Q.6896·Miscellaneous·2018·EasyCoordinates of the points O, P, Q and R are respectively (0,0,0), (4,6,2m), (2,0,2n) and (2,4,6). Let L, M, N and K be points on the sides OR, OP, PQ and QR respectively such that LMNK is a parallelogram whose two adjacent sides LK and LM are each of length √2. What are the values of m and n respectively?View question
Q.6897·Miscellaneous·2018·EasyWhat is the distance of the point (2, 3, 4) from the plane 3x – 6y + 2z + 11 = 0?View question
Q.6899·Miscellaneous·2018·EasyWhat is the equation of straight line passing through the point of intersection of the lines x/2 + y/3 = 1 and x/3 + y/2 = 1, and parallel to the line 4x + 5y – 6 = 0?View question
Q.6900·Miscellaneous·2018·EasyConsider the following statements: 1. The distance between the lines y = mx + c1 and y = mx + c2 is |c1–c2|/√(1+m^2). 2. The distance between the lines ax + by + c1 = 0 and ax + by + c2 = 0 is |c1–c2|/√(a^2+b^2). 3. The distance between the lines x = c1 and x = c2 is |c1–c2|. Which of the above statements are correct?View question
Q.6901·Miscellaneous·2018·EasyThe second degree equation x^2 + 4y^2 – 2x – 4y + 2 = 0 representsView question
Q.6902·Miscellaneous·2018·EasyThe equation of a circle whose end points of a diameter are (x1, y1) and (x2, y2) isView question
Q.6903·Miscellaneous·2018·EasyThe ratio of roots of the equations ax^2 + bx + c = 0 and px^2 + qx + r = 0 are equal. If D1 and D2 are respective discriminants, then what is D1/D2 equal to?View question
Q.6904·Miscellaneous·2018·EasyWhat is the sum of all three-digit numbers that can be formed using all the digits 3, 4 and 5, when repetition of digits is not allowed?View question
Q.6905·Miscellaneous·2018·EasyIf a, b, c are in AP or GP or HP, then (a–b)/(b–c) is equal toView question
Q.6906·Miscellaneous·2018·EasyIf the second term of a GP is 2 and the sum of its infinite terms is 8, then the GP isView question
Q.6907·Miscellaneous·2018·EasyConsider the following values of x: 1. 8 2. –4 3. 1/6 4. –1/4 Which of the above values of x is/are the solution(s) of the equation tan^–1(2x) + tan^–1(3x) = π/4 ?View question
Q.6908·Miscellaneous·2018·EasyA is an angle in the fourth quadrant. It satisfies the trigonometric equation 3(3 – tan^2A – cotA)^2 = 1. Which one of the following is a value of A?View question
Q.6909·Miscellaneous·2018·EasyA balloon is directly above one end of a bridge. The angle of depression of the other end of the bridge from the balloon is 48°. If the height of the balloon above the bridge is 122 m, then what is the length of the bridge?View question
Q.6910·Miscellaneous·2018·EasyIf A+B+C = 180°, then what is sin2A – sin2B – sin2C equal to?View question
Q.6911·Miscellaneous·2018·EasyConsider the following in respect of matrices A and B of same order: 1. A^2 – B^2 = (A+B)(A–B) 2. (A–I)(I+A) = O ⇔ A^2 = I where I is the identity matrix and O is the null matrix. Which of the above is/are correct?View question
Q.6912·Miscellaneous·2018·EasyIf A, B and C are the angles of a triangle and | 1 1 1 | | 1+sinA 1+sinB 1+sinC | | sinA+sin^2A sinB+sin^2B sinC+sin^2C | = 0, then which one of the following is correct?View question