Q. 1
Which of the following values of x satisfies the equations (2-3x)/4
<9 and x<-5? Indicate all correct options.
- A. 1
- B. -1
- C. 5
- D. -6
- E. -10
- Answer: D and E
-
Explanation:
(2-3x)/4
<9 2-3x<36 -3x<36-2=34 x>-34/3 and x
<-5 Only x=- 6 and -10 satisfy the given equations.
Q. 2
Which of the following is true? Indicate all correct options.
- A. (3,4) lies in the first quadrant
- B. (5,-2) lies in the fourth quadrant
- C. (3,0) lies on the y-axis
- D. (0,3) lies of the x-axis
- E. (-2,-2) lies in the fourth quadrant
- Answer: A and B
-
Explanation:
(3,4) lies in the first quadrant. Option A is true. (5,-2) lies in the fourth quadrant. Option B is true. (3,0)
lies on the x-axis and (0,3) lies on the y-axis. Options C and D are false. (-2,-2) lies in the third quadrant.
Option E is false.
Q. 3
A shopkeeper sold 200 tables at a loss. His loss was equal to the selling price of 4 tables. Which of the following
statements is true? Indicate all correct options.
- A. His loss was Rs.2000
- B. His loss % was 100/51%
- C. His selling price was Rs.500 per table
- D. The selling price cannot be determined
- E. The total loss cannot be determined
- Answer: B, D and E
-
Explanation:
Let the selling price of one table be Rs.x. We are given that the loss is equal to the selling price of 4 tables. Hence,
the total loss can be written in terms of the selling price i.e. 4x. 200 tables were sold and the cost price
of 200 tables can be calculated as C.P. = SP + loss = 200x + 4x = 204x Since the loss percent is calculated
with respect to the cost price, it is independent of x Loss % = loss/CP*100 = (4x/204x) *100 = 100/51% Opions
B, D and E are true.
Q. 4
P(n,4) = 20 P(n,2). Which of the following is true? Indicate all correct options. P is Probability
- A. n = 7
- B. n = -2
- C. n can have only positive values
- D. n is negative
- E. n has two values
- Answer: A and C
-
Explanation:
P(n,4) = 20 P(n,2) n!/(n-4)! = 20*n!/(n-2)! (n-2)!=20(n-4)! (n-2)(n-3)(n-4)!=20(n-4)! (n-2)(n-3)=20 n^2 – 5n
+ 6 – 20 = 0 n^2 – 5n – 14 = 0 n^2 – 7n + 2n – 14 = 0 n(n-7) + 2(n-7) = 0 (n+2)(n-7) = 0 n = -2,7 Since n is
positive, n = 7. Options A and C are true.
Q. 5
C(n,r) = 120 and P(n,r) = 720. Which of the following is true? Indicate all correct options.
- A. r =9
- B. n = 9
- C. n = 8
- D. r = 3
- E. r = 7
- Answer: C and D
-
Explanation:
C(n,r) = 120 n!/[(n-r)!r!] = 120…(1) P(n,r) = 720 n!/(n-r)! = 720…(2) Dividing (2) by (1), we get [n!/(n-r)!] / n!/[(n-r)!r!] = 720/120 r! = 6 = 3! r = 3 Putting r = 3 in (2), we get n!/(n-3)! = 720 n(n-1)(n-2)(n-3)!/(n-3)!
= 720 n(n-1)(n-2) = 720 Clearly, n = 8 Options C and D are true.
Q. 6
Which of the following is the LCM of 3!, 5! and 7!? Indicate all correct options.
- A. 7!
- B. 3!
- C. 5!
- D. 5040
- E. 12
- Answer: A and D
-
Explanation:
LCM of 3!, 5! and 7! = LCM of 3!, 5*4*3! and 7*6*5*4*3! = 3!*4*5*6*7 = 7! = 5040
Q. 7
The mth term of an A.P. is 1/n. The nth term is 1/m. Which of the following is true? Indicate all correct options.
- A. The first term of the AP is m/n
- B. The first term of the AP is n/m
- C. The first term of the AP is 1/mn
- D. The common difference of the AP is 1/mn
- E. The first term of the AP is equal to the common difference.
- Answer: C, D and E
-
Explanation:
Let a be the first term and d be the common difference of the AP According to the given conditions, we have 1/n = a + (m-1)d
1/m = a + (n-1)d Subtracting one equation from the other, we get 1/n – 1/m = (m-n)d (m-n)/mn = (m-n)d d = 1/mn
Putting this value of d in any of the above equations, we get 1/n = a + (m-1)*1/mn a = 1/n – (m-1)*1/mn = (m-m+1)/mn
= 1/mn The first term of the AP is 1/mn and the common difference is 1/mn Options C, D and E are true.
Q. 8
f is a real function defined by f(x) = x^3 – 3x + 5. Which of the following is true? Indicate all correct options.
[x^3=x*x*x]
- A. f(-2) = f(1)
- B. f(-1) = f(1)
- C. f(-1) = f(2)
- D. f(3) = 23
- E. f(3) = f(2) + 7
- Answer: A, C and D
-
Explanation:
f(-2) = (-2)^3 -3*(-2) + 5 = -8 + 6 + 5 = 3 f(-1) = (-1)^3 – 3*(-1) + 5 = -1 + 3 + 5 = 7 f(1) = 1^3 -3*1 + 5 = 1 – 3 + 5
= 3 f(2) = 2^3 – 3*2 + 5 = 8 – 6 + 5 = 7 f(3) = 3^3 – 3*3 + 5 = 27 – 9 + 5 = 23 Options A, C and D are true.
[2^3=2*2*2]
Q. 9
The sum of two consecutive even positive numbers is less than 25 and each number is larger than 8. Which of the
following is true? Indicate all correct options.
- A. One number is 12
- B. The smaller number is 12
- C. The sum of the numbers is less than 22
- D. The smaller number is 10
- E. The two numbers are multiples of 4
- Answer: A and D
-
Explanation:
Let one number be x. The other number will be x+2 x+x+2
< 25 2x+2<25 2x<25-2=23 x<23/2=1 1.5 8 < x <11.5 The numbers are 10 and 10+2=1 2 The smaller number is 10 and the larger number is 12 The sum of the numbers is 10+12=2 2 The two numbers are not multiples of 4 Hence, options A and D are true.
Q. 10
If (n+1)! = 12 (n ??? 1)!, then which of the following is true for n? Indicate all correct options.
- A. n = 4
- B. n = 3
- C. n = -4
- D. n > 0
- E. n < 0
- Answer: B and D
-
Explanation:
(n+1)! = 12 (n ??? 1)! (n+1).n.(n-1)!=12(n-1)! (n+1).n = 12 n^2 + n -12=0 n^2 + 4n – 3n -12=0 n(n+4) -3(n+4) =
0 (n-3)(n+4) =0 n = 3, -4 Since n cannot be negtive, n = 3 Options B and D are true.
Q. 11
Which of the following statements is true? Indicate all such statements. [(4!)^2 = 4!*4!]
- A. 9!*10 = 90!
- B. 4!*5!*6 = 6!
- C. 7!*8*9 = 9!
- D. 5-1)!5! = [(4!)^2]*5
- E. 4! = 12*3!
- Answer: C and D
-
Explanation:
9!*10 = 10! Option (A) is not true. 4!*5!*6 = 4!*(4!*5)*6 = 4!*6! Option (B) is not true. 7!*8*9 = 9! Option (C) is true.
(5-1)!5! = 4!*5! = 4!*4!*5 = [(4!)^2]*5 Option (D) is true. 4! = 3!*4 12*3! = 3*4*3! = 3*4! Option (E) is not
true.
Q. 12
Which of the following statements is true? Indicate all correct options.
- A. Every rectangle is a square
- B. Every square is a rectangle
- C. Every parallelogram is a rhombus
- D. Every rhombus is a parallelogram
- E. Every square is a rhombus
- Answer: B, D and E
-
Explanation:
In a rectangle opposite sides are equal and each angle is a right angle. In a square all sides are equal. Option A is false
and B is true. A parallelogram is a quadrilateral in which both the pairs of opposite sides are parallel and
equal. A rhombus is a parallelogram in which all sides are equal. Option C is false and D and E are true.
Q. 13
When a number x is increased by 17, it equals 60 times its reciprocal. Which of the following statements is true?
Indicate all correct options.
- A. There are two possible values of x
- B. There are two positive values of x
- C. x = -3
- D. x = 20
- E. x = -20
- Answer: A and E
-
Explanation:
x+17 = 60*1/x x^2 + 17x = 60 x^2 + 17x – 60=0 x^2 +20x – 3x – 60=0 x(x+20) – 3(x+20) = 0 x = 3, -20 Options A and E are true.
[x^2=x*x]
Q. 14
If two buses starting from points A and B go in the same direction, then they meet in 6 hours. If they go in
opposite directions, then they meet in 2 hours. The distance between points A and B is 120 km. Which of the
following is true? Indicate all correct options.
- A. The faster bus travels at a speed of 40 km/hr
- B. The difference between the speeds of the buses is 20 km/hr
- C. The faster bus is twice as fast as the slower bus
- D. The slower bus travels at a speed of 40 km/hr
- E. The speeds of the buses cannot be determined
- Answer: A, B and C
-
Explanation:
Let the buses start in the same direction, from A towards B and beyond. They meet in 6 hours at a point at a
distance of say x km from point B. Distance travelled by bus at A = (120 + x) km Distance travelled by bus
at B = x km in 6 hours. Let the buses start in the opposite directions, towards each other. They meet in 2
hours at a point at a distance of say y km from point B. Distance travelled by bus at A = (120 – y) km Distance
travelled by bus at B = y km in 2 hours. Speed =distance/time We equate the speeds of the buses in the two
situations (120+x)/6 = (120-y)/2 and x/6 = y/2 120+x = 360-3y and x = 3y 120 + 3y = 360 – 3y 6y = 360 – 120
y = 240/6 = 40 Speed of bus at A = (120+3*40)/6 = 240/6 = 40 km/hr Speed of bus at B = y/2 = 40/2 = 20 km/hr
Options A, B and C are true.
Q. 15
Which of the following is true? Indicate all correct options.
- A. Sqrt(2) is an integer
- B. Sqrt(2) is an irrational number
- C. Sqrt(2) is a real number
- D. -5/4 is an integer
- E. 5 is an integer
- Answer: B, C and E
-
Explanation:
Sqrt(2) = 1.41421 is a non-terminating repeating decimal. Hence, it is not an integer and it is an irrational real number.
Options B and C are true. -5/4 is not an integer and 5 is an integer. Option E is true. All other options are
false.
Score: 0/10
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