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If y = log₁₀x + logₓ10 + logₓx + log₁₀10 then what is (dy/dx)ₓ₌₁₀ equal to? | 0 | 0 | 0 |

If log(base a) (ab) = x, then what is log(base b)(ab) equal to? | 0 | 0 | 0 |

What is the number of different messages that can be represented by three 0's and two 1's? | 0 | 0 | 0 |

The system of linear equations kx + y + z = 1, x + ky + z = 1 and x + y + kz = 1 has a unique solution under which one of the following conditions? | 0 | 0 | 0 |

What is the number of four-digit decimal numbers (<1) in which no digit is repeated? | 0 | 0 | 0 |

If one root of the equation (l - m)x² + l.x + 1 = 0 is double the other and l is real, then what is the greatest value of m? | 0 | 0 | 0 |

What is the number of ways in which 3 holiday travel tickets are to be given to 10 employees of an organization, if each employee is eligible for any one or more of the tickets? | 0 | 0 | 0 |

A fair coin is tossed 100 times. What is the probability of getting tails an odd number of times? | 0 | 0 | 0 |

Consider the following statements in respect of a histogram : 1. The total area of the rectangles in a histogram is equal to the total area bounded by the corresponding frequency polygon and the x-axis. 2. When class intervals are unequal in a frequency distribution, the area of the rectangle is proportional to the frequency. Which of the above statements is/are correct? | 0 | 0 | 0 |

For the data 3,5,1,6,5,9,2,8,6 the mean, median and mode are x, y and z respectively. Which one of the following is correct? | 0 | 0 | 0 |

A point is chosen at random inside a rectangle measuring 6 inches by 5 inches. What is the probability that the randomly selected point is at least one inch from the edge of the rectangle? | 0 | 0 | 0 |

What is the probability of 5 Sundays in the month of December? | 0 | 0 | 0 |

For two mutually exclusive events A and B, P(A) = 0.2 and P(A'∩B) 0.3. What is P(A| (A U B)) equal to? | 0 | 0 | 0 |

A certain type of missile hits the target with probability p = 0.3. What is the least number of missiles should be fired so that there is at least 80% probability that target is hit? | 0 | 0 | 0 |

If two dice are thrown, then what is the probability that the sum on the two faces is greater than or equal to 4? | 0 | 0 | 0 |

A card is drawn from a well-shuffled deck of 52 cards. What is the probability that it is queen of spade? | 0 | 0 | 0 |

if the total number of observations is 20, Σ(xi) = 1000 and Σ (xi²) = 84000, then what is the variance of the distribution? | 0 | 0 | 0 |

A coin is tossed three times. What is the probability of getting head and tail alternatively? | 0 | 0 | 0 |

Two independent events A and B have P(A) = 1/3 and P(B) = 3/4. What is the probability that exactly one of the two events A or B occurs? | 0 | 0 | 0 |

Three dice are thrown simultaneously. What is the probability that the sum on the three faces is at least 5? | 0 | 0 | 0 |

What is the mean deviation from the mean of the numbers 10, 9, 21, 16, 24? | 0 | 0 | 0 |

If A = ( cos 12° - cos 36° )( sin 96° + sin 24° ) and B = (sin 60° - sin 12° )( cos 48° - cos 72° ), then what is A/B equal to? | 0 | 0 | 0 |

Consider the following statements: 1. If ABC is an equilateral triangle then 3.tan( A + B ).tan C = 1. 2. If ABC is a triangle in which A = 78°, B = 66°, then tan(A/2 + C) < tan A. 3. If ABC is any triangle, then tan( A+B/2 ). sin(C/2) < cos(C/2). Which of the above statements is/are correct? | 0 | 0 | 0 |

(a, 2b) is the mid-point of the line segment joining the points (10, 06) and (k, 4). If a - 2b = 7, then what is the value of k? | 0 | 0 | 0 |

What is the number of natural numbers less than or equal to 1000 which are neither divisible by 10 nor 15 nor 25? | 0 | 0 | 0 |

What is ∫ 0→4π ( | cos x | )dx equal to? | 0 | 0 | 0 |

Let R be a relation on the set N of natural numbers defined by 'nRm Ì n is a factor of m'. Then which one of the following is correct? | 0 | 0 | 0 |

What is the binary equivalent of the decimal number 0.3125? | 0 | 0 | 0 |

If A is square matrix, then what is adj(A.¹) - (adj A).¹ equal to? | 0 | 0 | 0 |

What is lim x→0 e⁻¹/ˣ² equal to? | 0 | 0 | 0 |

If lim x→0 Φ( x ) = a^2, where a ≠ 0, then what is lim x→0 Φ( x/a ) equal to? | 0 | 0 | 0 |

If ∫ (-2→5) f(x)dx = 4 and ∫ (0→5) { 1 + f(x) }dx = 7 then what is ∫ (-2→0) f(x)dx equal to? | 0 | 0 | 0 |

What is ∫ (-2→2) x dx - ∫ (-2→2) [ x ] dx equal to, where [ . ] is the greatest integer function? | 0 | 0 | 0 |

What are the order and degree respectively of the differential equation whose solution is y = cx + c² - 3c³/² + 2, where c is a parameter? | 0 | 0 | 0 |

Consider the following statements : 1.There exists ƒÆ ¸ ( -ƒÎ/2, ƒÎ/2) for which tan.1 ( tan ƒÆ ) ‚ ƒÆ. 2. sin.1 (1/3) - sin.1 (1/5) = sin.1 ( 2ã2( ã3 - 1)/15) . Which of the above statements is/are correct? | 0 | 0 | 0 |

Consider a circle passing through the origin and the points (a, b) and (-b, -a). What is the sum of the squares of the intercepts cut off by the circle on the axes? | 0 | 0 | 0 |

Consider a circle passing through the origin and the points (a, b) and (-b, -a). On which line does the centre of the circle lie? | 0 | 0 | 0 |

Let f(x) be the greatest integer functions and g(x) be the modulus function. What is (f ¡ã f) (-9/5) + (g ¡ã g)(-2) equal to? | 0 | 0 | 0 |

Let f(x) be the greatest integer functions and g(x) be the modulus function. What is (g ¡ã f) (-5/3) - (f ¡ã g)(-5/3) equal to? | 0 | 0 | 0 |

Consider the function f(x) = | x² - 5x + 6 |. What is f' '(2.5) equal to? | 0 | 0 | 0 |

Consider the function f(x) = | x² - 5x + 6 |. What is tf'(4) equal to? | 0 | 0 | 0 |

A plane P passes through the line of intersection of the planes 2x - y + 3z = 2, x + y - z =1 and the point (1, 0, 1). If the plane P touches the sphere x² + y² + z² = r², then what is r equal to? | 0 | 0 | 0 |

A plane P passes through the line of intersection of the planes 2x - y + 3z = 2, x + y - z =1 and the point (1, 0, 1). What is the equation of the plane P? | 0 | 0 | 0 |

A plane P passes through the line of intersection of the planes 2x - y + 3z = 2, x + y - z =1 and the point (1, 0, 1). What are the direction ratios of the line of intersection of the given planes? | 0 | 0 | 0 |

Let f: ℝ->ℝ be a function such that f(x) = x³ + x²f'(1) + xf''(2) + f'''(3) for x∈ℝ. Consider the following: 1. f(2) = f(1) - f(0) 2. f' '(2) - f'(1) = 12 . Which of the above is/are correct? | 0 | 0 | 0 |

Let f: .->. be a function such that f(x) = x3 + x2f'(1) + xf' '(2) + f' ' '(3) for x¸.. What is f' '(10) equal to? | 0 | 0 | 0 |

Let f: ℝ->ℝ be a function such that f(x) = x³ + x²f'(1) + xf''(2) + f'''(3) for x∈ℝ. What is f'(1) equal to? | 0 | 0 | 0 |

Let f: R->R be a function such that f(x) = x3 + x2f'(1) + xf''(2) + f'''(3) for x¸.. What is f(1) equal to? | 0 | 0 | 0 |

Consider a parallelogram whose vertices are A(1,2), B(4,y), C(x,6) and D(3,5) taken in order. What is the area of parallelogram? | 0 | 0 | 0 |

Consider a parallelogram whose vertices are A(1,2), B(4,y), C(x,6) and D(3,5) taken in order. What is the point of intersection of the diagonals? | 0 | 0 | 0 |