Inclusion Criteria:

          -  The subject has a histologic or cytologic diagnosis of squamous cell carcinoma of the
             oral cavity, oropharynx, paranasal sinuses, hypopharynx, nasopharynx, or larynx;
             squamous cell carcinoma of unknown primary in cervical lymph node can be included only
             if human papillomavirus (HPV) status is positive

          -  Patients must have refractory, recurrent or metastatic disease, which is deemed to be
             inoperable

          -  In case patients received prior systemic therapy within the definitive or metastatic
             setting, disease progression must be documented following prior therapy; this can be
             in the recurrent or metastatic setting or in the concurrent setting

          -  Measurable disease per Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 as
             determined by the investigator

          -  A maximum of one prior radiotherapy regimen, curative or palliative, to the head and
             neck is allowed; if the radiation is combined with chemotherapy, a minimum of 4 months
             must elapse between the end of radiotherapy and registration; if the radiation is
             given alone, a minimum of 8 weeks must elapse between the end of radiotherapy and
             registration; a minimum of 3 weeks must elapse between prior radiation to other areas
             and registration; treatment areas should be healed with no sequelae from radiation
             therapy (RT) that would predispose to fistula formation

          -  The subject has had an assessment of all known disease sites eg, by computerized
             tomography (CT) scan, magnetic resonance imaging (MRI), bone scan or positron emission
             tomography (PET)/CT scan as appropriate, within 28 days before the first dose of
             cabozantinib

          -  Life expectancy of greater than 3 months

          -  The subject has an Eastern Cooperative Oncology Group (ECOG) performance status of 0
             or 1

          -  Recovery to baseline or ≤ grade 1 Common Terminology Criteria for Adverse Events
             (CTCAE) version (v.)4.0 from toxicities related to any prior treatments, unless AE(s)
             are clinically nonsignificant and/or stable on supportive therapy

          -  Within 7 days before the first dose of cabozantinib: The absolute neutrophil count
             (ANC) ≥ 1000/mm³ without colony stimulating factor support

          -  Within 7 days before the first dose of cabozantinib: Platelets ≥ 100,000/mm³

          -  Within 7 days before the first dose of cabozantinib: Hemoglobin ≥ 9 g/dL

          -  Within 7 days before the first dose of cabozantinib: Bilirubin ≤ 1.5 x the upper limit
             of normal (ULN); for subjects with known Gilbert's disease, bilirubin ≤ 3.0 mg/dL

          -  Within 7 days before the first dose of cabozantinib: Serum albumin ≥ 2.8 g/dl

          -  Within 7 days before the first dose of cabozantinib: Serum creatinine ≤ 1.5 x ULN or
             creatinine clearance (CrCl) ≥ 40 mL/min; for creatinine clearance estimation, the
             Cockcroft and Gault equation should be used

          -  Within 7 days before the first dose of cabozantinib: Alanine aminotransferase (ALT)
             and aspartate aminotransferase (AST) ≤ 2.0 x ULN

          -  Within 7 days before the first dose of cabozantinib: Lipase < 2.0 x the upper limit of
             normal and no radiologic or clinical evidence of pancreatitis

          -  Within 7 days before the first dose of cabozantinib: Urine protein/creatinine ratio
             (UPCR) ≤ 1

          -  Within 7 days before the first dose of cabozantinib: Serum phosphorus, calcium,
             magnesium and potassium ≥ lower limit of normal (LLN)

          -  The subject is capable of understanding and complying with the protocol requirements
             and has signed the informed consent document

          -  Sexually active subjects (men and women) must agree to use medically accepted barrier
             methods of contraception (eg, male or female condom) during the course of the study
             and for 4 months after the last dose of study drug(s), even if oral contraceptives are
             also used; all subjects of reproductive potential must agree to use both a barrier
             method and a second method of birth control during the course of the study and for 4
             months after the last dose of study drug(s)

          -  Female subjects of childbearing potential must not be pregnant at screening; females
             of childbearing potential are defined as premenopausal females capable of becoming
             pregnant (ie, females who have had any evidence of menses in the past 12 months, with
             the exception of those who had prior hysterectomy); however, women who have been
             amenorrheic for 12 or more months are still considered to be of childbearing potential
             if the amenorrhea is possibly due to prior chemotherapy, antiestrogens, low body
             weight, ovarian suppression or other reasons

        Exclusion Criteria:

          -  Patients who have HPV negative squamous cell carcinoma of unknown primary in cervical
             lymph node

          -  The subject has received cytotoxic chemotherapy (including investigational cytotoxic
             chemotherapy) or biologic agents (eg, cytokines or antibodies) within 4 weeks, or
             nitrosoureas/mitomycin C within 6 weeks before the first dose of study treatment

          -  Prior treatment with cabozantinib or pembrolizumab

          -  Radiation therapy for bone metastasis within 2 weeks, any other external radiation
             therapy within 4 weeks before the first dose of study treatment; systemic treatment
             with radionuclides within 6 weeks before the first dose of study treatment; subjects
             with clinically relevant ongoing complications from prior radiation therapy are not
             eligible

          -  Receipt of any type of small molecule kinase inhibitor (including investigational
             kinase inhibitor) within 14 days before the first dose of study treatment

          -  The subject has received any other type of investigational agent within 28 days or 5
             half-lives, whichever is shorter, before the first dose of study treatment

          -  Known brain metastases or cranial epidural disease unless adequately treated with
             radiotherapy and/or surgery (including radiosurgery) and stable for at least 4 weeks
             before the first dose of study treatment; eligible subjects must be neurologically
             asymptomatic and without corticosteroid treatment at the time of the start of study
             treatment

          -  The subject has prothrombin time (PT)/institutional normalized ratio (INR) or partial
             thromboplastin time (PTT) test ≥ 1.3 x the laboratory ULN within 7 days before the
             first dose of study treatment

          -  Concomitant anticoagulation at therapeutic doses with oral anticoagulants (eg,
             warfarin, direct thrombin and factor Xa inhibitors) or platelet inhibitors (eg,
             clopidogrel)

               -  Note: Low-dose aspirin for cardioprotection (per local applicable guidelines),
                  low-dose warfarin (< 1 mg/day), and low dose, low molecular weight heparins
                  (LMWH) are permitted; anticoagulation with therapeutic doses of LMWH is allowed
                  in subjects who are on a stable dose of LMWH for at least 6 weeks before first
                  dose of study treatment, and who have had no clinically significant hemorrhagic
                  complications from the anticoagulation regimen or the tumor

          -  The subject has experienced any of the following:

               -  Clinically-significant GI bleeding within 6 months before the first dose of study
                  treatment

               -  Hemoptysis of ≥ 0.5 teaspoon (2.5 ml) of red blood within 3 months before the
                  first dose of study treatment

               -  Any other signs indicative of pulmonary hemorrhage within 3 months before the
                  first dose of study treatment

          -  The subject has radiographic evidence of cavitating pulmonary lesion(s)

          -  The subject has tumor invading or encasing any major blood vessels

          -  The subject has evidence of tumor invading the gastrointestinal (GI) tract (esophagus,
             stomach, small or large bowel, rectum or anus), or any evidence of endotracheal or
             endobronchial tumor within 28 days before the first dose of cabozantinib

          -  The subject has uncontrolled, significant intercurrent or recent illness including,
             but not limited to, the following conditions:

               -  Cardiovascular disorders including:

                    -  Congestive heart failure (CHF): New York Heart Association (NYHA) class III
                       (moderate) or class IV (severe) at the time of screening;

                    -  Concurrent uncontrolled hypertension defined as sustained blood pressure
                       (BP) > 150 mm Hg systolic or > 100 mm Hg diastolic despite optimal
                       antihypertensive treatment within 7 days of the first dose of study
                       treatment;

                    -  Any history of congenital long QT syndrome;

                    -  Any of the following within 6 months before the first dose of study
                       treatment:

                         -  Unstable angina pectoris;

                         -  Clinically-significant cardiac arrhythmias;

                         -  Stroke (including transient ischemic attack (TIA), or other ischemic
                            event);

                         -  Myocardial infarction;

               -  GI disorders particularly those associated with a high risk of perforation or
                  fistula formation including:

                    -  Tumors invading the GI tract, active peptic ulcer disease, inflammatory
                       bowel disease (eg, Crohn's disease), diverticulitis, cholecystitis,
                       symptomatic cholangitis or appendicitis, acute pancreatitis or acute
                       obstruction of the pancreatic duct or common bile duct, or gastric outlet
                       obstruction

                    -  Abdominal fistula, GI perforation, bowel obstruction, intra-abdominal
                       abscess within 6 months before randomization

                         -  Note: Complete healing of an intra-abdominal abscess must be confirmed
                            prior to randomization. Also no pre-existing fistula of head and neck
                            area; no pre-existing osteonecrosis of jaw (ONJ)

               -  Other clinically significant disorders that would preclude safe study
                  participation

          -  Major surgery within 12 weeks before the first dose of study treatment; complete wound
             healing from major surgery must have occurred 1 month before the first dose of study
             treatment; minor surgery (including uncomplicated tooth extractions) within 28 days
             before the first dose of study treatment with complete wound healing at least 10 days
             before the first dose of study treatment; subjects with clinically relevant ongoing
             complications from prior surgery are not eligible

          -  Corrected QT interval by Fridericia's formula (QTcF) > 500 msec within 1 month before
             the first dose of study treatment

               -  Three electrocardiography (ECG)s must be performed for eligibility determination;
                  if the average of these three consecutive results for QTcF is ≤ 500 msec, the
                  subject meets eligibility in this regard

          -  Pregnant or lactating females

          -  Inability to swallow intact tablets or inability to take pembrolizumab or cabozantinib

          -  Previously identified allergy or hypersensitivity to components of the study treatment
             formulations

          -  Patients with a history of other prior malignancy must have been treated with curative
             intent and must have remained disease-free for 1 year post diagnosis; patients with a
             prior history of squamous cell or basal carcinoma of the skin or in situ cervical
             cancer must have been curatively treated