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If y = log₁₀x + logₓ10 + logₓx + log₁₀10 then what is (dy/dx)ₓ₌₁₀ equal to?000
If log(base a) (ab) = x, then what is log(base b)(ab) equal to?000
What is the number of different messages that can be represented by three 0's and two 1's?000
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?000
What is the number of four-digit decimal numbers (<1) in which no digit is repeated?000
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?000
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?000
A fair coin is tossed 100 times. What is the probability of getting tails an odd number of times?000
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?000
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?000
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?000
What is the probability of 5 Sundays in the month of December?000
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?000
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?000
If two dice are thrown, then what is the probability that the sum on the two faces is greater than or equal to 4?000
A card is drawn from a well-shuffled deck of 52 cards. What is the probability that it is queen of spade?000
if the total number of observations is 20, Σ(xi) = 1000 and Σ (xi²) = 84000, then what is the variance of the distribution?000
A coin is tossed three times. What is the probability of getting head and tail alternatively?000
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?000
Three dice are thrown simultaneously. What is the probability that the sum on the three faces is at least 5?000
What is the mean deviation from the mean of the numbers 10, 9, 21, 16, 24?000
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?000
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?000
(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?000
What is the number of natural numbers less than or equal to 1000 which are neither divisible by 10 nor 15 nor 25?000
What is ∫ 0→4π ( | cos x | )dx equal to?000
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?000
What is the binary equivalent of the decimal number 0.3125?000
If A is square matrix, then what is adj(A.¹) - (adj A).¹ equal to?000
What is lim x→0 e⁻¹/ˣ² equal to?000
If lim x→0 Φ( x ) = a^2, where a ≠ 0, then what is lim x→0 Φ( x/a ) equal to?000
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?000
What is ∫ (-2→2) x dx - ∫ (-2→2) [ x ] dx equal to, where [ . ] is the greatest integer function?000
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?000
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 ( 2ã2( ã3 - 1)/15) . Which of the above statements is/are correct?000
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?000
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?000
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?000
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?000
Consider the function f(x) = | x² - 5x + 6 |. What is f' '(2.5) equal to?000
Consider the function f(x) = | x² - 5x + 6 |. What is tf'(4) equal to?000
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?000
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?000
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?000
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?000
Let f: .->. be a function such that f(x) = x3 + x2f'(1) + xf' '(2) + f' ' '(3) for x¸.. What is f' '(10) equal to?000
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?000
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?000
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?000
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?000