PYQ Vault

Day 114: CBSE Class 10 Maths

5 questions (9 parts). Try each one first, then open its answer.

  1. Question 1

    Probability. Asked once: 2025 (same type asked 2 times)

    Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the options given below.
    20
    In an experiment of throwing a die, Assertion (A) : Event E1E_1 : getting a number less than 3 and Event E2E_2 : getting a number greater than 3 are complementary events. Reason (R) : If two events E and F are complementary events, then P(E)+P(F)=1P(E) + P(F) = 1.

    Tap an option to check your answer.

  2. Question 2

    Quadratic Equations. Asked once: 2026 (same type asked 2 times)

    1
    The value of k for which the equation kx2−6x−4=0kx^2 - 6x - 4 = 0 has real and equal roots, is

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  3. Question 3

    Quadratic Equations. Asked once: 2025 (same type asked 2 times)

    34 (a)
    The perimeter of a right triangle is 60 cm and its hypotenuse is 25 cm. Find the lengths of other two sides of the triangle.

  4. Question 4 (case study, 2 parts)

    Some Applications of Trigonometry. Asked once: 2022 (same type asked 2 times)

    Kite Festival Kite festival is celebrated in many countries at different times of the year. In India, every year 14th14^{\text{th}} January is celebrated as International Kite Day. On this day many people visit India and participate in the festival by flying various kinds of kites. The picture given below, shows three kites flying together. In Fig. 5, the angles of elevation of two kites (Points A and B) from the hands of a man (Point C) are found to be 30∘30^\circ and 60∘60^\circ respectively. Taking AD = 50 m and BE = 60 m, find
    13 (1)
    the lengths of strings used (take them straight) for kites A and B as shown in the figure.
    13 (2)
    the distance ‘d’ between these two kites

  5. Question 5 (case study, 4 parts)

    Some Applications of Trigonometry. Asked once: 2025 (same type asked 2 times)

    A lighthouse stands tall on a cliff by the sea, watching over ships that pass by. One day a ship is seen approaching the shore and from the top of the lighthouse, the angles of depression of the ship are observed to be 30∘30^\circ and 45∘45^\circ as it moves from point P to point Q. The height of the lighthouse is 50 metres. Based on the information given above, answer the following questions :
    37 (i)
    Find the distance of the ship from the base of the lighthouse when it is at point Q, where the angle of depression is 45∘45^\circ.
    37 (ii)
    Find the measures of ∠PBA\angle PBA and ∠QBA\angle QBA.
    37 (iii) (a)
    Find the distance travelled by the ship between points P and Q.
    37 (iii) (b)
    If the ship continues moving towards the shore and takes 10 minutes to travel from Q to A, calculate the speed of the ship in km/h, from Q to A.