of 10 will appear is

a)

(a) 3/5

b)

(b) 2/7

c)

(c) 5/7

d)

(d) 7/9

25.

Two dice are thrown the events A, B, C are as follows A: Getting an odd number on the first die. B: Getting a total of 7 on the two dice. C: Getting a total of greater than or equal to 8 on the two dice. Then AUB is equal to

a)

(a) 15

b)

(b) 17

c)

(c) 19

d)

(d) 21

26.

Two numbers are chosen from {1, 2, 3, 4, 5, 6} one after another without replacement. Find the probability that the smaller of the two is less than 4.

a)

(a) 4/5

b)

(b) 1/15

c)

(c) 1/5

d)

(d) 14/15

27.

The probability that when a hand of 7 cards is drawn from a well-shuffled deck of 52 cards, it contains 3 Kings is

a)

(a) 1/221

b)

(b) 5/716

c)

(c) 9/1547

d)

(d) None of these

28.

A certain company sells tractors which fail at a rate of 1 out of 1000. If 500 tractors are purchased from this company, what is the probability of 2 of them failing within first year

a)

(a) e^-1/2/2

b)

(b) e^-1/2/4

c)

(c) e^-1/2/8

d)

(d) none of these

29.

The probability that in a random arrangement of the letters of the word INSTITUTION the three T are together is

a)

(a) 0.554

b)

(b) 0.0554

c)

(c) 0.545

d)

(d) 0.0545

30.

Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is

a)

(a) 2/9

b)

(b) 1/9

c)

(c) 8/9

d)

(d) 7/9

31.

A bag contains 5 brown and 4 white socks . A man pulls out two socks. The probability that both the socks are of the same colour is

a)

(a) 9/20

b)

(b) 2/9

c)

(c) 3/20

d)

(d) 4/9

32.

When a coin is tossed 8 times getting a head is a success. Then the probability that at least 2 heads will occur is

a)

(a) 247/265

b)

(b) 73/256

c)

(c) 247/256

d)

(d) 27/256

33.

A couple has two children. The probability that both children are females if it is known that the elder child is a female is

a)

(a) 0

b)

(b) 1

c)

(c) 1/2

d)

(d) 1/3

34.

A certain company sells tractors which fail at a rate of 1 out of 1000. If 500 tractors are purchased from this company, what is the probability of 2 of them failing within first year

a)

(a) e^-1/2/2

b)

(b) e-^-1/2/4

c)

(c) e^-1/2/8

d)

(d) none of these

35.

A random variable X has poison distribution with mean 2. Then, P (X > 1.5) equals

a)

(a) 1 – 3/e²

b)

(b) 2/e²

c)

(c) 3/e²

d)

(d) 0

36.

Let A and B are two mutually exclusive events and if P(A) = 0.5 and P(B ̅) = 0.6 then P(A∪B) is

a)

(a) 0

b)

(b) 1

c)

(c) 0.6

d)

(d) 0.9

37.

The probability of getting 53 Sundays in a leap year is

a)

(a) 1/7

b)

(b) 2/7

c)

(c) 3/7

d)

(d) None of these

38.

The probability of getting the number 6 at least once in a regular die if it can roll it 6 times?

a)

(a) 1 – (5/6)⁶

b)

(b) 1 – (1/6)⁶

c)

(c) (5/6)⁶

d)

(d) (1/6)⁶

39.

On his vacation, Rahul visits four cities (A, B, C, and D) in a random order. The probability that he visits A first and B last is

a)

(a) 1/2

b)

(b) 1/6

c)

(c) 1/10

d)

(d) 1/12

e)

(

40.

Equation of (x+1)²-x²=0 has number of real roots equal to:

a)

(a) 1

b)

(b) 2

c)

(c) 3

d)

(d) 4

41.

The roots of 100x² – 20x + 1 = 0 is:

a)

(a) 1/20 and 1/20

b)

(b) 1/10 and 1/20

c)

(c) 1/10 and 1/10

d)

(d) None of the above

42.

The sum of two numbers is 27 and product is 182. The numbers are:

a)

(a) 12 and 13

b)

(b) 13 and 14

c)

(c) 12 and 15

d)

(d) 13 and 24

43.

If ½ is a root of the quadratic equation x²-mx-5/4=0, then value of m is:

a)

(a) 2

b)

(b) -2

c)

(c) -3

d)

(d) 3

44.

The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, the other two sides of the triangle are equal to:

a)

(a) Base=10cm and Altitude=5cm

b)

(b) Base=12cm and Altitude=5cm

c)

(c) Base=14cm and Altitude=10cm

d)

(d) Base=12cm and Altitude=10cm

45.

The roots of quadratic equation 2x² + x + 4 = 0 are:

a)

(a) Positive and negative

b)

(b) Both Positive

c)

(c) Both Negative

d)

(d) No real roots

46.

The value of √6+√6+√6………6+6+6……… is:

a)

(a) 4

b)

(b) 3

c)

(c) 3.5

d)

(d) -3

47.

The sum of the reciprocals of Rehman’s ages 3 years ago and 5 years from now is 1/3. The present age of Rehman is:

a)

(a) 7

b)

(b) 10

c)

(c) 5

d)

(d) 6

48.

A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.

a)

(a) 30 km/hr

b)

(b) 40 km/hr

c)

(c) 50 km/hr

d)

(d) 60 km/hr

49.

If one root of equation 4x2-2x+k-4=0 is reciprocal of the other. The value of k is:

a)

(a) -8

b)

(b) 8

c)

(c) -4

d)

(d) 4

50.

Which one of the following is not a quadratic equation?

a)

(a) (x + 2)2 = 2(x + 3)

b)

(b) x2 + 3x = (–1) (1 – 3x)2

c)

(c) (x + 2) (x – 1) = x2 – 2x – 3

d)

(d) x3 – x2 + 2x + 1 = (x + 1)3

51.

Which of the following equations has 2 as a root?

a)

(a) x2 – 4x + 5 = 0

b)

(b) x2 + 3x – 12 = 0

c)

(c) 2x2 – 7x + 6 = 0

d)

(d) 3x2 – 6x – 2 = 0

52.

A quadratic equation ax2 + bx + c = 0 has no real roots, if

a)

(a) b2 – 4ac < 0

b)

(b) b2 – 4ac = 0

c)

(c) b2 – 4ac < 0

d)

(d) b2 – ac < 0

53.

The product of two consecutive positive integers is 306. To find the integers, this can be represented in the form of quadratic equation as

a)

(a) x2 + x + 360 = 0

b)

(b) x2 + x – 360 = 0

c)

(c) 2x2 + x – 360

d)

(d) x2 – 2x – 360 = 0

54.

The equation which has the sum of its roots as 3 is

a)

(a) 2x2 – 3x + 6 = 0

b)

(b) –x2 + 3x – 3 = 0

c)

(c) √2x2 – 3/√2x + 1 = 0

d)

(d) 3x2 – 3x + 3 = 0

55.

The quadratic equation 2x² – √5x + 1 = 0 has

a)

(a) two distinct real roots

b)

(b) two equal real roots

c)

(c) no real roots

d)

(d) more than 2 real roots

56.

The equation (x + 1)² – 2(x + 1) = 0 has

a)

(a) two real roots

b)

(b) no real roots

c)

(c) one real root

d)

(d) two equal roots

57.

The quadratic formula to find the roots of a quadratic equation ax² + bx + c = 0 is given by

a)

(a) [-b ± √(b2-ac)]/2a

b)

(b) [-b ± √(b2-2ac)]/a

c)

(c) [-b ± √(b2-4ac)]/4a

d)

(d) [-b ± √(b2-4ac)]/2a

58.

The quadratic equation x² + 7x – 60 has

a)

(a) two equal roots

b)

(b) two real and unequal roots

c)

(c) no real roots

d)

(d) two equal complex roots

59.

The maximum number of roots for a quadratic equation is equal to

a)

(a) 1

b)

(b) 2

c)

(c) 3

d)

(d) 4

60.

If a, b, c are in G.P., then the equations ax² + 2bx + c = 0 and dx² + 2ex + f = 0 have a common root if d/a, e/b, f/c are in

a)

(a) AP

b)

(b) GP

c)

(c) HP

d)

(d) none of these

Exam_Focus_Math_Test

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