Q.3997·Miscellaneous·2021·EasyWhat is the area bounded by y = [x], the x-axis and the lines x = -1.5 and x = -1.8?View question
Q.3998·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.3999·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.4000·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.4001·Miscellaneous·2021·EasyHow many distinct matrices exist with all four entries taken from {1, 2}?View question
Q.4002·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.4003·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.4004·Miscellaneous·2021·EasyThe coordinates of three consecutive vertices of a parallelogram ABCD are A(1, 3), B(–1, 2) and C(3, 5). What is the equation of the diagonal BD?View question
Q.4005·Miscellaneous·2021·EasyThe coordinates of three consecutive vertices of a parallelogram ABCD are A(1, 3), B(–1, 2) and C(3, 5). What is the area of the parallelogram?View question
Q.4006·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.4007·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 is the equation of the altitude through B on AC?View question
Q.4008·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.4009·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.4010·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.4011·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
Q.4012·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.4013·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.4014·Miscellaneous·2021·EasyConsider the following statements in respect of sets: 1. The union over intersection of sets is distributive. 2. The complement of union of two sets is equal to intersection of their complements. 3. If the difference of two sets is equal to empty set, then the two sets must be equal. Which of the above statements are correct?View question