Q.3997·Miscellaneous·2021·EasySeven white balls and three black balls are randomly placed in a row. What is the probability that no two black balls are placed adjacently?View question
Q.3998·Miscellaneous·2021·EasyWhat is the order of the differential equation of all ellipses whose axes are along the coordinate axes?View question
Q.3999·Miscellaneous·2021·EasyWhat is the degree of the differential equation of all circles touching both the coordinate axes in the first quadrant?View question
Q.4000·Miscellaneous·2021·EasyWhere does the tangent to the curve y = e^x at the point (0, 1) meet x-axis?View question
Q.4001·Miscellaneous·2021·EasyConsider the following statements in respect of the function f(x) = x + 1/x : 1. The local maximum value of f(x) is less than its local minimum value. 2. The local maximum value of f(x) occurs at x = 1. Which of the above statements is/are correct?View question
Q.4002·Miscellaneous·2021·EasyWhat is the maximum area of a rectangle that can be inscribed in a circle of radius 2 units?View question
Q.4003·Miscellaneous·2021·EasyThe equations of the sides AB, BC and CA of a triangle ABC are x – 2 = 0, y + 1 = 0 and x + 2y – 4 = 0 respectively. What are the coordinates of circumcentre of the triangle?View question
Q.4004·Miscellaneous·2021·EasyThe two ends of the latus rectum of a parabola are (−2, 4) and (−2, −4). What is the maximum number of parabolas that can be drawn through these two points as end points of latus rectum?View question
Q.4005·Miscellaneous·2021·EasyThe two ends of the latus rectum of a parabola are (−2, 4) and (−2, −4). Consider the following statements in respect of such parabolas : 1. One of the parabolas passes through the origin (0, 0). 2. The focus of one of the parabolas lies at (−2, 0). Which of the above statements is/are correct?View question
Q.4006·Miscellaneous·2021·EasyIn this question each item consists of a sentence with an underlined word followed by four words. Select the option that is opposite in meaning to the underlined word and mark your response on your Answer Sheet accordingly. Planets move in their orbits.View question
Q.4007·Miscellaneous·2021·EasySuppose set A consists of first 250 natural numbers that are multiples of 3 and set B consists of first 200 even natural numbers. How many elements does A ∪ B have?View question
Q.4008·Miscellaneous·2021·EasyConsider the digits 3, 5, 7, 9. What is the number of 5-digit numbers formed by these digits in which each of these four digits appears?View question
Q.4009·Miscellaneous·2021·EasyIf x = a / (b – c), y = b / (c – a), z = c / (a – b) then what is the value of the following? | 1 –x x | | 1 –y y | | 1 z 1 |View question
Q.4010·Miscellaneous·2021·EasyConsider the following in respect of the matrix A = [1 1 1] [1 1 1] [1 1 1] 1. Inverse of A does not exist 2. A³ = A 3. 3A = A² Which of the above are correct?View question
Q.4011·Miscellaneous·2021·EasyA circle is passing through the points (5, –8), (–2, 9) and (2, 1). What are the coordinates of the centre of the circle?View question
Q.4012·Miscellaneous·2021·EasyA circle is passing through the points (5, –8), (–2, 9) and (2, 1). If r is the radius of the circle, then which one of the following is correct?View question
Q.4013·Miscellaneous·2021·EasyThe two vertices of an equilateral triangle are (0, 0) and (2, 2). Consider the following statements: 1. The third vertex has at least one irrational coordinate. 2. The area is irrational. Which of the above statements is/are correct?View question
Q.4014·Miscellaneous·2021·EasyThe two vertices of an equilateral triangle are (0, 0) and (2, 2). The difference of coordinates of the third vertex isView question