NCERT Solutions for Class 10 Maths Chapter 3 Exercise 3.5

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CBSE X Related Questions

  • 1.
    Prove that: \[ \frac{\cos \theta - 2 \cos^3 \theta}{\sin \theta - 2 \sin^3 \theta} + \cot \theta = 0 \]


      • 2.

        Two identical cones are joined as shown in the figure. If radius of base is 4 cm and slant height of the cone is 6 cm, then height of the solid is

          • 8 cm
          • \(4\sqrt{5}\) cm
          • \(2\sqrt{5}\) cm
          • 12 cm

        • 3.
          Let $p$, $q$ and $r$ be three distinct prime numbers. Check whether $pqr + q$ is a composite number or not. Further, give an example for three distinct primes $p$, $q$, $r$ such that
          (i) $pqr + 1$ is a composite number
          (ii) $pqr + 1$ is a prime number


            • 4.
              The number of red balls in a bag is three more than the number of black balls. If the probability of drawing a red ball at random from the given bag is $\dfrac{12}{23}$, find the total number of balls in the given bag.


                • 5.

                  In the adjoining figure, $\triangle CAB$ is a right triangle, right angled at A and $AD \perp BC$. Prove that $\triangle ADB \sim \triangle CDA$. Further, if $BC = 10$ cm and $CD = 2$ cm, find the length of AD.


                    • 6.
                      Solve the equation \(4x^2 - 9x + 3 = 0\), using quadratic formula.

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