Q.1·Miscellaneous·2025·EasyABC is an equilateral triangle and AD is the altitude on BC. If coordinates of A are (1, 2) and D are (-2, 6), then what is the equation of BC?View question
Q.2·Miscellaneous·2025·EasyA(1, 2), B(2, 5) and C(4, 4) are three vertices of a rectangle. What is its area ?View question
Q.3·Miscellaneous·2025·EasyA man at M, standing 100 m away from the base (P) of a chimney of height 50 m, observes the angle of elevation of the highest point (Q) of the smoke to be 45°.The highest point of the chimney is at R. Further, P, R and Q are in a straight line and the straight line is perpendicular to PM. What is the angle RMQ equal to ?View question
Q.4·Miscellaneous·2025·EasyThe vertices of a triangle are A(1, 1), B(0, 0) and C(2, 0). The angular bisectors of the triangle meet at P. What are the coordinates of P?View question
Q.5·Miscellaneous·2025·EasyWhat is the equation of the circle whose diameter is 10 cm and the equations of two of its diameters are x + y = 0 and x - y = 0?View question
Q.7·Miscellaneous·2025·EasyConsider the following for the two (02) items that follow: In a triangle ABC, two sides BC and CA are in the ratio 2:1 and their opposite corresponding angles are in the ratio 3:1. Consider the following statements: I. The triangle is right-angled. II. One of the sides of the triangle is 3 times the other. III. The angles A, C and B of the triangle are in AP. Which of the statements given above is/are correct ?View question
Q.8·Miscellaneous·2025·EasyThe mode of the set {5, 8, 8, 10, 11, 11, 11, 12, 13, 14, 15} is: What is the mean of the given set?View question
Q.9·Miscellaneous·2025·EasyIf p and q are real numbers between 0 and 1 such that the points (p, 1), (1, q) and (0, 0) form an equilateral triangle, then what is (p + q) equal to ?View question
Q.12·Miscellaneous·2025·EasyWhat is PN equal to? The top (M) of a tower is observed from points P, Q, R lying in a straight line along foot (N) of the tower. Angles of elevation from P, Q, R are 30°, 45°, 60°, respectively. Let PQ = a and QR = b.View question
Q.14·Miscellaneous·2025·EasyThe sides of triangle ABC are AB = 3 cm, BC = 5 cm, and CA = 7 cm. Consider the following statements: I. The triangle is obtuse-angled. II. The sum of acute angles of the triangle is also acute. Which of the statements given above is/are correct?View question
Q.15·Miscellaneous·2025·EasyConsider the following for the two [02] items that follow : Let ABC be a triangle right-angled at B and AB + AC = 3 units. What is the maximum area of the triangle ?View question
Q.16·Miscellaneous·2025·EasyConsider the following for the two (02) items that follow: In a triangle ABC, two sides BC and CA are in the ratio 2:1 and their opposite corresponding angles are in the ratio 3:1. One of the angles of the triangle isView question
Q.17·Miscellaneous·2025·EasyThe mode of the set {5, 8, 8, 10, 11, 11, 11, 12, 13, 14, 15} is: What is the mode of the given set?View question
Q.18·Miscellaneous·2025·EasyABC is right-angled at B. If A(k, 1, -1), B(2k, 0, 2) and C(2 + 2k, k, 1) are the vertices, then what is k ?View question