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IAS Coaching in Nagpur

The Civil Services Exam is one of the most sought after and prestigious examinations conducted in the country, and aspirants across India look... View Article

25 Aug 2021: The Hindu Analysis

UPSC Current Affairs Preparation: The Hindu Analysis Watch expert analysis of ‘The Hindu’ dated 25th Aug 2021. Important news and views to boost... View Article

Find the value of a, if the distance between the points A (-3, -14) and B (a, -5) is 9 units.

Given The distance between the points A (–3, –14) and B (a, –5) is 9 units Find out We have to determine the value of a... View Article

What type of a quadrilateral do the points A (2, -2), B (7, 3), C (11, -1) and D (6, -6) taken in that order, form?

The points are A (2, –2), B (7, 3), C (11, –1) and D (6, –6) Using distance formula, d = √ ((x2 –... View Article

Find the points on the x-axis which are at a distance of 2√5 from the point (7, -4). How many such points are there?

Solution It isgiven that the point lies on x axis) Let coordinates of the point=(x, 0) x1=7. y1=-4 x2=x. y2=0 Distance =√(x2-x1)2+... View Article

Name the type of triangle formed by the points A (-5, 6), B (-4, -2) and C (7, 5).

Solution The points are A (–5, 6), B (–4, –2) and C (7, 5) We know that distance formula, d = √... View Article

Points A (4, 3), B (6, 4), C (5, -6) and D (-3, 5) are the vertices of a parallelogram. State whether the following statement is true or false. Justify your answer.

The given statement is False Solution The given points are A (4, 3), B (6, 4), C (5, –6) and D (–3, 5) To determine the distance... View Article

Points A (3, 1), B (12, -2) and C (0, 2) cannot be the vertices of a triangle. State whether the following statement is true or false. Justify your answer.

The given statement is True Solution Coordinates of A = (x1, y1) = (3, 1) Coordinates of B = (x2, y2) = (12, – 2) Coordinates of C =... View Article

Point P (0, 2) is the point of intersection of y-axis and perpendicular bisector of line segment joining the points A (-1, 1) and B (3, 3). State whether the following statement is true or false. Justify your answer.

The given statement is False Solution We know that, the points lying on perpendicular bisector of the line segment joining the two points is... View Article

The points (0, 5), (0, -9) and (3, 6) are collinear. State whether the following statement is true or false. Justify your answer.

Answer The given statement is False Solution The points are collinear if area of a triangle formed by its points is equals to the zero.... View Article

Point P (- 4, 2) lies on the line segment joining the points A (- 4, 6) and B (- 4, – 6). State whether the following statement is true or false. Justify your answer.

The given statement is True. Solution Plotting the points P(- 4, 2), A (- 4, 6) and B (- 4, – 6) on a graph paper and connecting the points... View Article

△ABC with vertices A (-2, 0), B (2, 0) and C (0, 2) is similar to △DEF with vertices D (-4, 0) E (4, 0) and F (0, 4). State whether the following statement is true or false. Justify your answer.

Answer The given statement is True. Solution We know that Distance formula, d = √ ((x2 – x1)2 + (y2 –... View Article

The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is (A) 5 (B) 12 (C) 11 (D) 7+ √5

The correct answer is (B) 12 Solution The vertices of a triangle are (0, 4), (0, 0) and (3, 0). The perimeter of ΔAOB = Sum of the length... View Article

AOBC is a rectangle whose three vertices are vertices A (0, 3), O (0, 0) and B (5, 0). The length of its diagonal is (A) 5 (B) 3 (C) √34 (D) 4

The correct answer is (C) √34 The three vertices are: A = (0, 3), O = (0, 0), B = (5, 0) The diagonals of a rectangle are of equal... View Article

The distance between the points (0, 5) and (-5, 0) is (A) 5 (B) 5√2 (C) 2√5 (D) 10

The correct answer is (B) 5√ 2 Solution We know that, Distance formula is given by d2 = (x2 – x1)2 +... View Article

The distance of the point P (-6, 8) from the origin is (A) 8 (B) 2√7 (C) 10 (D) 6

Answer: (C) 10 Distance between two points can be evaluated if we know the coordinates of the two points in the XY plane. If P(x1, y1) and Q(x2,... View Article

The distance between the points A (0, 6) and B (0, -2) is (A) 6 (B) 8 (C) 4 (D) 2

The correct answer is (B) 8 Solution We know that, Distance formula is given by d2 = (x2 – x1)2 + (y2 – y1)2... View Article

The distance of the point P (2, 3) from the x-axis is (A) 2 (B) 3 (C) 1 (D) 5

The correct answer is (B) 3 Solution We know that, (x, y) is a point on the Cartesian plane in the first quadrant. Let the given point be... View Article

A flag pole 18 m high casts a shadow 9.6 m long. Find the distance of the top of the pole from the far end of the shadow.

Solution Let MN = 18 m be the flag pole and its shadow be LM = 9.6 m. The distance of the top of the pole, N from the far end, L of the... View Article

For going to a city B from city A, there is a route via city C such that AC⊥CB, AC = 2 x km and CB = 2 (x + 7) km. It is proposed to construct a 26 km highway which directly connects the two cities A and B. Find how much distance will be saved in reaching city B from city A after the construction of the highway.

Answer According to the given details AC⊥CB, AC = 2x km, CB = 2 (x + 7) km and AB = 26 km Thus, we get ∆ ACB right angled at C.... View Article

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