NCERT Solutions for Class 9 Maths Chapter 6 Exercise 6.1 Solutions

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CBSE X Related Questions

  • 1.
    In a right triangle ABC, right-angled at A, if $\sin B = \dfrac{1}{4}$, then the value of $\sec B$ is

      • 4
      • $\dfrac{\sqrt{15}}{4}$
      • $\sqrt{15}$
      • $\dfrac{4}{\sqrt{15}}$

    • 2.

      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.


        • 3.
          \(\alpha, \beta\) are zeroes of the polynomial \(3x^2 - 8x + k\). Find the value of \(k\), if \(\alpha^2 + \beta^2 = \dfrac{40}{9}\)


            • 4.
              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


                • 5.

                  Given that $\sin \theta + \cos \theta = x$, prove that $\sin^4 \theta + \cos^4 \theta = \dfrac{2 - (x^2 - 1)^2}{2}$.


                    • 6.

                      In the adjoining figure, TS is a tangent to a circle with centre O. The value of $2x^\circ$ is

                        • 22.5
                        • 45
                        • 67.5
                        • 90

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