{"id":10213,"date":"2025-02-17T10:16:07","date_gmt":"2025-02-17T04:46:07","guid":{"rendered":"https:\/\/cracku.in\/blog\/?p=10213"},"modified":"2025-02-20T17:36:36","modified_gmt":"2025-02-20T12:06:36","slug":"surds-and-indices-questions-for-cat-pdf","status":"publish","type":"post","link":"https:\/\/cracku.in\/blog\/surds-and-indices-questions-for-cat-pdf\/","title":{"rendered":"Surds and Indices Questions for CAT PDF"},"content":{"rendered":"

Surds and Indices are some of the basics of number system theory. The questions may include simplification of equations to find the simplified equations. Practice more questions on Surds and indices for CAT<\/a>.<\/p>\n

Surds and Indices Questions for CAT PDF:<\/strong><\/span><\/p>\n

Download\u00a0Surds and Indices Questions for CAT PDF<\/a><\/p>\n

CAT Online Coaching<\/a><\/p>\n

Download CAT Quant Questions PDF<\/a><\/p>\n

Take Free Mock Test for CAT 2023<\/a><\/p>\n

Question 1: \u00a0<\/strong>If $3^{2x + 3} – 244*3^x = -9$, then which of the following statements is true?<\/p>\n

a) \u2018x\u2019 is a positive number
\nb) \u2018x\u2019 is a negative number
\nc) \u2018x\u2019 can be either a positive number or a negative number
\nd) None of the above<\/p>\n

Question 2: <\/strong>If x = -0.5, then which of the following has the smallest value?<\/p>\n

a) $2^{1\/x}$
\nb) $1\/x$
\nc) $1\/x^2$
\nd) $2^x$
\ne)$1\/\\sqrt{-x}$<\/p>\n

Question 3:\u00a0<\/strong>Which of the following is true?<\/p>\n

a) $7^{(3^2)} = (7^3)^2$
\nb) $7^{(3^2)} > (7^3)^2$
\nc) $7^{(3^2)} < (7^3)^2$
\nd) None of these<\/p>\n

Question 4: <\/strong>Which among $2^{1\/2}, 3^{1\/3}, 4^{1\/4}, 6^{1\/6}$, and $12^{1\/12}$ is the largest?<\/p>\n

a) $2^{1\/2}$
\nb) $3^{1\/3}$
\nc) $4^{1\/4}$
\nd) $6^{1\/6}$
\ne)$12^{1\/12}$<\/p>\n

Question 5:\u00a0<\/strong>$2^{73}-2^{72}-2^{71}$ is the same as<\/p>\n

a) $2^{69}$
\nb) $2^{70}$
\nc) $2^{71}$
\nd) $2^{72}$<\/p>\n

Solutions for\u00a0Surds and Indices Questions for CAT PDF:<\/strong><\/span><\/p>\n

Solutions:<\/strong><\/p>\n

1) Answer (C)<\/strong><\/p>\n

The equation can be written as follow:
\n$3^{2x} * 3^3 – 244 * 3^x + 9 = 0$
\nLet $3^x = t$
\n=> $27t^2 – 244t + 9 = 0$
\n=> $27t^2 – 243t – t + 9 = 0$
\n=> $27t(t – 9) – 1(t – 9) = 0$
\n=> t = 9 or t = 1\/27
\n=> $3^x = 9 or 3^x = 1\/27$
\n=> $3^x = 3^2 or 3^x = 3^{-3}$
\nSo, x = 2 or x = -3
\nSo, \u2018x\u2019 can be either a positive number or a negative number. Option c) is the correct answer<\/p>\n

Download Quantitative Ability for CAT<\/a><\/p>\n

2) Answer (B)<\/strong><\/p>\n

$2^p$ is always positive
\n$x^2$ is always non negative.
\n$1\/\\sqrt{-x}$ is always positive.
\n$\\frac{1}{x}$ is negative when x is negative.
\nIn this case, x is negative => $\\frac{1}{x}$ is smallest.<\/p>\n

3) Answer (B)<\/strong><\/p>\n

$7^{(3^2)} = 7^9$
\n$(7^3)^2 = 7^6$
\nSo $7^{(3^2)} > (7^3)^2$<\/p>\n

4) Answer (B)<\/strong><\/p>\n

Make the power equal and compare the denominators.
\n$2^{1\/2}$ can be written as $64^{1\/12}$
\n$3^{1\/3}$ can be written as $81^{1\/12}$
\n$4^{1\/4}$ can be written as $64^{1\/12}$
\n$6^{1\/6}$ can be written as $36^{1\/12}$
\nAmong these, $81^{1\/12}$ is the greatest => $3^{1\/3}$ is the greatest.<\/p>\n

5) Answer (C)<\/strong><\/p>\n

$2^{71} (2^2 – 2^1 – 1)$
\n$2^{71} (4-2-1)$
\n$2^{71}$<\/p>\n

Practice more surds and Indices CAT questions<\/a><\/p>\n

CAT Mock Tests<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Surds and Indices are some of the basics of number system theory. The questions may include simplification of equations to find the simplified equations. Practice more questions on Surds and indices for CAT. Surds and Indices Questions for CAT PDF: Download CAT Quant Questions PDF Take Free Mock Test for CAT 2023 Question 1: \u00a0If […]<\/p>\n","protected":false},"author":21,"featured_media":10223,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"om_disable_all_campaigns":false,"_mi_skip_tracking":false,"footnotes":""},"categories":[3,169,125],"tags":[6106,200,222,217],"class_list":{"0":"post-10213","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-cat","8":"category-downloads","9":"category-featured","10":"tag-cat-2023","11":"tag-cat-pdf","12":"tag-cat-quant","13":"tag-cat-quantitative-aptitude"},"better_featured_image":{"id":10223,"alt_text":"Surds and Indices Questions for CAT PDF","caption":"Surds and Indices Questions for CAT PDF","description":"Surds and Indices Questions for CAT 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