Q) Find the discriminant of the quadratic equation 4×2 – 5 = 0 and hence comment on the nature of the equation. Ans: Given equation is 4×2 – 5 = 0 or we can say that, Find the discriminant of 4×2 + 0x – 5 = 0 Let’s compare it with standard quadratic equation ax2 +b […]
Q) If θ is an acute angle and sin θ = cos θ, find the value of tan2 θ + cot2 θ – 2. Ans: tan2 θ + cot2 θ – 2. = + – 2 By sin θ = cos θ (given), = + – 2 = 1 + 1 – 2 = 0
If θ is an acute angle and sin θ = cos θ, find the value of tan^2 θ + cot^2 θ – 2. Read More »
Q) Evaluate (5/cot2 30°) + (1/ sin2 60°) – cot2 45° + 2 sin2 90° Ans: Givent that, – cot2 45 + 2 sin2 90 = + – (1)2 + 2 (1)2 = + – 1 + 2 = 3 – 1 + 2 = 4
Evaluate (5/cot^2 30) + (1/ sin^2 60) – cot^2 45 + 2 sin^2 90 Read More »
Q) Governing council of a local public development authority of Dehradun decided to build an adventurous playground on the top of a hill, which will have adequate space for parking. After survey, it was decided to build rectangular playground, with a semi-circular area allotted for parking at one end of the playground. The length and
Q) Jagdish has a field which is in the shape of a right angled triangle AQC. He wants to leave a space in the form of a square PQRS inside the field for growing wheat and the remaining for growing vegetables (as shown in the figure). In the field, there is a pole marked as
Jagdish has a field which is in the shape of a right angled triangle AQC. Read More »
Q) Two schools ‘P’ and ‘Q’ decided to award prizes to their students for two games of Hockey Rs. x per student and Cricket Rs. y per student. School ‘P’ decided to award a total of Rs. 9,500 for the two games to 5 and 4 students respectively; while school ‘Q’ decided to award Rs. 7,370
Two schools ‘P’ and ‘Q’ decided to award prizes to their students for two games of Read More »
Q) The monthly expenditure on milk in 200 families of a Housing Society is given below: Find the value of x and also, find the median and mean expenditure on milk. Ans: (i) Value of x: Let’s re-organize the data in the frequency table and calculate the value of x: By summing up the families,
The monthly expenditure on milk in 200 families of a Housing Society is given below: Read More »
Q) A student was asked to make a model like a cylinder with two cones attached to its ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its total length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained
Q) If AD and PM are medians of triangle ABC and PQR, respectively where Δ ABC ~ Δ PQR, prove that AB / PQ = AD / PM. Ans: Given that, Δ ABC ~ Δ PQR, therefore Since AD is median of BC, hence BC = 2BD Similarly, PM is median of QR, hence QR
Q) D is a point on the side BC of a triangle ABC such that ∠ ADC = ∠ BAC, prove that CA2 = CB.CD Ans: Let’s draw the diagram with triangle ABC. Let’s compare Δ CBA with Δ CAD ∠ ADC = ∠ BAC (given) ∠ C = ∠ C